# Calcr Canonical origin: https://calcr.app Coverage: all currently published public pages in en. Languages without published site settings are excluded. Private pages, drafts and unpublished translations are excluded. Product index: https://calcr.app/llms.txt Detailed reference: https://calcr.app/llms-full.txt Sitemap: https://calcr.app/sitemap.xml ## en Calcr provides free online calculators with formulas, worked examples and clear results. Choose a calculator, enter your values and check its calculation rules. No account is needed. ### Free online calculator URL: https://calcr.app/ 1. Enter an expression in the calculator above, or choose a tool for your task. 2. Select the calculation mode and enter your values. For trigonometry, check DEG or RAD before calculating. 3. Calculate, then check the result against the formula and examples on the tool page. Is Calcr free to use? Yes. Public calculators and browser games are free, without a visitor account, subscription or payment card. Where are my calculations processed? Calculator inputs are processed in your browser. Scientific history belongs to the current session. Optional analytics is separate and requires consent. How can I check a calculation? Use the formulas, worked examples and limits on each tool page. Check units, rounding and date-counting conventions before relying on an answer. 15% × 80 = 12 (https://calcr.app/tools/percentage-calculator) 2/3 + 5/12 = 13/12 (https://calcr.app/tools/fraction-calculator) 18:24 = 3:4 (https://calcr.app/tools/ratio-calculator) 4, 8, 12 = 8 (https://calcr.app/tools/average-calculator) [OpenStax: applications of percent](https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent) [OpenStax: adding and subtracting unlike fractions](https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators) - [Free online calculators](https://calcr.app/tools): Find free online calculators for paychecks, mortgages, BMI, calories, math and dates. Check formulas and worked examples, with no account needed. - [Free browser games](https://calcr.app/games): Play free browser games with touch or keyboard controls. Open an available game directly or use a Code Mode shortcut. No downloads or accounts needed. - [Calculator guides & worked examples](https://calcr.app/blog): Learn how to calculate percentages, fractions, ratios, weighted grades and calendar dates. Follow formulas, worked examples and checks for each result. ### Scientific calculator URL: https://calcr.app/tools/scientific-calculator Last publication: 2026-11-11T02:59:53.054Z Free scientific calculator for expressions, powers, roots and trigonometry. Choose degrees or radians, check worked examples and review calculation rules. ## Scientific calculator: Enter a scientific expression Use parentheses to make grouping explicit, then calculate. The calculator supports arithmetic, powers, square roots, sin, cos, tan, base-10 log, natural log, pi and e. Select DEG for degrees or RAD for radians before using trigonometry. Your recent calculations stay in the current session. ## Order of operations and examples Parentheses are evaluated first. Powers precede multiplication and division; addition and subtraction follow. Use an explicit multiplication sign when entering a product. - Grouping: 18 / (2 * 3) = 3. Without those parentheses, 18 / 2 * 3 = 27. - Angles: in DEG mode, sin(30) = 0.5. In RAD mode, sin(pi / 6) = 0.5. - Percent: 240 * 15% = 36. The percent sign means divide by 100, so 200 + 10% = 200.1. To increase 200 by 10%, enter 200 * (1 + 10%). ## Precision and limits Calculations use decimal BigNumber arithmetic with 32 significant digits internally and show up to 12 significant digits. A displayed decimal can be rounded. Division by zero, real square roots of negative numbers and unsupported expressions return an error. Expressions are limited to 512 characters and a short execution budget. This is a numerical calculator, not a symbolic algebra system. ## When to use this scientific calculator Use this free scientific calculator when the task can be written as a numerical expression and you want to inspect the steps yourself. It suits checking a homework calculation, evaluating a formula with known measurements, converting a percentage into a multiplier, or comparing two numerical scenarios. Write the expression on paper first if the relationship is unclear. The calculator can evaluate a formula, but it cannot decide which formula describes your problem. Keep units consistent before entering numbers. For a rectangle measuring 2 metres by 35 centimetres, convert 35 centimetres to 0.35 metres before calculating 2 * 0.35. The numerical answer is 0.7 and its area unit is square metres. Entering 2 * 35 instead produces 70, which describes neither the intended square metres nor a valid conversion. Units are part of your setup even though the expression field contains numbers. Use another tool when the output needs a different kind of reasoning. The fraction calculator preserves a rational result as a fraction. The grade calculator checks assessment weights. A calendar tool knows that February and March have different lengths. This calculator does not solve equations with unknown variables, prove identities, manipulate matrices or provide complex-number answers. A rejected expression can indicate an unsupported operation rather than a mathematical impossibility. ### Example: checking a geometric formula Suppose a right triangle has perpendicular sides of 9 and 12 in the same unit. The hypotenuse is sqrt(9^2 + 12^2). Squaring the inputs gives 81 and 144, adding gives 225, and taking the square root gives 15. The parentheses keep the entire sum inside the root. Entering sqrt(9^2) + 12^2 asks a different question and gives 153. Both expressions are numerically valid, so grouping is the check that catches the mistake. This example assumes a right angle; the same expression does not calculate an arbitrary triangle's third side. Keep the result in the original length unit. If the sides are measurements rounded to the nearest centimetre, a display showing many digits would not make the measurement more precise. The tool reports arithmetic precision, while the original observations determine useful reporting precision. ### Example: growth with repeated percentage changes An illustrative quantity starts at 500, increases by 8%, then decreases by 5%. Enter 500 * 1.08 * 0.95 to obtain 513. The first step gives 540, and the second step removes 27. The net change is 13, or 2.6% of the starting quantity. Subtracting 5 from 8 and calling the outcome a 3% increase would ignore that the second change uses 540 as its base. To check the net percentage in one expression, enter (513 - 500) / 500 * 100. This produces 2.6. Keep the growth factors unrounded until the final step, especially when repeating them many times. This is a numerical scenario, not a promise about investment performance or any real-world rate. Before sharing a result, copy the expression, the angle mode and the final answer together. An answer such as 0.5 alone does not show whether it came from sin(30) in degrees or another expression. For a longer calculation, check one intermediate value at a time and compare the rough size with what you expected. If a result looks implausible, inspect the inputs and grouping before adding more decimal places. An error does not leave the last successful answer as the result of the new expression. Correct the input and calculate again. For example, sqrt(-1) is outside this real-number calculator, while sqrt(1) returns 1. If a copied formula contains a multiplication symbol or a superscript from another document, rewrite it using the supported keypad or plain expression syntax before retrying. Check that every opening parenthesis has a closing partner. For the underlying arithmetic and function conventions, see the openly available [OpenStax Algebra and Trigonometry reference](https://openstax.org/details/books/algebra-and-trigonometry-2e). ## FAQ ### Why does sin give an unexpected result? Check DEG/RAD first. The number 30 means different angles in the two modes. ### What is the difference between log and ln? Log uses base 10; ln uses base e. For example, log(100) = 2 and ln(e) = 1. ### Is a rounded result exact? Not necessarily. Keep full intermediate precision and round only the final answer when possible. Use the fraction calculator for exact rational arithmetic. ### Why does a negative number raised to a power need parentheses? Parentheses state whether the negative sign belongs to the base. The expression (-3)^2 squares negative three and gives 9. The expression -(3^2) negates a square and gives -9. When a formula contains a negative input, group that input explicitly so the expression records your intention. This matters even when you can perform the small example mentally; in a long formula the same sign mistake is harder to see. ### Can I recover my calculations on another device? The recent-history panel belongs to the current browser session. It is useful for reviewing nearby calculations, but it is not an account-backed notebook or a synced record. Copy important expressions and results into your own notes before leaving the session. Avoid including personal or confidential measurements when you only need to demonstrate how an expression works. ## Related tools and guides - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Fraction calculator](https://calcr.app/tools/fraction-calculator) - [Average calculator](https://calcr.app/tools/average-calculator) - [Calculation methodology](https://calcr.app/pages/methodology) ### Math calculators URL: https://calcr.app/categories/math Last publication: 2026-11-11T02:59:26.069Z Work with expressions, percentages, fractions, ratios, averages and weighted grades using tools with clear formulas and examples. ## Choose the calculation you need Use the scientific calculator for a numerical expression, the fraction calculator when the exact rational answer matters, or the percentage calculator when a quantity is compared with a stated total. Ratio reduction and missing-term proportions handle ordered relationships. For a list of equally weighted values, choose the arithmetic average. For percentage scores with different course weights, use the grade calculator instead. Its weights must total 100%; an unfinished assessment is not automatically a zero. ## Check the setup Read the mode and units before calculating. A wrong base can make a percentage arithmetically consistent but unsuitable for your question. DEG and RAD can likewise give different trigonometric results. The tool pages show the rules and examples so you can check the result. ## Use the right kind of average or comparison An arithmetic mean gives every observation equal weight. A weighted course result gives each assessment the share stated in a syllabus. A ratio compares ordered quantities, while a percentage needs an identified base. Choose the tool that matches that relationship before entering numbers; a plausible answer cannot repair the wrong setup. For example, 15% of 80 is 12, but asking what percent 15 is of 80 produces 18.75%. Both calculations use the same two numbers and answer different questions. Write the unknown in a sentence first, then match it to the form's mode. For exact parts such as thirds, retain the fraction until the final reporting step rather than rounding it early. These tools explain numerical methods and reject unsupported input. They do not solve symbolic proofs, infer units or decide an institution's policy. Keep the inputs and assumptions with a copied result so another person can reproduce it. No account is required, and the calculations run on your device. ## Related tools and guides - [Scientific calculator](https://calcr.app/tools/scientific-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Fraction calculator](https://calcr.app/tools/fraction-calculator) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Average calculator](https://calcr.app/tools/average-calculator) - [Grade calculator](https://calcr.app/tools/grade-calculator) ### About Calcr URL: https://calcr.app/about Last publication: 2026-11-10T18:35:06.292Z Calcr provides free calculators with visible rules and worked examples, plus a small collection of browser games for a break. ## Practical calculations, with the rules visible Calcr helps you finish common numerical tasks: evaluate an expression, work with fractions and percentages, estimate a weighted grade, or compare dates and clock times. Calculators are free to use. Visitors do not need an account, subscription or payment card. Each tool pairs the interactive calculation with formulas, worked examples and limits. When a convention can affect the answer, such as inclusive date counting or a leap-day anniversary, the documentation states it. The [methodology page](https://calcr.app/pages/methodology) collects those choices. ## A small space to play Browse the games directory to open a short browser game, or use Code Mode as an optional shortcut with public codes. It does not change ordinary calculator expressions or claim to bypass another website's controls. ## Funding and independence Calcr provides its calculators and games without subscriptions or paid unlocks. Optional Google Analytics helps us understand page and tool use only after you choose Allow analytics. Advertising remains off. Calculators and games work when you reject analytics. You can change your choice through Privacy settings in the footer; see the [privacy policy](https://calcr.app/privacy) and [cookie policy](https://calcr.app/cookie). Calcr is an independent website. It does not claim to be another calculator service, a school, a certification body or an official source of academic records. ## Corrections and contact Calcr is operated by Calcr Team. For questions or corrections, email [support@calcr.app](mailto:support@calcr.app). The [contact page](https://calcr.app/contact) explains which details help reproduce a calculation issue. ## Related tools and guides - [All calculators](https://calcr.app/tools) - [Guides](https://calcr.app/blog) - [Calculation methodology](https://calcr.app/pages/methodology) - [Limitations and disclaimer](https://calcr.app/pages/disclaimer) ### How to calculate percentage change URL: https://calcr.app/blog/how-to-calculate-percentage-change Last publication: 2026-11-10T14:31:08.604Z Use the original value as the base for percentage change. Work through increases, decreases, reverse changes and percentage points. Percentage change measures a difference relative to the original value. To calculate it, subtract the original value from the new value, divide by the original, then multiply by 100. The denominator answers the essential question: compared with what? ## Calculate percentage change in three steps Suppose a weekly count rises from 48 to 60. - Find the difference: 60 - 48 = 12. - Divide by the original count: 12 / 48 = 0.25. - Convert to percent: 0.25 * 100 = 25%. In the [percentage calculator](https://calcr.app/tools/percentage-calculator), choose change, enter 48 as the original value and 60 as the new value. A positive answer indicates an increase for this positive starting value. ## Why reversing the values changes the answer Return from 60 to 48 and the difference becomes -12. The base is now 60, so -12 / 60 * 100 = -20%. The decrease is smaller in percentage terms because it is measured against a larger amount. This also explains why equal percentage increases and decreases do not cancel. An amount of 200 reduced by 15% becomes 170. Increasing 170 by 15% gives 195.5. Recovering 200 requires an increase of 30 / 170 * 100, approximately 17.6471%. ## Percentage points answer a different question A rate moving from 12% to 15% rises by 3 percentage points. Its relative percentage change is (15 - 12) / 12 * 100 = 25%. Use percentage points to state the direct gap between rates; use percentage change to state the relative increase. ## Handle zero and negative starting values carefully From zero to a positive amount, the formula divides by zero and has no defined percentage change. State the absolute change instead. With negative starting values, the sign can conflict with ordinary language about improvement or growth. Give the original and new values alongside any computed percentage. ## FAQ ### Do I divide by the old or the new value? The old value. Dividing by the new value answers a different comparison. ### Can an increase exceed 100%? Yes. A rise from 20 to 50 is 150% because the increase of 30 is 1.5 times the original. ### How should I round the answer? Retain precision through the division and round at the end. Two decimal places may be enough for a simple report; the appropriate precision depends on the data. Use the original value consistently, and label a gap between rates as percentage points when that is what you mean. These two checks prevent most percentage-change mistakes. The base-value definition is described in [OpenStax: applications of percent](https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent). The examples and calculations above are original to this guide. ## Related tools and guides - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Discount calculator](https://calcr.app/tools/discount-calculator) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Average calculator](https://calcr.app/tools/average-calculator) ### Percentage calculator URL: https://calcr.app/tools/percentage-calculator Last publication: 2026-11-11T03:00:00.556Z Free percentage calculator to find a percent of a number, a part as a percentage, an original total or percentage change. Check formulas and worked examples. ## Percentage calculator: Choose the question you need The four modes answer different questions: find a portion, find a percentage, recover a total, or measure a change. Enter the known values rather than moving a percent sign between fields. ## Percentage formulas - Portion = total * percentage / 100. - Percentage = portion / total * 100. - Total = portion / (percentage / 100). - Percentage change = (new value - original value) / original value * 100. The original value is the denominator for change. A percentage is a relative comparison, while percentage points are a subtraction between two percentages. ## Worked examples A part of a total: 15% of 80 is 0.15 * 80 = 12. Conversely, 18 out of 72 is 18 / 72 * 100 = 25%. Recover the total: if 27 represents 30%, the total is 27 / 0.30 = 90. Change: a quantity rising from 80 to 100 increases by 25%. Returning from 100 to 80 is a 20% decrease because the starting value has changed. ## Limits A zero total cannot be used to calculate a proportion. A zero percentage cannot recover a unique total. Percentage change from zero is undefined; negative starting values can produce a mathematically valid result that is hard to interpret in everyday comparisons. ## When to use this percentage calculator Use this free percentage calculator when your question identifies a part and a whole, a percent and a base, or an original and a new value. It is useful for checking a survey response share, scaling a budget, comparing counts over time, and recovering a total from a known portion. Decide which quantity is the denominator before selecting a mode. The same two numbers can answer several different questions, each with a different result. Write a short sentence with the unknown left blank. “Fifteen percent of eighty is blank” asks for a portion. “Twelve is blank percent of eighty” asks for a percentage. “Twelve is fifteen percent of blank” asks for a total. This translation is often the most important step. A percent sign describes a relationship; it does not make every operation involving that number interchangeable. Do not use a simple percentage change when the starting value is zero or the comparison hides changes in the population being measured. Going from zero orders to ten orders is an increase of ten orders, but it has no finite relative percentage increase. Likewise, comparing two classes' pass rates does not establish that the same number of students passed. Keep the group sizes available alongside the percentages. ### Example: a survey with a stated denominator A survey receives 240 valid responses, and 42 select one option. Choose the part-as-percentage mode and enter 42 as the part and 240 as the whole. The calculation is 42 / 240 * 100 = 17.5%. A quick check is that one quarter of 240 would be 60; because 42 is smaller than 60, the result should be below 25%. If the original invitation went to 300 people, 42 / 300 * 100 = 14% answers a different question: the share of all invitees choosing the option. Neither denominator is automatically correct. Label the first result “17.5% of valid responses” and the second “14% of invited people.” This prevents a mathematically correct number from becoming a misleading summary. Rounding both to whole percentages would also discard detail, so choose a reporting precision that fits the purpose. ### Example: comparing increases and percentage points A process improves from 60 successful attempts out of 100 to 75 out of 100. The rates are 60% and 75%. Subtracting the rates gives 15 percentage points. To find the relative increase in the rate, choose percentage change and compare 60 with 75: (75 - 60) / 60 * 100 = 25%. The phrases “15 percentage points” and “25% relative increase” describe the same change from different viewpoints. Now suppose the second group contains 200 attempts with 150 successes. Its rate is still 75%, but the number of successes rose from 60 to 150, a 150% increase. Counts and rates answer different questions. Keep the quantity you are comparing consistent across both periods, and do not substitute the rate's relative change for the count's relative change. For money, carry the unrounded percentage through the calculation and round the final amount according to the relevant currency or checkout rule. For repeated changes, multiply the remaining or growth factors instead of adding percentages. A 10% increase followed by a 10% decrease changes 100 to 110 and then 99. The percentage calculator can check each step; the scientific calculator can evaluate the full product in one expression. A final reasonableness check can be faster than repeating the whole calculation. Ten percent of 80 is 8, so fifteen percent should lie between 8 and 16. A part of 42 out of 240 must be below 100%, while a part larger than its whole can legitimately exceed 100%. In change mode, compare the sign with the direction of the change when the starting value is positive. These checks catch a swapped part and whole or a missing decimal point. They do not replace identifying the correct base in the original question. ## FAQ ### Is 120% allowed? Yes. It means 1.2 times the base; 120% of 50 is 60. ### Does a 20% increase undo a 20% decrease? No. Starting at 100 gives 80, then 96. Each change uses a different base. ### Is a change from 10% to 15% a 5% increase? It is 5 percentage points, or a 50% relative increase. ### How do I find the original amount before an increase? Divide the final amount by the growth factor. If a value is 120 after a 20% increase, the original is 120 / 1.20 = 100. Taking 20% away from 120 gives 96 and does not reverse the increase. In reverse mode, you can enter 120 as the known part and 120 as the percentage, because the final amount is 120% of the original. State that base explicitly when recording the answer. ### Is a negative percentage always an error? No. A negative change can correctly describe a decrease from a positive starting value. A negative portion may also be meaningful in a signed accounting calculation. However, negative starting values make ordinary growth language difficult: moving from -20 to -10 produces -50% using the signed original denominator even though the number increased. Report the actual values and absolute difference when a relative percentage would confuse the reader. ## Related tools and guides - [Percentage change guide](https://calcr.app/blog/how-to-calculate-percentage-change) - [Discount calculator](https://calcr.app/tools/discount-calculator) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Fraction calculator](https://calcr.app/tools/fraction-calculator) ### Everyday calculators URL: https://calcr.app/categories/everyday Last publication: 2026-11-11T02:59:33.931Z Calculate calendar age, date differences, clock durations and discounted prices with explicit counting and rounding conventions. ## Dates, times and sale prices Use the age calculator to count completed calendar years, months and days. Use the date calculator for elapsed calendar days or to add and subtract days. A clock-duration calculation is a different task: it compares hours and minutes and requires an explicit next-day choice for an overnight interval. The discount calculator separates savings from the final price and applies sequential percentage reductions to the remaining amount. An optional entered tax rate applies after discounts; delivery and fixed coupons are outside that calculation. ## Name the convention A date range can mean elapsed days or a count including both endpoints. A sale can round each stage differently from an unrounded mathematical result. Check the explanation and state the convention when sharing an answer. These tools do not decide legal deadlines, verify identity or guarantee a retailer's checkout amount. ## Turn an everyday question into clear inputs For an event from Monday through Friday, ask whether you need four elapsed date-to-date steps or five included calendar dates. For a shift ending after midnight, select next day explicitly rather than relying on the clock reading to imply it. Calendar days and clock hours are different units, so a dated daylight-saving interval needs more information than these simple forms collect. For a sale, identify the original price, the order of percentage reductions and any separately supplied tax rate. Twenty percent off followed by ten percent off leaves 72% of the original price, rather than 70%. Shipping and fixed coupons need separate treatment. The worked examples on each tool page show how to check these assumptions before trusting the final number. Use the results for planning and arithmetic checks, then verify the applicable booking, merchant or organizational rules before acting. Dates and amounts can be invented when you are exploring a feature. There is no need to share an actual birthday or personal schedule to learn the method. ## Related tools and guides - [Age calculator](https://calcr.app/tools/age-calculator) - [Date calculator](https://calcr.app/tools/date-calculator) - [Time duration calculator](https://calcr.app/tools/time-duration-calculator) - [Discount calculator](https://calcr.app/tools/discount-calculator) ### Contact and report an issue URL: https://calcr.app/contact Last publication: 2026-11-10T14:31:52.829Z Report a calculation error with the tool URL, sample inputs, expected answer and the rule you used. Avoid sharing private information. ## Get in touch Email [support@calcr.app](mailto:support@calcr.app) to contact Calcr Team, the operator of Calcr. ## Report a calculation problem A useful calculation report includes: - The tool's page URL and the calculation mode. - A short sample that reproduces the problem. - The result you expected, the result displayed and your calculation rule or source. - The browser and device type if the form or controls failed. Use invented or non-sensitive values whenever possible. A date issue can usually be demonstrated without a real birthday. Never send passwords, session cookies, identity documents, private grade reports or account recovery links. ## Content, privacy and advertising questions For a content correction, identify the paragraph or formula and explain the change. For privacy questions, state the category of data or browser storage you are asking about rather than sending private records. Include the affected page if an advertisement interferes with a control. [Calculation methodology](https://calcr.app/pages/methodology) · [Privacy](https://calcr.app/privacy) · [Terms](https://calcr.app/terms) ### How to add and subtract fractions URL: https://calcr.app/blog/how-to-add-and-subtract-fractions Last publication: 2026-11-10T14:31:14.143Z Find a common denominator, combine the numerators and simplify. Follow worked fraction and mixed-number examples without rounding. To add or subtract fractions, first express them in equal-sized parts. Once the denominators match, combine the numerators and keep the common denominator. Simplify the result after the operation. ## Find a common denominator For 2/5 + 1/6, the smallest positive common denominator is 30. Multiply 2/5 by 6/6 to get 12/30, and multiply 1/6 by 5/5 to get 5/30. The value of each fraction stays the same because multiplying by a number divided by itself multiplies by one. Now add: 12/30 + 5/30 = 17/30. Adding denominators would give a different quantity, so 3/11 is not the sum. Try the example in the [fraction calculator](https://calcr.app/tools/fraction-calculator), which keeps the result exact rather than converting each input to a rounded decimal. ## Subtraction follows the same method For 7/8 - 1/3, use a denominator of 24. The equivalent fractions are 21/24 and 8/24. Subtracting their numerators gives 13/24. The first numerator can be smaller. For 1/4 - 2/3, calculate 3/12 - 8/12 = -5/12. A negative result is valid; it means more was subtracted than the starting amount. ## Convert mixed numbers before combining A mixed number represents a whole amount plus a fraction. Convert 1 3/4 to (1 * 4 + 3) / 4 = 7/4. Then 1 3/4 - 2/3 becomes 7/4 - 2/3 = 21/12 - 8/12 = 13/12, or 1 1/12. A negative mixed number such as -1 3/4 means -7/4, with the negative sign applying to the whole value. ## Simplify and check the result If the numerator and denominator share a common factor, divide both by it. For example, 5/12 + 1/12 = 6/12 = 1/2. A quick magnitude check helps: adding two positive fractions must produce a value larger than either input. ## FAQ ### Must I use the smallest common denominator? No. Any common denominator works. The smallest usually keeps the arithmetic shorter. ### Can a denominator be zero? No. Division by zero is undefined. ### Why keep an exact fraction? Some fractions repeat as decimals. Keeping 1/3 exact avoids replacing it with an approximation before the next calculation. For reliable fraction addition and subtraction, match the denominator, combine the numerators and reduce. Use decimal output only when an approximation is useful for the task. For the common-denominator method, see [OpenStax: adding and subtracting unlike fractions](https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators). The worked examples here use separate values. ## Related tools and guides - [Fraction calculator](https://calcr.app/tools/fraction-calculator) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) ### Fraction calculator URL: https://calcr.app/tools/fraction-calculator Last publication: 2026-11-11T03:00:09.512Z Free fraction calculator to add, subtract, multiply and divide fractions or mixed numbers. Get a reduced exact answer, decimal result and worked examples. ## Fraction calculator: Calculate with exact fractions Enter two fractions or mixed numbers and choose add, subtract, multiply or divide. A mixed number such as 1 1/2 means 1 + 1/2. The result includes a reduced exact fraction and a decimal approximation. ## Formulas For fractions a/b and c/d, addition is (ad + bc)/(bd), subtraction is (ad - bc)/(bd), multiplication is ac/(bd), and division is ad/(bc). Reduce the answer by the greatest common divisor of the numerator and denominator. A negative mixed number such as -1 1/2 means -(1 + 1/2). ## Worked examples - Unlike denominators: 2/3 + 5/12 = 8/12 + 5/12 = 13/12, or 1 1/12. - Division: 3/4 divided by 9/10 = 3/4 * 10/9 = 30/36 = 5/6. - Mixed number: 1 1/2 - 2/3 = 3/2 - 2/3 = 9/6 - 4/6 = 5/6. ## Limits Denominators cannot be zero, and division by a zero-valued fraction is undefined. Integer arithmetic preserves exact rational results within the tool's input limits. Each input is limited to 100 characters. Integers, finite decimals and properly formatted mixed numbers are accepted. A decimal such as 0.833333333333 is only an approximation to 5/6. ## When to use this fraction calculator Use this free fraction calculator when a quantity is naturally an exact part of a whole: recipe portions, lengths marked in fractional inches, or arithmetic exercises with rational numbers. Keeping 1/3 as a fraction avoids replacing it with a rounded decimal before later operations. Enter the numerator and denominator as written, choose the operation, and review the reduced fraction before using its decimal approximation. Fractions still require matching units. Adding 1/2 metre to 1/4 metre gives 3/4 metre. Adding 1/2 metre to 1/4 centimetre without converting would mix different-sized wholes. A fraction names a count of equal parts of a stated unit; the denominator alone does not identify that unit. For a mixed number, separate the whole part from the fraction clearly, and do not type a decimal point where a space belongs. Use another calculator if your input is an irrational quantity such as the square root of two, a trigonometric expression or a symbolic variable. A finite decimal is rational and can be converted exactly, but a few typed digits from an infinite decimal do not recover the original exact value. Entering 0.333 means exactly 333/1000, not exactly 1/3. The calculator cannot infer the digits that you omitted. ### Example: increasing a recipe without decimal rounding A recipe needs 3/4 cup of an ingredient for one batch. You want 1 1/2 batches. Choose multiplication and enter 3/4 and 1 1/2. Convert the mixed number to 3/2, then multiply: 3/4 * 3/2 = 9/8. The result is 1 1/8 cups, or 1.125 cups as a decimal. The exact fraction is convenient when a measuring cup has eighth-cup markings. The increase is not 3/4 + 1/2, because the second number describes a number of batches rather than an extra amount in cups. Check the units in the sentence: cups per batch multiplied by batches gives cups. If you also scale other ingredients, apply the same 3/2 multiplier separately to each original quantity. Rounding 1.125 to 1.1 before measuring would change the intended ratio. ### Example: measuring a difference with a negative result Suppose a planned cut is 5/8 inch and the available piece is 3/4 inch. To calculate available length minus planned length, enter 3/4 - 5/8. Convert 3/4 to 6/8, then subtract to obtain 1/8 inch left over. Reversing the inputs gives -1/8, which records a signed difference rather than a physically negative piece of material. The order matters for subtraction and division. When a result has an unexpected sign, check which quantity you intended to subtract from which. If a cutting process removes material along the cut, that width is a separate measurement; this arithmetic example does not automatically allow for it. You would need to include that additional amount in the original setup before deciding whether a real piece is long enough. To check any reduced answer, multiply the reduced numerator and denominator by the same factor and confirm that the value remains unchanged. For example, 5/6 and 30/36 describe the same number. Reduction changes the representation, not the amount. A result denominator of one means the answer is an integer. A zero numerator means zero as long as the denominator is nonzero. Keep these simple checks in mind before trusting a complicated-looking input. Check each denominator before submitting, including the fraction used as a divisor. The input 0/5 is a valid zero, but 5/0 is undefined, and dividing by 0/5 is also undefined. An error should lead you back to the operation and its inputs rather than to a guessed replacement value. For multiplication, estimate whether each factor is above or below one; multiplying a positive number by 1/2 should halve it. For addition, do not add denominators: 1/2 + 1/2 equals one, not 2/4. These small checks help detect a copied operation sign. If a result will be used in a measurement, also record the unit and whether the original quantities were exact or approximate. An exact fraction for approximate inputs does not make the measurements exact. ## FAQ ### Why does the denominator change when adding? The fractions must describe equal-sized parts before their numerators can be combined. ### Can an answer exceed one? Yes. An improper fraction such as 13/12 is valid and can also be written as a mixed number. ### Should I round before calculating? Keep the fraction exact when possible. Rounding each input can change the final result. ### Can a denominator be negative? A negative denominator represents a negative fraction, provided it is not zero. The calculator normalizes the sign so the displayed denominator is positive. Thus 2/-3 and -2/3 have the same value, while -2/-3 is positive 2/3. For clarity, place the minus sign in front of the fraction when writing your own notes. Never remove both minus signs unless the numerator and denominator are both negative. ### How is a negative mixed number interpreted? The sign applies to the whole mixed quantity. Entering -1 1/2 means -(1 + 1/2), which equals -3/2. It does not mean -1 + 1/2, which would equal -1/2. If that distinction is easy to miss in a longer expression, convert the mixed number to an improper fraction first. Reviewing the decimal approximation, -1.5 in this example, is another way to catch a sign misunderstanding. ## Related tools and guides - [Adding and subtracting fractions](https://calcr.app/blog/how-to-add-and-subtract-fractions) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) ### Finance calculators URL: https://calcr.app/categories/finance Last publication: 2026-11-11T02:59:40.091Z Free finance calculators for US 2026 paycheck withholding, fixed-rate mortgages and monthly compound interest, with assumptions and worked examples. ## Choose a finance calculator for the question you have Use the paycheck calculator to examine US 2026 regular employee pay after federal withholding and FICA. Use the mortgage calculator to estimate a fixed-rate monthly payment with your entered property tax and home insurance. Use the compound interest calculator to compare a fixed-rate savings scenario with regular month-end contributions. These are different models, so begin with the decision you are trying to understand rather than a large final number. ## Keep assumptions beside the result The paycheck form assumes a simple 2020-or-later W-4, with Step 2 unchecked and Steps 3–4 blank. It does not include state or local taxes or benefits. Year-to-date wages affect Social Security and Additional Medicare withholding on the current check. A withholding estimate is not a calculation of your final tax return or an exact deposit prediction. For a mortgage, enter the loan balance after the down payment and use the nominal note rate. Monthly principal and interest is only part of housing costs; mortgage insurance, association dues, maintenance and closing costs are excluded. For compound interest, a fixed nominal annual rate and monthly deposits describe an illustration, not a forecast of investment returns. Fees, taxes, inflation and losses require additional modeling. ## Compare scenarios carefully Change one input at a time when comparing terms, contribution amounts or payment frequencies. Keep the units and time periods consistent. A monthly salary input cannot be compared directly with the same dollar amount paid every two weeks. Likewise, an APY is not interchangeable with a nominal rate in a monthly compounding formula. Each tool includes worked examples, limitations and links to official or primary references. The calculations run on your device without an account. Use them to understand arithmetic and prepare better questions, then verify payroll details, written loan terms or account conditions with the relevant provider. These pages are for reference and do not provide individualized financial, investment, tax or legal advice. ## Related tools and guides - [Paycheck calculator](https://calcr.app/tools/paycheck-calculator) - [Mortgage calculator](https://calcr.app/tools/mortgage-calculator) - [Compound interest calculator](https://calcr.app/tools/compound-interest-calculator) ### Privacy policy URL: https://calcr.app/privacy Last publication: 2026-11-10T18:35:22.779Z Learn how Calcr handles local calculations, Cloudflare hosting, browser storage and optional Google Analytics after consent. Advertising remains off. ## Who operates Calcr Calcr is operated by Calcr Team. For privacy questions or requests, email [support@calcr.app](mailto:support@calcr.app). ## Calculations and page requests Calcr's public calculators process their numerical inputs in your browser. A visitor account is not required. The application does not send raw numbers, dates, grades or calculation results as analytics events. 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External sites linked from Calcr have their own privacy policies. ### How to simplify ratios and find a missing term URL: https://calcr.app/blog/how-to-simplify-ratios Last publication: 2026-11-10T14:31:21.678Z Simplify ratios with a common divisor, align units before comparing, and use a proportion to scale a quantity or find a missing value. A ratio describes quantities in a stated order. Simplifying it changes the size of the counting unit without changing the relationship. Divide both terms by the same nonzero factor until they have no common factor greater than one. ## Simplify a whole-number ratio For 42:56, the greatest common divisor is 14. Divide each term by 14 to get 3:4. Check the result by scaling back: 3 * 14 = 42 and 4 * 14 = 56. The [ratio calculator](https://calcr.app/tools/ratio-calculator) can reduce the pair. Label what the first and second terms mean before entering them, especially when the ratio describes different ingredients or groups. ## Match units before reducing Compare 1.2 metres with 80 centimetres by converting the first quantity to 120 centimetres. The ratio is 120:80 = 3:2. Using the bare numbers 1.2:80 would compare quantities expressed in inconsistent units. For a decimal pair such as 1.5:2.5, multiply both by 10 to get 15:25, then reduce to 3:5. Multiplying both terms by the same amount preserves the ratio. ## Find a missing value with a proportion Suppose 4:7 = 20:x. The first term grew by a factor of 5, so the second must also: x = 7 * 5 = 35. Cross multiplication gives the same result: 4x = 7 * 20, so x = 140 / 4 = 35. Keep the order consistent. Swapping only one pair would create a different proportion. Check your answer by substituting it back: 20:35 reduces to 4:7. ## Separate a part-to-part ratio from a share A 3:4 mix has 7 equal parts altogether. The first ingredient's share is 3/7, approximately 42.8571%. It is not 3/4 of the mix. If the total amount is 350 units, one part is 350 / 7 = 50, giving amounts of 150 and 200. ## FAQ ### Can a simplified ratio contain zero? One term can be zero in a meaningful comparison, such as 0:5 becoming 0:1. The pair 0:0 has no unique reduced relationship. ### Does 3:4 mean the same as 4:3? No. The order identifies which quantity is being compared with which. ### Is a ratio always unitless? A ratio of like measurements can cancel units after conversion. Comparisons such as distance per time retain a rate unit. When simplifying ratios, preserve the order, align units and divide both terms together. When solving a proportion, substitute the missing term back into the original relationship as a check. See [OpenStax: ratios and rate](https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate) for the distinction between ratios and rates. ## Related tools and guides - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Fraction calculator](https://calcr.app/tools/fraction-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Discount calculator](https://calcr.app/tools/discount-calculator) ### Ratio calculator URL: https://calcr.app/tools/ratio-calculator Last publication: 2026-11-11T03:00:18.700Z Free ratio calculator to simplify ratios or solve a missing proportion. Use fractions or decimals, check units and follow examples for scaling and shares. ## Ratio calculator: Simplify or complete a ratio Use the reduction mode for a pair of nonnegative quantities, including fractions and decimals. Use the missing-value mode when three terms of a proportion are known. Keep the quantities in the same order on each side. ## Ratio formulas To simplify a:b, divide both terms by their greatest common divisor. For a:b = c:d, cross multiplication gives a * d = b * c, provided the denominators in the corresponding fractions are nonzero. ## Worked examples Simplifying: 24:36 reduces to 2:3 because both terms divide by 12. Scaling a recipe: 3:5 = 18:x gives 3x = 90, so x = 30. Both original terms were multiplied by 6. Part versus whole: a mix with ratio 2:3 contains 5 equal parts altogether. The first ingredient is 2/5 of the mix, or 40%, rather than 2/3 of the whole. ## Limits and units Convert comparable measurements to one unit before reducing: 1 metre to 50 centimetres is 100:50 = 2:1. The all-zero ratio has no unique simplest form. This tool uses nonnegative quantities. In missing-value mode, the first term must be positive so the unknown can be recovered without dividing by zero. ## When to use this ratio calculator Use this free ratio calculator when two quantities have an ordered relationship and you need either the simplest form or a proportional missing value. Examples include combining ingredients, scaling a drawing, comparing counts, and dividing a total into shares. Name each term before entering numbers: flour to water is different from water to flour. Keep the labels in that order throughout your calculation. When comparing like measurements, convert to a common unit first. A drawing length of 4 centimetres representing 2 metres is a ratio of 4:200, which reduces to 1:50. Writing 4:2 and reducing to 2:1 would ignore the unit conversion. Ratios can also compare unlike units, such as distance and time, but the result is then a rate with units. Cancelling the labels would remove information you need to interpret it. Do not assume that every relationship is proportional. Doubling the number of people does not necessarily double the time required for a task. A delivery charge with a fixed starting fee does not have the same cost-to-distance ratio for every trip. Cross multiplication works when the underlying ratios really are equal; the calculator does not establish that condition from three numbers alone. ### Example: dividing a fixed total into shares Two groups share 250 items in the ratio 2:3. Add the ratio terms to find five equal shares. Each share contains 250 / 5 = 50 items. The first group receives 2 * 50 = 100, and the second receives 3 * 50 = 150. Checking 100:150 in reduction mode returns 2:3. Checking the sum, 100 + 150 = 250, confirms that all items were assigned. The first group does not receive 2/3 of the total. The expression 2/3 compares the first group with the second group, whereas 2/5 compares the first group with the whole. For an indivisible total that is not a multiple of five, an exact whole-item allocation may be impossible. The ratio calculator can describe the intended proportions, but you still need an agreed rule for distributing leftover items. ### Example: scaling a drawing with a missing term A drawing uses 3 centimetres to represent a real length of 150 centimetres. Another line is 8 centimetres on the same drawing. In missing-value mode, set 3:150 = 8:x. Cross multiplication gives 3x = 1200, so x = 400 centimetres, or 4 metres. The drawing-to-real scale is 1:50 throughout, and multiplying 8 by 50 provides an independent check. If you instead need the drawing length for a real object, place the quantities in the corresponding positions before solving. A real length of 400 centimetres has a drawing length of 400 / 50 = 8 centimetres. This reversal changes which term is unknown, not the scale itself. Avoid using a measured printout after it has been resized unless you verify that the stated scale still applies. For a practical ratio, retain enough digits to describe the measurements honestly. A mathematically reduced ratio such as 137:250 may be exact for the numbers typed, but if those numbers were approximate measurements it does not imply laboratory precision. State whether the ratio describes a target mix, an observation or a rounded estimate. That small piece of context is often more useful than forcing every result into a familiar-looking pair of integers. Use a scale-factor check after solving. If 3 becomes 18, the multiplier is six, so the paired value of 5 must become 30. If the two sides require different multipliers, they are not the same proportion. In reduction mode, dividing both original terms by the same positive number preserves the relationship. Dividing only the first term changes it. For fractional inputs, inspect the reduced integer pair and confirm its order against your labels. Keep any conversion from metres to centimetres in your notes so the simplified ratio can be traced back to its original measurements. ## FAQ ### Are 2:3 and 3:2 the same? No. Reversing the order changes which quantity each term describes. ### Is a ratio a percentage? A ratio compares quantities; a percentage compares a part with a stated base of 100. Identify the whole before converting. ### Can I enter a decimal ratio in reduction mode? Yes. The tool scales fractions and decimals to integer terms before reducing them. For example, 1.5:2 = 15:20 = 3:4. ### How do I convert a part-to-part ratio into percentages? Add the terms to identify the whole. For a ratio of 3:7, there are ten equal parts, so the first share is 3/10 = 30% and the second is 7/10 = 70%. Dividing 3 by 7 gives a comparison between the two shares instead. Use the percentage calculator after deciding which denominator matches your question, and keep the original labels beside the result. ### Can a simplified ratio contain a zero? Yes, a zero paired with a positive quantity can describe the absence of one component. For example, 0:8 reduces to 0:1. The pair 0:0 has no unique proportional scale and is rejected. Also distinguish reduction from solving a missing value: this tool requires a positive first term in missing-value mode so the calculation does not divide by zero. A valid reduced pair does not make every arrangement of a proportion solvable. ## Related tools and guides - [Simplifying ratios guide](https://calcr.app/blog/how-to-simplify-ratios) - [Fraction calculator](https://calcr.app/tools/fraction-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Average calculator](https://calcr.app/tools/average-calculator) ### Health calculators URL: https://calcr.app/categories/health Last publication: 2026-11-11T02:59:45.887Z Free health calculators for adult BMI and maintenance calories. Review formulas, worked examples, applicable ages and limits before interpreting results. ## Understand adult BMI and maintenance energy The BMI calculator relates adult weight to height and shows the corresponding CDC screening category. The calorie calculator estimates adult resting energy using the Mifflin–St Jeor equation, then applies a selected activity multiplier to describe a maintenance scenario. Both tools explain their formulas and assumptions. Neither measures a person's health directly or replaces a clinical assessment. ## Check the intended population first Adult BMI categories in this tool apply from age 20. Children and teenagers need age- and sex-specific growth references, so their results must not be interpreted using an adult cutoff table. BMI also cannot distinguish fat from muscle or bone, and the tool is not intended for pregnancy assessment. A clinician can interpret measurements alongside medical history and other findings. The calorie equation supports ages 19–78, matching the original study range. Its male and female coefficients belong to that published model; choosing one does not establish that it suits every individual. Activity factors are explicit assumptions rather than measured energy requirements. The calculator is not for pregnancy, breastfeeding, illness-related nutrition or eating-disorder management, and it does not generate a calorie deficit or weight-loss prescription. ## Read numbers without overstating precision Choose kilograms and centimetres or pounds and total inches before entering values. Five feet nine inches means 69 total inches, not 5.9. Check the unit labels whenever a result looks surprising. Retain the measurement date and assumptions when comparing results over time, and remember that a rounded display can hide values close to a category boundary. Use these tools to learn the arithmetic and prepare questions for a qualified professional. The body text links to CDC information and the original energy-equation study so you can inspect the basis of the calculation. You can try every feature with invented measurements, and calculations run in your browser without an account. If a result raises a health concern or conflicts with professional guidance, seek appropriate care rather than making a diagnosis or changing treatment from this page. All results are for reference and are not medical advice. ## Related tools and guides - [BMI calculator](https://calcr.app/tools/bmi-calculator) - [Calorie calculator](https://calcr.app/tools/calorie-calculator) - [Age calculator](https://calcr.app/tools/age-calculator) ### Terms of use URL: https://calcr.app/terms Last publication: 2026-11-10T14:32:05.819Z Use Calcr’s free calculators and games responsibly. Understand the informational purpose of results, service limits and permitted access. ## Operator and contact Calcr Team operates Calcr. Contact [support@calcr.app](mailto:support@calcr.app) with questions about these terms. ## Using the public tools Calcr provides free numerical tools, explanatory content and browser games. Public use does not require a subscription or visitor account. Use information you are entitled to enter, and avoid entering sensitive information when an invented example will serve the same purpose. Do not attempt unauthorized administrator access, interfere with the operation of the website, upload malicious material or misrepresent Calcr's results as an official certification. The administrator-only area is not a public account service. ## Results and reliance Results depend on the inputs, selected mode, numerical precision and stated conventions. Explanations and examples help you check them; they do not guarantee that every possible use is error-free. Independently verify results used in important decisions. See the [methodology](https://calcr.app/pages/methodology) and [disclaimer](https://calcr.app/pages/disclaimer). ## Availability and external services Features, content and availability can change as errors are fixed or tools are maintained. Browser storage is not a backup service. Clearing it can remove local game records or preferences. If advertising or external links are present, those third parties operate their own services. An advertisement is not a recommendation or a prerequisite for calculating. Do not click an ad to support the website; engage with it only if the offer interests you. ## Content and feedback You may read the guides and use the tools for their intended purpose. These terms do not grant ownership of Calcr's code, branding or original explanatory text, or claim ownership of third-party material linked as a source. Refer to any separately supplied license when reusing material. For a correction, follow the [contact instructions](https://calcr.app/contact) and provide a reproducible, non-sensitive example. These terms do not limit rights you have under applicable law. ### How to calculate weighted grades URL: https://calcr.app/blog/how-to-calculate-weighted-grades Last publication: 2026-11-10T14:31:29.701Z Convert scores to percentages, multiply by their course weights and add the contributions. Check weights and unfinished work before calculating. A weighted grade gives some assessments more influence than others. Convert each component to a percentage, multiply it by its share of the course, then add the contributions. Copy the weights from the course rules before calculating. ## Convert points into percentage scores If an assessment awards 36 points out of 40, its percentage is 36 / 40 * 100 = 90%. Enter 90 as the score, rather than entering the raw 36 next to a course weight. For components containing several assignments, your course may combine earned and possible points before applying the component weight. Do not average assignment percentages equally unless that matches the course policy. ## Calculate a weighted grade step by step Consider three hypothetical components: Component | Score | Course weight | Contribution | Coursework | 78% | 20% | 15.6 | Project | 88% | 30% | 26.4 | Exam | 94% | 50% | 47 | The weights add to 100%. The final percentage is 15.6 + 26.4 + 47 = 89%. Reproduce the calculation in the [grade calculator](https://calcr.app/tools/grade-calculator). ## Why the ordinary average can disagree The arithmetic mean of 78, 88 and 94 is approximately 86.6667%. It differs from 89% because it gives each component one third of the influence. The weighted version gives the strong exam result half of the influence. With two equal 50% weights, scores of 70 and 90 give 80%, matching their ordinary average. Equal weights are the special case where both methods agree. ## Do not silently fill in unfinished work Suppose two known components account for only 60% of a course. The remaining 40% is not automatically a zero and cannot simply disappear. A current-grade estimate may renormalize completed work, while a projected final grade needs an explicit assumption for the remaining component. Calcr requires a complete set of positive weights totaling 100% for the calculation shown here. ## FAQ ### Why does the result differ from my gradebook? Check category point totals, missing-work policy, dropped scores, extra credit and rounding. A course can apply rules beyond a weighted mean. ### Can I turn the result into a letter grade? Only with the grading scale for that course. A percentage does not imply a universal letter grade or GPA. ### What if my weights add to 99%? Confirm whether the syllabus rounded the displayed weights. Do not invent the missing percentage; ask the course owner which values govern the result. Use weighted grades as a transparent calculation aid. Your institution's published grading rules determine the official result. For an example of a learning platform's component-weight method, see [Instructure's guide to weighted assignment groups](https://community.instructure.com/en/kb/articles/660669-unknown). This guide does not claim Calcr reproduces every gradebook rule. ## Related tools and guides - [Grade calculator](https://calcr.app/tools/grade-calculator) - [Average calculator](https://calcr.app/tools/average-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) ### Average calculator URL: https://calcr.app/tools/average-calculator Last publication: 2026-11-11T03:00:24.620Z Free average calculator for mean, median, sum, count, minimum and maximum. Enter a number list and learn when equal-weight averages can give a useful result. ## Average calculator: Calculate an arithmetic mean Enter a list of numbers, using the separators accepted by the form. Review the count as well as the average to check that every intended value was included. The result also shows the sum, median, minimum and maximum. Up to 1,000 numbers can be processed in one list. ## Formula and examples Arithmetic mean = sum of all values / number of values. Every value has equal weight, including repeated numbers and zero. - For 4, 7, 7 and 10, the sum is 28 and the count is 4, so the average is 7. The minimum is 4 and the maximum is 10. - For -3, 0 and 6, the sum is 3, so the average is 1. - For 10, 10 and 100, the average is 40. The large value pulls the mean upward even though most values are 10. ## What this average does not tell you The main result is the arithmetic mean. The median is shown separately: sort the values and take the middle one, or the mean of the two middle values for an even-length list. This tool does not calculate a mode or geometric mean. Values with different units should not be combined. Averaging class percentages equally is inappropriate when the classes have different sizes or assignment weights. A list is limited to 10,000 characters. An empty list has no mean; malformed or non-finite values need correction rather than silent removal. ## When to use this average calculator Use this free average calculator for a collection of equally weighted observations measured in the same unit. It can summarize daily counts, repeated measurements, or a set of comparable prices. The arithmetic mean describes the total divided equally among the observations; the median describes the middle of an ordered list. Looking at both can help you notice when a large or small observation changes the story. Prepare the list before calculating. Decide which observations belong to the group, keep repeated values when they represent separate observations, and distinguish a recorded zero from missing data. Five daily counts with one missing day are not the same as five counts with one day known to be zero. The calculator cannot decide how your study, class or accounting process should treat an absent observation. Do not combine values with different weights as though they were equally important. A final examination worth 60% of a course cannot be treated like a short quiz worth 5%. Use the grade calculator for that setup. Nor should you combine unrelated units: averaging 10 kilometres with 20 minutes creates a number that has no useful interpretation. Define the quantity you are summarizing before pasting a long list. ### Example: the mean and median tell different stories Consider five delivery times in minutes: 12, 13, 14, 15 and 46. Their sum is 100, so the mean is 100 / 5 = 20 minutes. The sorted middle value is 14 minutes, which is the median. Four deliveries took less than the mean because the one long delivery pulled the mean upward. Neither summary is arithmetically wrong; they describe different features of the same observations. Before removing 46, investigate whether it is a valid observation or a recording error. Deleting a real delayed delivery just to make the average smaller would change the question being answered. If you report both mean and median, include the count of five and note that the results describe this particular sample. The calculator does not infer what caused the delay or whether it will happen again. ### Example: combining group averages correctly One group of 10 observations has an average of 8, while another group of 30 has an average of 12. The underlying totals are 10 * 8 = 80 and 30 * 12 = 360. The combined total is 440 over 40 observations, so the combined mean is 11. Simply averaging 8 and 12 gives 10, which incorrectly treats the smaller group as equally large. If you have the original 40 values, enter them directly. If you only have the two group summaries, use the scientific calculator to evaluate (10 * 8 + 30 * 12) / 40. The average calculator does not accept a separate weight column. This example also assumes that the group averages have not already been heavily rounded; otherwise the reconstructed total is approximate rather than exact. Check the result against the minimum and maximum. For a nonempty set of equally weighted real numbers, the mean cannot be below the smallest observation or above the largest. A surprising value inside that range can still be correct, particularly with negative values or an uneven distribution. For example, -10 and 6 average to -2. Read the count to catch an omitted separator, an accidental duplicate or a missing value before interpreting the final number. A count mismatch is a useful warning even when the mean looks reasonable. If you expect seven daily observations and the result says six, inspect the pasted list before interpreting it. Use plain numeric entries and an accepted separator rather than inserting currency symbols, unit names or thousands separators into individual values. For a short list, add the numbers manually as a check; for a longer list, compare the reported minimum and maximum with the expected range. A valid calculation confirms the arithmetic for the supplied list, not that the list contains every intended observation. ## FAQ ### Does zero count? Yes. A recorded zero is a value. A missing observation is different and should be handled according to the purpose of your calculation. ### Does the average have to appear in the list? No. The average of 2 and 3 is 2.5. ### Can I average averages? Only directly when their underlying groups have equal sizes. Otherwise use the group counts as weights. ### Should I remove an unusually large or small number? Only with a reason appropriate to the data, such as a verified entry error or a documented exclusion rule. An unusual observation can be real and important. First check the original record, then consider reporting the mean and median together. This calculator does not automatically remove outliers, because doing so would silently change the dataset. If you calculate a revised list, record what was excluded and why. ### Can I use the arithmetic mean for an average speed? Sometimes, but not in every travel setup. For equal time intervals, the arithmetic mean of the speeds matches total distance divided by total time. For equal distances, it generally does not. Travelling 60 kilometres at 60 km/h and another 60 at 30 km/h takes three hours in total, giving 40 km/h overall, rather than the simple mean of 45 km/h. Calculate total distance and total time when the intervals differ. ## Related tools and guides - [Grade calculator](https://calcr.app/tools/grade-calculator) - [Weighted grades guide](https://calcr.app/blog/how-to-calculate-weighted-grades) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) ### Cookies and browser storage URL: https://calcr.app/cookie Last publication: 2026-11-10T18:35:36.924Z See which site functions use browser storage, how to clear local preferences and scores, and how optional consent controls affect advertising. ## What browser storage does Cookies and browser storage can keep information on your device between interactions. Calcr uses them for specific functions rather than to store a public visitor account. Category | Purpose | What clearing it changes | Theme preference | Remember the selected appearance | The theme returns to its default or system preference | Language preference | Remember a language choice where available | The site may choose its default language again | Local game records | Keep best results in this browser | Local records can be lost | Privacy choices | Remember optional-service choices | A choice may need to be made again | Administrator session | Authenticate authorized administrators | The administrator may need to sign in again | Optional analytics cookies | Let Google Analytics associate visits and events with this browser after permission | Analytics browser/session identifiers can reset; the separately stored consent choice may remain | Scientific calculation history stays in the current session rather than a synced account history. Calculator inputs and results are not included in analytics events. ## Optional services and your choices On your first visit, Google Analytics stays blocked until you choose Allow analytics. Choosing Reject optional services keeps it blocked. After permission, Google Analytics can write analytics cookies and use browser/session identifiers to associate visits and events. Advertising remains off. Calculators and games work when analytics is rejected or unavailable. The application sends fixed published page addresses without the raw query string or fragment, a fixed page title and a blank page-referrer field. It does not include raw calculator inputs or results in analytics events. Google still receives the technical information needed for its network requests; see [Google's privacy policy](https://policies.google.com/privacy). Open Privacy settings in the footer to change your choice. A saved permission can apply on later visits to eligible pages. Withdrawing stops subsequent analytics events from the Calcr application; it does not automatically delete existing analytics cookies or data Google already received. Reopening or changing these controls does not delete your theme preferences or local game records. ## Manage data on your device Use your browser's site-data controls to inspect, delete or restrict storage for calcr.app. Deletion can reset preferences and local game records. Restricting administrator session cookies can prevent signing in to the CMS, while ordinary public calculations do not need an administrator session. See the [privacy policy](https://calcr.app/privacy) for information about page requests and administrator access, or [contact](https://calcr.app/contact) for questions about your data. ### How to calculate age between two dates URL: https://calcr.app/blog/how-to-calculate-age Last publication: 2026-11-10T14:31:35.872Z Count completed calendar years, months and days, rather than dividing by 365. Understand Calcr’s leap-day and month-end convention. To calculate calendar age, count completed years first, then completed months, then the remaining days. This keeps the result tied to calendar anniversaries rather than assuming every year and month has the same length. ## Fix the comparison date Age changes over time, so write down the date on which it is measured. A birth date of 2000-06-15 has a different age on 2026-06-14 and 2026-06-15. An explicit comparison date also makes an example reproducible. Use the [age calculator](https://calcr.app/tools/age-calculator) with invented dates if you are learning the method. The calculation does not need a name or other identifying details. ## Count complete calendar units For 2000-06-15 to 2026-11-10: - Complete 26 years to reach 2026-06-15. - Complete 4 further months to reach 2026-10-15. - Count 26 remaining days to reach 2026-11-10. The result is 26 years, 4 months and 26 days. For a birth date of 2010-11-11 measured on 2026-11-10, only 15 years are complete; the next anniversary is still one day away. ## Understand leap days and month ends The Gregorian leap-year rule adds February 29 in years divisible by 4, except century years not divisible by 400. Thus 2000 was a leap year and 2100 will not be. Calcr uses a stated calculation convention: year and month candidates keep the original birth day when possible. If it does not exist in a destination month, that candidate is clamped to the month's last day. Later candidates remain anchored to the original birth day rather than to a previously clamped day. Under this convention, the non-leap-year anniversary of February 29 is February 28. Likewise, moving a January 31 date into February stops at February's last valid day. This is a software convention, not a claim about legal birthdays, benefit eligibility or age restrictions. Those rules can depend on jurisdiction and context. ## Why dividing days by 365 is different A total-day count measures elapsed calendar days. Dividing it by 365 mixes leap days into a rough decimal-year figure, which can cross a whole-number threshold before the birthday. Use total days when that is the quantity needed and calendar units when the question concerns anniversaries. ## FAQ ### Can I measure a past or future age? Yes. Choose the comparison date explicitly, provided it is not before the birth date. ### Does the tool use time of birth? No. It works with dates and does not calculate hours or time-zone offsets. ### Is the displayed age verified? No. It is computed from your inputs and cannot establish identity or prove eligibility. For a reproducible age calculation, retain both dates and the month-end convention with the result. The calendar rule is documented by the [U.S. Naval Observatory: leap years](https://aa.usno.navy.mil/faq/leap_years). The anniversary convention above is Calcr's own stated behavior. ## Related tools and guides - [Age calculator](https://calcr.app/tools/age-calculator) - [Date calculator](https://calcr.app/tools/date-calculator) - [Counting days guide](https://calcr.app/blog/how-to-count-days-between-dates) - [Calculation methodology](https://calcr.app/pages/methodology) ### Grade calculator URL: https://calcr.app/tools/grade-calculator Last publication: 2026-11-11T03:00:32.342Z Free grade calculator for weighted percentage scores. Check contributions and weights totaling 100%, compare exam scenarios and avoid common grading errors. ## Grade calculator: Enter scores and their weights Enter between 1 and 30 scores as percentages from 0 to 100 and the weight each contributes to the final result. Weights must be positive and total 100%. A blank score needs attention; it is not silently converted into a zero. ## Weighted-grade formula Final percentage = (score 1 * weight 1 + score 2 * weight 2 + ...) / 100. The weight belongs to the component, not to its raw number of points. Convert 18 points out of 20 to 90% before entering it. ## Worked examples Two components: coursework at 80% with weight 40% contributes 32 points. An exam at 90% with weight 60% contributes 54. The final result is 86%. Three components: 75% at 20%, 84% at 30% and 92% at 50% give 15 + 25.2 + 46 = 86.2%. Equal weights: scores of 60% and 100% at 50% each produce 80%. Their arithmetic mean happens to match because the weights are equal. ## Limits Use the weights in your syllabus. This calculator does not infer letter grades, GPA, extra-credit policy, dropped assessments or a school's treatment of unfinished work. It rejects incomplete totals instead of assuming the missing weight. A calculation is an estimate, not an official academic record. ## When to use this weighted grade calculator Use this free grade calculator when your course expresses each component as a percentage score and assigns it a percentage weight. It can check a completed course result or compare clearly labelled hypothetical scores. Gather the syllabus weights and convert each assessment's earned points to a percentage before entering it. The calculation works from those supplied values; it does not retrieve a school's grading policy. Keep the level of the weights consistent. If quizzes make up 20% of the course, the individual quiz weights inside that category may need to be combined before you enter the category score. Do not enter a quiz's internal weight as though it were its share of the entire course. A component can contribute fewer final percentage points than its own score because its weight is only one part of the final result. Do not use this tool to infer a GPA, an institution's letter grade or an official pass decision. Those may depend on grade boundaries, minimum exam requirements, attendance rules or rounding policies that are absent from the arithmetic. Extra credit above 100% is also outside this form's supported score range. If an institutional calculator disagrees, compare the inputs and policy rather than assuming one decimal result settles the issue. ### Example: converting points before applying weights A project earns 36 of 40 points and has a course weight of 25%. The project percentage is 36 / 40 * 100 = 90%. An exam earns 68 of 80 points, or 85%, and has a weight of 75%. Enter scores of 90 and 85 with weights of 25 and 75. Their contributions are 22.5 and 63.75 final percentage points, producing a weighted result of 86.25%. Entering raw scores of 36 and 68 would incorrectly treat them as percentages out of 100. Adding earned points and dividing by all possible points would give 104 / 120 * 100, approximately 86.67%, which describes a points-based scheme rather than the stated 25%/75% scheme. Either system can exist in a course, so use the one specified by your syllabus. The weighted calculator does not choose between them automatically. ### Example: checking a hypothetical final examination Suppose completed coursework has a score of 88% and is worth 70% of the course. The final exam is worth 30%. Testing an exam score of 75% gives 88 * 0.70 + 75 * 0.30 = 84.1%. Testing 90% gives 61.6 + 27 = 88.6%. Changing only the exam input makes the comparison clear, while all weights still total 100%. If you want to find the exam score required for a target, rearrange the equation separately. A target of 85% requires (85 - 61.6) / 0.30 = 78% on the exam. Entering 78 in the exam row checks that the result is 85%. This is a scenario, not a prediction of your performance. It also assumes there is no separate minimum exam mark or other course rule. For an unfinished course, do not silently type zero for every future assignment. A zero is a specific assumed score and can make a hypothetical final result look like a current official grade. If the school's current grade excludes ungraded work, its calculation may renormalize the completed weights. This tool instead requires a complete 100% setup. Either enter explicitly hypothetical future scores or calculate the completed portion separately with its policy stated. Keep a copy of the weights and assumptions alongside the answer. Check the sum of the weights before examining the final percentage. Weights of 20, 30 and 40 total 90%, leaving part of the course unspecified; the tool rejects that setup rather than guessing the remaining component. A single assessment can have a weight of 100%, but every entered weight must be positive. If a course drops one assessment, first determine how the remaining weights are redistributed under its rules. Removing the row without revising the weights can leave a different grading model. Record any hypothetical score clearly so it cannot be mistaken for an earned mark. ## FAQ ### Why do my weights need to add to 100%? They must describe the complete result for this calculation. The tool does not automatically renormalize them. ### Can I enter points instead of percentages? Convert earned points / possible points * 100 first. ### Should an ungraded assignment be zero? Only if your course explicitly treats it that way. A missing score and an earned zero are different. ### Why does a high score add only a few points to the final result? Its contribution depends on its course weight. A score of 100% on a quiz worth 5% contributes five final percentage points. A score of 80% on an exam worth 50% contributes forty. Compare contributions rather than scores alone when checking which assessments affect the total most. The result remains a percentage of the complete course, not a sum of raw assessment marks. ### Should I round every assessment before calculating? Use the score precision and rounding policy specified by the course. When no intermediate rounding is required, retaining the supplied decimals until the final calculation avoids accumulating avoidable rounding differences. A mathematical result of 89.95% does not automatically become a particular letter grade; a school may round, truncate or apply a boundary directly. Verify that rule with the official course documentation before interpreting a borderline result. ## Related tools and guides - [Weighted grades guide](https://calcr.app/blog/how-to-calculate-weighted-grades) - [Average calculator](https://calcr.app/tools/average-calculator) - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) ### Calculation methodology URL: https://calcr.app/pages/methodology Last publication: 2026-11-10T14:32:16.626Z Review Calcr’s numerical precision, exact fractions, weighting rules, calendar conventions and the boundaries of each calculation. ## Arithmetic and display precision The scientific calculator evaluates permitted scalar real-number expressions with mathjs BigNumber arithmetic configured to 32 significant digits. Displayed results use up to 12 significant digits. Transcendental values and displayed decimals can be approximate. DEG is the initial angle mode; switch to RAD explicitly when needed. Postfix percent means division by 100, so 200 + 10% means 200.1. Expressions have a length limit and an execution budget. Unsupported functions, non-real outputs, non-finite results and invalid operations are rejected. This calculator does not execute user programs or provide symbolic proofs. ## Percentages, fractions and ratios Percentages use the base appropriate to the chosen question. Change divides the difference by the original value and is undefined for an original value of zero. Fraction arithmetic uses integer numerator/denominator operations, normalizes the sign and reduces by a greatest common divisor. Exact fractions remain distinct from decimal approximations. A zero denominator and division by a zero-valued fraction are invalid. Ratio reduction scales nonnegative integer, decimal or fraction inputs to whole-number terms and divides by their greatest common divisor. Missing-term proportions use equivalent cross products and reject a division-by-zero case. Keep units and term order consistent. ## Averages and grades The arithmetic mean is sum / count, giving each number equal influence. The average calculator also shows the sorted middle value as the median, or the mean of the two middle values for an even count. The grade calculator uses percentage scores and positive percentage weights totaling 100. It does not treat a blank score as zero or silently rescale an incomplete set of weights. School-specific grading, extra credit and letter-grade conversions are outside its scope. ## Calendar conventions Date calculations use the Gregorian calendar and date-only values. A signed day difference is end minus start, independent of the user's time zone. Inclusive mode increases the range size by one while preserving direction; the same date counts as one inclusive day. The public date form adds or subtracts whole calendar days and includes weekends and holidays. Age counts completed years, then completed months, then remaining days. Year and month candidates retain the original birth day where possible, clamping to the destination month's last day only when that day is invalid. Candidates are anchored to the original day rather than repeatedly advancing an already clamped date. Under this convention, a February 29 anniversary in a non-leap year is February 28. This is a calculation convention, not a rule for legal eligibility. ## Clock durations and discounts Clock duration subtracts minutes-after-midnight values, with 1,440 minutes added only when next day is explicitly selected. It excludes time-zone and daylight-saving transitions and does not deduct breaks. Successive percentage discounts multiply the remaining-price factors. An optional entered sales-tax rate applies after the discounts. Amounts display two decimal places with half-up rounding. Shipping, fixed coupons and merchant-specific tax or rounding rules are not inferred. Keep full intermediate precision and compare the displayed price with the actual checkout. ## Verification and corrections Worked examples are intended to be reproducible with the listed inputs and modes. Important results should be independently checked. A result can be arithmetically correct yet inappropriate when the task uses a different convention. Report a discrepancy with a non-sensitive example using the [contact instructions](https://calcr.app/contact). References: [mathjs BigNumber documentation](https://mathjs.org/docs/datatypes/bignumbers.html), [OpenStax prealgebra](https://openstax.org/books/prealgebra-2e/pages/preface) and [U.S. Naval Observatory leap-year rules](https://aa.usno.navy.mil/faq/leap_years). Product-specific conventions are stated above. ### How to count days between dates URL: https://calcr.app/blog/how-to-count-days-between-dates Last publication: 2026-11-10T14:31:41.934Z Distinguish elapsed days from inclusive date counts. Work through leap days, reversed ranges and date addition without time-zone assumptions. Before counting days between dates, decide whether you mean elapsed calendar days or the number of dates included in a range. The same start and end can correctly produce different answers when the counting rule changes. ## Elapsed days measure the gap From 2026-11-10 to 2026-11-13, three day boundaries pass: the 11th, 12th and 13th. The elapsed difference is 3 days. From a date to itself, no day has elapsed, so the difference is zero. In the [date calculator](https://calcr.app/tools/date-calculator), leave inclusive end off to calculate this signed difference. If the end is before the start, the answer is negative; reversing the example produces -3. ## Inclusive counting includes both boundaries If you need to count the listed calendar dates, include November 10, 11, 12 and 13: four dates. For a forward range, this is elapsed difference + 1. A single-date range then counts as 1. Calcr preserves direction for reversed ranges: the inclusive result for November 13 back to November 10 is -4. A negative count indicates direction, not a negative number of dates in the set. State the convention when sharing the result. ## Check month and year boundaries From 2024-02-28 to 2024-03-01 is 2 elapsed days because 2024 contains February 29. In 2025, February 28 to March 1 is only 1 elapsed day. For date addition, 2026-12-31 plus 1 day becomes 2027-01-01. Subtracting 7 days from 2026-11-10 gives 2026-11-03. Use the add/subtract mode when you know the starting date and length rather than both boundary dates. ## Calendar days are not business days or hours Every date counts here, including weekends and public holidays. A contract may exclude particular days or set a local cutoff time; that requires rules beyond this calculator. Likewise, a local day affected by a daylight-saving transition need not contain 24 elapsed hours. Calcr compares dates independently of a time zone. Use a time-zone-aware timestamp calculation for actual elapsed hours between two instants. ## FAQ ### Should I include the first day? That depends on the task. Use elapsed difference for the gap and inclusive counting for a list containing both boundary dates. ### Does the tool skip holidays? No. It is a calendar-day calculator, not a regional business-day calendar. ### Why is a leap-year February different? It contains an additional valid date. The Gregorian rule determines which years include that date. Label the counting rule with your result. A clear “3 elapsed calendar days” or “4 dates including both endpoints” is more useful than an unexplained number. For calendar background, see the [U.S. Naval Observatory's introduction to calendars](https://aa.usno.navy.mil/faq/calendars). Calcr's inclusive and signed-range conventions are specified above. ## Related tools and guides - [Date calculator](https://calcr.app/tools/date-calculator) - [Age calculator](https://calcr.app/tools/age-calculator) - [Time duration calculator](https://calcr.app/tools/time-duration-calculator) - [Calendar age guide](https://calcr.app/blog/how-to-calculate-age) ### Age calculator URL: https://calcr.app/tools/age-calculator Last publication: 2026-11-11T03:00:39.395Z Free age calculator to find completed years, months and days on a chosen date. Check birthday, leap-day and month-end examples with clear calendar rules. ## Age calculator: Calculate age on a chosen date Enter a birth date and the date on which you want to measure age. The answer counts completed Gregorian calendar years, then months, then remaining days. Use an explicit comparison date when you need a reproducible result rather than relying on today's date. ## How calendar age works A year has 365 or 366 days, and months have different lengths. Dividing total days by 365 does not reliably produce a birthday-based age. Year and month candidates keep the original birth day when possible. If that day does not exist in the target month, it is clamped to that month's last day; later candidates still refer to the original birth day. ## Worked examples - Born on 2000-06-15, measured on 2026-11-10: 26 years, 4 months and 26 days. - Born on 2010-11-11, measured on 2026-11-10: 15 completed years. The sixteenth birthday is still one day away. - Born on 2000-02-29, measured on 2025-02-28: 25 years under this tool's clamped-anniversary convention. A birth date after the comparison date is invalid. ## Limits and privacy The inputs are dates, not times of birth. Time zones, hours and legal rules for reaching an age are outside the calculation. The month-end convention is a calculation choice and should not be used as a legal eligibility decision. You can use invented dates when exploring the tool. ## When to use this age calculator Use this free age calculator when you need a calendar interval from a birth date to a specific comparison date. It can help check an age stated in a biography, prepare a birthday timeline or compare dates in an educational example. Enter both dates explicitly when sharing the result. A person's age changes over time, so an answer without an “as of” date is incomplete even if the arithmetic is correct today. The main answer reports completed years, months and days rather than an approximate number of decimal years. Each unit has a calendar meaning. One month can contain 28, 29, 30 or 31 days, so the month component is not a fixed block of thirty days. Read the separate total-days result when you need a day count instead of a birthday-based interval. Do not use the result as proof of identity or a ruling about legal eligibility. Requirements for school entry, benefits, employment or medical care can use a jurisdiction's own definitions and cutoff rules. This tool does not know those rules, verify a document or check an actual time of birth. You can understand all its features with invented dates, so there is no need to enter a real person's birthday just to try it. ### Example: the day before and after a birthday A person born on 1995-09-20 has completed 29 years on 2025-09-19. The next day, 2025-09-20, marks 30 completed years. Measuring on 2025-09-21 gives 30 years and one day. Subtracting the year numbers alone would incorrectly label the first date as age 30 because the birthday had not yet occurred in that calendar year. For a reproducible comparison, enter these dates in turn and keep the birth date unchanged. The difference illustrates why an age range should specify the exact date being used. If a form asks only for completed years, use the years component; do not round 29 years and eleven months up to 30. Rounding a decimal estimate is a different operation from counting completed birthdays. ### Example: a month-end birth date Consider a birth date of 2023-01-31 and a comparison date of 2023-03-30. One month candidate lands on 2023-02-28 after clamping to February's last valid date. Two months from the original day would land on 2023-03-31, which is still in the future. The result is therefore zero completed years, one completed month and 30 remaining days under this tool's convention. On 2023-03-31 the same birth date gives exactly two completed months. This does not mean that every month in the earlier result was thirty days long. It means that the calculator tests calendar anniversaries against the original day and then counts the leftover days. Another system that repeatedly adds clamped months can produce a different representation, so name the convention when month-end precision matters. Leap-day birthdays need the same care. The tool uses February 28 as the clamped anniversary in a non-leap year, while a legal or organizational policy may use another rule. Consult the policy before making an eligibility decision. The number of elapsed days between two dates is separate from deciding which calendar date counts as an anniversary for a particular purpose. Before recording an age, check the date order and format. A birth date after the comparison date cannot produce a nonnegative age and is rejected. When reading a numeric date from another document, verify whether its author meant month/day or day/month. Selecting dates through the form and recording them as year-month-day avoids that ambiguity. The calculator cannot correct a valid but unintended birthday. An additional check is to compare the result with the next anniversary. On the day before a birthday, the completed-years component should still show the previous age. On the birthday, it should increase by one. For month-end and leap-day examples, repeat that check using the documented clamped date. Do not substitute a locale-dependent date string from memory when recreating a result: year-month-day makes the intended calendar date clear. If two systems disagree, compare their input dates and anniversary conventions before assuming the disagreement is caused by a timezone or an arithmetic error. ## FAQ ### Can I calculate age in the past? Yes. Set the comparison date to the past date you need. ### Is a year always 365 days? No. Gregorian leap years contain 366 days. ### Can this prove a person's age? No. It calculates from the dates you supply and does not verify identity or documents. ### Why is calendar age different from total days divided by 365? Calendar age follows anniversaries, while a division by 365 treats every year as the same length. Leap days make the second approach drift, especially over long intervals. Months create a further difference because their lengths vary. Use completed years for a birthday-based age and the total-days detail for a count of date boundaries. Neither should be relabelled as the other without stating an approximation. ### Can I calculate an age on a future date? Yes. Choose the future comparison date you want, provided it is not before the birth date. This is useful for planning an anniversary or checking a hypothetical timeline. Record the future date with the result, because it is an age on that date rather than an age today. The tool performs calendar arithmetic only and does not determine whether a person will meet any future program's eligibility conditions. ## Related tools and guides - [Calendar age guide](https://calcr.app/blog/how-to-calculate-age) - [Date calculator](https://calcr.app/tools/date-calculator) - [Time duration calculator](https://calcr.app/tools/time-duration-calculator) - [Calculation methodology](https://calcr.app/pages/methodology) ### Limitations and disclaimer URL: https://calcr.app/pages/disclaimer Last publication: 2026-11-10T14:32:22.449Z Calcr offers informational calculations from your inputs. Check rounding, calendar conventions and source rules before relying on a result. ## Informational calculations Calcr calculates from the values and modes you choose. It does not verify those inputs, identify a person, certify an academic result or determine legal eligibility. Content is provided to explain calculations and support ordinary numerical tasks. ## Check the rule as well as the number A rounded decimal may differ from an exact fraction. Calendar age depends on the stated anniversary convention. Inclusive date counts differ from elapsed-day differences. Weighted grades depend on the actual course policy. Review the tool's limits and the [methodology](https://calcr.app/pages/methodology) before using a result. The website does not provide personalized medical, financial or legal advice. Important decisions need an independent check using the relevant records, rules and qualified sources. A general disclaimer does not make an incorrect calculation acceptable; reproducible errors should be corrected. ## Availability and third parties Features may be interrupted or changed during maintenance. Local browser records can be lost when storage is cleared. External sources and advertisements, when present, are operated by their respective providers and are not proof that a calculated result is correct. Use [contact](https://calcr.app/contact) for instructions on reporting an error. Source links explain the underlying methods; they do not certify an individual calculation or its suitability for your decision. ### Date calculator URL: https://calcr.app/tools/date-calculator Last publication: 2026-11-11T03:00:46.650Z Free date calculator to count days between dates or add years, months and days. Choose inclusive counting and check leap-year and month-end examples. ## Date calculator: Count days or shift a date Choose the difference mode to compare two dates. Use date addition to move forward or backward by a whole number of calendar days. Check the inclusive option when your task counts both boundary dates. ## Counting rule The default signed difference is end date minus start date on the Gregorian calendar. Moving from Monday to Tuesday is one elapsed calendar day. Inclusive counting adds the boundary day to the size of the range while preserving its direction. ## Worked examples A short range: 2026-11-10 to 2026-11-13 is 3 days apart. Including both dates gives a count of 4. A leap day: 2024-02-28 to 2024-03-01 is 2 days apart because February has 29 days that year. Adding 2 days to 2024-02-28 produces 2024-03-01. Going backward: subtracting 1 day from 2027-01-01 produces 2026-12-31. A reversed range has a negative elapsed difference. ## Limits These are calendar dates, not time-zone-aware timestamps. Weekends and public holidays are counted. A contractual deadline may use business-day rules or a different treatment of boundary days. Choose those rules separately rather than assuming this count is a deadline decision. ## When to use this date calculator Use this free date calculator to count calendar days for a plan, compare two dated events or find a date a stated number of days away. Choose elapsed or inclusive counting before interpreting the answer. The appropriate convention depends on the question: a stay measured by nights usually describes date differences, while a list of every date in an event can include both endpoints. For a signed interval, keep the order of the dates visible. A negative result tells you that the entered end date is earlier than the start. It is useful when checking the direction of a schedule change, but it does not represent a negative number of actual calendar dates. If you need only the size of an interval, use the magnitude and state that you have ignored direction. Do not treat this as a business-day, court-deadline or timezone conversion calculator. Weekends and holidays remain in the count, and there is no jurisdiction-specific calendar. Nor does a count of two calendar days establish that exactly 48 hours elapsed between two local timestamps. Dates and timed events answer different questions, particularly around daylight-saving transitions or travel between time zones. ### Example: counting an event's displayed dates An event runs from 2026-06-10 through 2026-06-14, with activities on both the first and last dates. The elapsed difference is four days because there are four date-to-date steps. Inclusive counting gives five dates: June 10, 11, 12, 13 and 14. Select the inclusive option if the question is how many dated daily programs need printing. If accommodation is instead booked with arrival on June 10 and departure on June 14, the four-date difference can describe four nights under that booking setup. The calendar arithmetic has not changed; the meaning of the counted units has. Label the result “five event dates” or “four nights” rather than copying the same number into both decisions. Actual booking and billing terms still control a real reservation. ### Example: moving across a month boundary Start with 2026-01-31 and add one month using the year/month/day addition mode. February has no day 31 in 2026, so the result clamps to 2026-02-28. Adding 30 days instead gives 2026-03-02. The difference shows why “one month later” and “thirty days later” are not interchangeable instructions. The tool applies years first, months second and days last. Each year or month step clamps independently to the last valid day when necessary. If you repeat an operation from its previous result, the new starting date may have a different day number. For a recurring schedule, decide whether each occurrence should refer to the original day or the last result; a single date calculation cannot infer your recurrence policy. For a leap-year check, February 29 exists when the Gregorian year is divisible by four, except century years that are not divisible by four hundred. Thus 2000 contains a leap day, while 1900 does not. The tool validates actual dates rather than treating a month as a fixed number of days. An input that looks plausible, such as February 30, must be corrected instead of normalized silently to a date in March. Before sharing an answer, write down the start date, end date, direction and endpoint convention. If you are adding time, include separate year, month and day quantities rather than compressing them into an approximate day count. That record makes it possible for another person to reproduce the result and identify a convention mismatch without guessing what you meant. Use the age calculator when the specific goal is completed years since a birthday. For a short range, list the dates manually to check the selected convention. From the tenth to the thirteenth there are three transitions but four named dates. For addition, test a simple one-day movement before entering a larger year/month/day combination. If you need subtraction, choose that direction rather than typing a negative value into a field that expects a nonnegative amount. Keep the order of year, month and day adjustments visible. A valid result confirms the stated calendar operation; it does not establish that a scheduling instruction intended those units or that endpoint rule. ## FAQ ### Why are the same dates zero days apart? No day has elapsed. Inclusive counting treats that single date as one counted day. ### Are weekends excluded? No. Every calendar date counts. ### Does daylight saving time change the answer? No. This tool counts date boundaries, not elapsed hours on a clock. ### Why can adding a month and then subtracting it give a different date? Clamping can lose the original day number. Starting at January 31 and adding one month may produce February 28. Subtracting one month from that new date gives January 28, since the new starting day is 28. This is a calendar convention rather than a numerical rounding error. Keep the original date if you need to compare repeated operations against the same anniversary. ### Can I use the result for a deadline stated in working days? Not directly. This tool counts all calendar dates and has no holiday calendar, cutoff time or rule for moving a deadline that lands on a weekend. A working-day deadline needs those additional rules. Verify them with the relevant organization or governing document, then use a suitable business-day calculation. A correct calendar-day answer does not establish that a contractual or legal deadline has been calculated correctly. ## Related tools and guides - [Counting days guide](https://calcr.app/blog/how-to-count-days-between-dates) - [Age calculator](https://calcr.app/tools/age-calculator) - [Time duration calculator](https://calcr.app/tools/time-duration-calculator) - [Calculation methodology](https://calcr.app/pages/methodology) ### Code Mode URL: https://calcr.app/code-mode Last publication: 2026-11-10T14:32:27.610Z Use a public code to open a currently available Calcr game. Code Mode is optional and separate from ordinary numerical calculations. ## Open a game with a public code Code Mode provides an optional shortcut to the games currently available on Calcr. Choose Code Mode explicitly, enter a code shown in the available-code list and open the matching game. You can also browse the [games directory](https://calcr.app/games) directly. ## Calculations keep their ordinary meaning Entering a number in the scientific calculator remains a numerical expression. A number does not silently open a game. Return to calculator mode when you want to evaluate arithmetic, powers or functions. ## Codes are shortcuts The codes are public navigation shortcuts, not passwords, subscriptions or access credentials. They do not promise to bypass school, workplace, browser or network restrictions. An unavailable code should produce a clear unavailable state rather than redirecting to an advertisement. Only games published in the current language appear in the available-code list. If a game is withdrawn, its old code does not guarantee access to an unpublished page. ## FAQ ### Do I need an account? No. Public games do not require registration or payment. ### Can I share a game without sharing a code? Yes. Share its ordinary page URL from the games directory. ### Does playing change my calculation history? Code Mode is a separate navigation action. Calculation history is session-based and is not a game account. ## Related tools and guides - [All games](https://calcr.app/games) - [All calculators](https://calcr.app/tools) - [Guides](https://calcr.app/blog) - [About Calcr](https://calcr.app/about) ### Time duration calculator URL: https://calcr.app/tools/time-duration-calculator Last publication: 2026-11-11T03:00:53.492Z Free time duration calculator for hours, minutes and seconds between clock times. Choose an overnight interval and convert the result to decimal hours. ## Time duration calculator: Measure a clock interval Enter the start and end times. If the end belongs to the following day, enable next day explicitly. A later clock date is a choice you make; the tool does not infer it from an earlier-looking end time. ## Formula Convert each time to minutes after midnight: hours * 60 + minutes. Duration = end minutes - start minutes, adding 1,440 minutes when next day is selected. Divide the result by 60 to recover whole hours and remaining minutes. ## Worked examples - 09:15 to 17:45 on the same day is 510 minutes, or 8 hours 30 minutes. - 22:40 to 01:10 with next day selected is 150 minutes, or 2 hours 30 minutes. - 08:00 to 08:00 is zero on the same day, or 24 hours when the end is the next day. ## Limits This is a clock-time calculation without dates or time zones. It does not account for daylight saving changes, travel between zones or leap seconds. Breaks are not deducted. For a work shift, subtract unpaid breaks separately and use your employer's rounding rules only if they apply. ## When to use this time duration calculator Use this free time duration calculator for an interval between two clock times under a stated same-day or next-day assumption. It can check a study session, a workshop timetable or the clock span of a work shift. Enter 24-hour times so morning and evening cannot be confused, and select next day only when the end is on the following calendar day. The result shows hours, minutes and seconds along with decimal hours and total minutes. These are different representations of the same interval. Choose the representation that matches the next task: a timetable may need hours and minutes, while multiplying a duration by an hourly amount needs decimal hours. A minute is one sixtieth of an hour, so the digits after a decimal point are not a minute field. Do not use this form for a flight between time zones, a dated interval crossing a daylight-saving change or a span across several days. It has no dates or timezone database. Next day adds exactly 24 hours to the end clock reading; it does not check whether a particular local calendar day contained 23 or 25 hours. Use a timestamp-aware tool when actual elapsed time matters. ### Example: separating a shift from its unpaid break A shift starts at 08:20 and ends at 16:50 on the same day. The clock span is 8 hours 30 minutes, or 510 minutes. If there is a 45-minute unpaid break under the applicable arrangement, subtract it separately: 510 - 45 = 465 minutes. Divide by 60 to get 7.75 hours, which is 7 hours 45 minutes. The result panel initially shows the full clock span, not the paid portion, because this form does not know the break length. Multiplying 7.45 by an hourly amount would be wrong if you meant 7 hours 45 minutes. Use 7.75 for decimal hours. Whether a break is paid and whether times are rounded depend on the relevant policy; this calculation supplies neither a payroll rule nor a legal decision. ### Example: an overnight interval with seconds Start at 23:50:30 and finish at 00:15:45 on the next day. There are 9 minutes 30 seconds until midnight and another 15 minutes 45 seconds afterward. The total is 25 minutes 15 seconds, or 1,515 seconds. Dividing by 60 gives 25.25 total minutes. Dividing by 3,600 gives approximately 0.420833333333 decimal hours. Without the next-day choice, the ending clock reading is earlier and the form rejects the interval. It does not silently guess that you crossed midnight. If the actual finish were the next evening instead, you would need to enter that actual clock time and date relationship. The two clock readings alone cannot distinguish a short overnight interval from a much longer event with missing dates. An end on the next day can also be later on the clock than the start. For example, 09:00 today to 10:00 tomorrow is 25 hours, not one hour. The next-day option records that extra calendar step explicitly. Read it before calculating a result you intend to share. Equal clock readings likewise mean zero hours on the same day or 24 hours with the next-day end selected. Keep raw clock records if the result will be reviewed later. Writing only “8.5” loses the start, end and next-day assumption. When combining several sessions, convert each to the same unit before adding, and calculate unpaid breaks separately as appropriate. If all you need is an average session length, use the average calculator with total minutes rather than mixing values such as 1.30 and 90. Check the representation before pasting a result into another program. A spreadsheet cell formatted as a time can interpret 8.5 as a number of days or another date value, depending on its format. If you need a numeric duration in hours, use the decimal-hours detail and label the column. If you need an elapsed clock display, retain hours, minutes and seconds separately. Copying the main result preserves its unit labels, but another application may still require a different input format. Review one known interval after importing a set of durations rather than assuming the format was preserved. ## FAQ ### Is 8 hours 30 minutes equal to 8.30 hours? No. Thirty minutes is half an hour, so the decimal duration is 8.5 hours. ### Why must I choose next day? The same two clock times can describe different intervals. Explicit selection avoids silently assuming an overnight shift. ### Can this calculate a multi-day interval? Use the date calculator for calendar days. This form measures one pair of clock times with an optional next-day end. ### How do I convert decimal hours back to minutes? Multiply the fractional part by 60. A duration of 2.75 hours contains two whole hours plus 0.75 * 60 = 45 minutes. A duration of 2.30 decimal hours contains two hours and eighteen minutes, not thirty minutes. Keep the label “decimal hours” when exporting a result so another person or spreadsheet does not read the digits as a clock display. ### Does the calculator round clock-in times to a payroll interval? No. It calculates from the exact clock values supplied and does not round them to five, six, ten or fifteen minutes. If an applicable policy requires a separate rounding procedure, check that policy and retain the original times. Rounding each endpoint can give a different result from rounding the final duration, so those operations should not be substituted for each other without an explicit rule. ## Related tools and guides - [Date calculator](https://calcr.app/tools/date-calculator) - [Counting days guide](https://calcr.app/blog/how-to-count-days-between-dates) - [Average calculator](https://calcr.app/tools/average-calculator) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) ### Discount calculator URL: https://calcr.app/tools/discount-calculator Last publication: 2026-11-11T03:01:00.569Z Free discount calculator for sale prices, stacked percentage discounts and optional sales tax. Compare savings, final prices and practical worked examples. ## Discount calculator: Calculate a sale price Enter the original price and a percentage discount. Enter sequential rates separated by commas when the offer applies further reductions to the remaining price. Set sales tax to zero to exclude tax, or enter a rate to apply after discounts. The result separates savings before tax, the discounted price, tax and the final amount. ## Discount formulas For one discount, savings = original price * rate / 100 and final price = original price * (1 - rate / 100). For sequential discounts a% and b%, final price = original price * (1 - a/100) * (1 - b/100). The combined rate is 100 * (1 - (1 - a/100) * (1 - b/100)). ## Worked examples One discount: 25% off 80 saves 20 and leaves 60 to pay. Two discounts: 20% off 100 leaves 80. Taking another 10% off 80 saves 8 more, so the final price is 72. The total saving is 28%, not 30%. With tax: a single 30% discount on 100 gives a subtotal of 70. Applying 5% sales tax adds 3.50, making the final price 73.50. With tax set to zero, the sequential 20%-then-10% offer has a final price of 72. ## Limits Enter 1 to 20 discount rates between 0% and 100%; prices cannot be negative. An optional sales-tax rate between 0% and 100% applies after all discounts. Final price = discounted price * (1 + tax / 100). Displayed amounts round half up to two decimal places. Delivery, fixed-amount coupons and merchant-specific fees are not included. A retailer may use different tax or intermediate-rounding rules; check the actual checkout total. ## When to use this discount calculator Use this free discount calculator when a sale is described as one or more percentage reductions from an original price. It separates the reduced item price from the amount saved and from any entered sales tax. This is useful for comparing two offers with the same starting price or checking whether a stacked promotion behaves as advertised under a simple percentage model. Start with the price that actually receives the discount. A list price, a previously reduced price and a cart subtotal can all be different bases. If an offer excludes certain items or applies only after a minimum spend, check those conditions before entering a number. The calculator cannot read a retailer's terms, decide which products qualify or verify that the original price was genuinely charged. Do not use it as a complete checkout or tax engine. Fixed-value vouchers, shipping, duties, membership charges, tax-inclusive pricing and store-specific rounding may require separate calculations. The optional tax field applies a single supplied rate after every percentage discount. It does not infer a rate from your location or determine whether a coupon changes a taxable amount under local rules. ### Example: comparing a single offer with stacked offers A product starts at 200. Store A offers 30% off, giving savings of 60 and an item price of 140. Store B offers 20% off followed by another 15% off. The first step leaves 160, and the second leaves 160 * 0.85 = 136. Store B's combined saving is 64, or 32% of the original price. The second offer is four units cheaper before any other charges. Adding 20% and 15% would incorrectly predict a 35% reduction and a price of 130. The second discount is calculated from 160, so it removes 24 rather than 30. Compare the final prices with identical tax and fee assumptions. A lower item subtotal does not guarantee a lower checkout total if the two stores have different shipping charges or eligibility rules. ### Example: tax after a percentage reduction An item costs 120 before tax and receives a 25% discount. The discounted price is 120 * 0.75 = 90, and the saving before tax is 30. With an entered tax rate of 8%, the tax is 90 * 0.08 = 7.20. The final result is 97.20. Enter the original price, a discount of 25 and tax of 8 to reproduce this scenario. Without the promotion, applying the same tax assumption would give 120 * 1.08 = 129.60. Comparing the two final totals gives a difference of 32.40, while the tool's “save before tax” detail remains 30. Those figures measure different things. Keep the before-tax label when discussing the displayed saving, and verify the merchant's actual taxable amount rather than assuming this simplified setup applies everywhere. Price displays round to two decimal places after the underlying calculation. With several small-price items, a shop that rounds each item or each promotion separately can arrive at a slightly different basket total. That difference need not mean the percentage formula is wrong. To investigate, compare the original item base, the sequence of discounts, the taxable subtotal and the rounding stage one by one. When checking a promotion, test an easy reference first. Ten percent off 100 should save 10; zero percent should leave the price unchanged; 100% should reduce the item subtotal to zero. Then enter your actual numbers. This gives you a quick way to catch a rate entered as 0.25 when you meant 25%, or a previously discounted price accidentally entered as the original base. To keep a comparison fair, use the same original price in both scenarios. A 30% reduction from 200 leaves 140, while a 25% reduction from 180 leaves 135. The larger percentage discount does not produce the lower final item price because the bases differ. Compare the actual amounts you would pay, and keep tax and delivery assumptions consistent. The saving percentage is useful only alongside its original base. If an offer advertises savings “up to” a rate, enter the rate that applies to your item rather than assuming the advertised maximum. ## FAQ ### Can I add two discount percentages? Not when the second applies to the reduced price. Multiply the remaining-price factors instead. ### Does discount order matter? Pure percentage discounts have the same product in either order before rounding. Fixed coupons and store rules can change that. ### Does 100% off mean a zero total? It means a zero item price in this calculation. Separate fees may still apply. ### How can I find the original price from a sale price? For a single discount below 100%, divide the sale price before tax by one minus the discount rate as a decimal. A sale price of 60 after 25% off implies 60 / 0.75 = 80 originally. Use the scientific or percentage calculator for that reverse calculation. Dividing by zero at a 100% discount cannot recover an original price because any original item price could have produced zero. ### Can this compare offers with a fixed coupon? Only after you calculate that coupon under its actual terms separately. Taking ten units off before a percentage discount can differ from taking ten off afterward. Minimum spends, excluded items and tax rules add further conditions. This form accepts percentage reductions only, so do not enter a fixed coupon amount as if it were a percentage. Compare the resulting checkout amounts with all applicable charges included. ## Related tools and guides - [Percentage calculator](https://calcr.app/tools/percentage-calculator) - [Percentage change guide](https://calcr.app/blog/how-to-calculate-percentage-change) - [Ratio calculator](https://calcr.app/tools/ratio-calculator) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) ### Paycheck calculator URL: https://calcr.app/tools/paycheck-calculator Last publication: 2026-11-11T03:01:05.859Z Free paycheck calculator for US 2026 federal withholding and employee FICA. Estimate pay per check, see the tax breakdown, and check year-to-date limits. ## Free paycheck calculator for US federal tax in 2026 Estimate one regular paycheck after federal income tax withholding and employee FICA. Enter gross pay for the current period, pay frequency, W-4 filing status and wages already paid by this employer during 2026. The result separates federal withholding, Social Security, Medicare and Additional Medicare. It does not estimate state or local taxes, benefits or other deductions, so it is not a complete bank-deposit prediction. ## Before you calculate This version uses the IRS 2026 percentage method for a 2020-or-later Form W-4 with Step 2 unchecked and Steps 3 and 4 blank. All entered gross wages are assumed taxable for both federal withholding and FICA. Weekly means 52 payments, every two weeks means 26, twice monthly means 24 and monthly means 12. Do not confuse biweekly with semimonthly. Use the year-to-date field for wages before the current check, from the same employer. It determines how much of this check remains below the Social Security cap or above the Additional Medicare withholding threshold. It does not turn this into a full-year tax-return calculation. Enter dollar amounts to no more than two decimal places. ## How the paycheck estimate works For federal withholding, the tool annualizes the current regular pay, applies Worksheet 1A's adjustment, uses the standard annual withholding schedule for the selected status, and divides the resulting annual withholding by the payment count. The adjustment is $12,900 for married filing jointly and $8,600 for the other supported statuses. These are worksheet adjustments, not additional personal deductions to claim on a return. See [IRS Publication 15-T for 2026](https://www.irs.gov/publications/p15t). Employee Social Security is 6.2% of covered wages up to the 2026 wage base of $184,500. Medicare is 1.45% without that cap. Additional Medicare withholding is 0.9% of this employer's wages above $200,000 during the year. The employer withholding threshold is not a determination of your final filing-status-dependent liability. These rules are documented by [IRS Publication 15](https://www.irs.gov/publications/p15) and the [SSA wage-base reference](https://www.ssa.gov/faqs/en/questions/KA-02387.html). Each tax component rounds to cents before subtraction from gross pay. The main result is current gross minus those four employee withholding amounts. Employer payroll taxes are not subtracted from the employee's pay in this model. ## Worked paycheck examples ### A regular biweekly check Gross pay of $2,000 every two weeks, single status and no prior wages gives annualized wages of $52,000. Worksheet 1A reduces that to an adjusted annual amount of $43,400. The standard schedule gives $4,060 annual withholding, or $156.15 per check after rounding. Social Security is $124 and Medicare is $29. There is no Additional Medicare withholding, leaving an estimate of $1,690.85. ### A monthly check For $4,000 monthly, single status and zero prior wages, annualized wages are $48,000. Federal withholding is $298.33 per check, Social Security is $248 and Medicare is $58. The estimated amount after these federal deductions is $3,395.67. This is not comparable to a $4,000 biweekly check: the annualized wages and payment count differ even though the per-check gross input looks identical. ### Crossing the Social Security cap With $183,000 already paid and a current biweekly check of $4,000, only $1,500 of the new check remains under the $184,500 Social Security cap. Social Security is therefore $93, rather than $248. For single status, federal withholding is $540.38 and Medicare is $58, leaving $3,308.62. The year-to-date input changes FICA on this check, not the annualized federal withholding formula. ### Crossing the Medicare withholding threshold Change prior wages to $199,000 while retaining that $4,000 biweekly check and single status. Social Security is already capped. Of the new pay, $3,000 exceeds $200,000, so Additional Medicare withholding is $27. With regular Medicare of $58 and federal withholding of $540.38, the result is $3,374.62. Entering only an annual salary would hide this within-year change. ## When to use this estimate, and when to use another method Use it to understand a simple regular check, compare payment frequencies under consistent assumptions or check the arithmetic behind employee FICA. Keep a pay stub beside the result and compare each line separately. A difference in federal taxable wages, benefit treatment or W-4 entries can explain why an actual check differs. Use the [IRS Tax Withholding Estimator](https://www.irs.gov/individuals/tax-withholding-estimator) or qualified assistance for multiple jobs, spouse income, credits, itemized deductions, midyear changes, nonresident status, tipped wages, overtime deductions, bonuses or self-employment. This form does not model those cases. It also does not apply state unemployment, disability or local payroll rules. Do not use its result to file payroll or decide a tax payment without checking the applicable rules. ## FAQ ### Is this my exact take-home pay? No. It covers the listed federal withholding components under fixed assumptions. A bank deposit can also reflect state tax, insurance, retirement contributions, garnishments and other adjustments. Compare the gross and taxable wage definitions before comparing net amounts. A matching total by chance does not verify every payroll line. ### Does federal withholding equal my final income tax? No. Withholding is collected during the year. Final liability depends on the return, income, deductions, credits and filing circumstances. This tool does not calculate a refund or balance due. Its selected W-4 status is an input to the withholding schedule, not advice about how you should file. ### Why did Social Security decrease on a later check? The annual wage cap may have been reached. Only the portion of the current check below the cap is taxed here. Enter prior wages accurately and exclude the current check from that field. Medicare has no corresponding wage cap, so regular Medicare continues after Social Security stops. ### Can I enter a yearly salary? First divide the regular annual salary by your actual payment count, then enter one period's gross pay. Do not enter the entire salary as monthly gross. This model assumes the current check represents regular recurring pay; irregular compensation or a 27-payment year needs a separate payroll treatment. ### Are my salary and tax inputs uploaded? The calculation runs in your browser. Optional site analytics do not receive calculator inputs or results, and you can leave optional services disabled. Copying a result or sending it elsewhere is a separate action under your control. Use invented values if you are only exploring how withholding changes. ## Related tools and guides - [Finance calculators](https://calcr.app/categories/finance) - [Mortgage calculator](https://calcr.app/tools/mortgage-calculator) - [Compound interest calculator](https://calcr.app/tools/compound-interest-calculator) For reference only. This estimate is not financial, tax or legal advice and does not replace an employer's payroll calculation. ### 2048 URL: https://calcr.app/games/2048 Last publication: 2026-11-10T14:30:52.249Z Slide a four-by-four board, merge equal tiles and build toward 2048. Play a short browser puzzle with keyboard or touch controls. ## How to play 2048 Move the board left, right, up or down with the arrow controls or a swipe. All tiles slide as far as they can. Adjacent equal tiles merge in the direction of movement, and a successful move introduces a new tile. ## Merges and scoring A tile merges at most once in one move. A row containing 2, 2, 2, 2 becomes 4, 4 after a left move; the two new fours do not merge again during that move. Each merge adds the resulting tile value to your score. Merging two eights adds 16 points. Reach a 2048 tile to achieve the named goal. You can continue afterward. A board is over when no empty cells or legal neighboring merges remain. A full board can still have a legal move when equal tiles touch horizontally or vertically. ## A useful way to start Try keeping a large tile near a corner and building smaller tiles toward it. Check the whole board before changing direction: a move that creates space can also split a useful pair. This is a strategy suggestion, not a guarantee; new tiles introduce uncertainty. ## FAQ ### Why did a row of four twos not become an eight? Each original tile merges only once per move. Two pairs create two fours. ### Do the arrow keys always control the game? Keyboard controls apply when the game is focused. They should not take over an unrelated form or calculator. ### Is my best score an online ranking? No. Best scores are stored in this browser. Clearing site storage or switching browsers can remove or separate them. Calcr's board is a local browser implementation. It has no account, paid unlock or launch-time game advertising. ## Related tools and guides - [All games](https://calcr.app/games) - [Code Mode](https://calcr.app/code-mode) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) - [About Calcr](https://calcr.app/about) ### BMI calculator URL: https://calcr.app/tools/bmi-calculator Last publication: 2026-11-11T03:01:11.018Z Free BMI calculator for adults age 20 and older. Use kg/cm or lb/in, see the adult screening category, and understand the limits of body mass index. ## Free BMI calculator for adults Calculate adult body mass index from weight and height using kilograms and centimetres or pounds and total inches. The result includes the index and its CDC adult screening category. This form is for adults aged 20 and older. BMI is one screening measure; it cannot diagnose a condition, measure body fat directly or determine an individual's overall health. ## How to enter your measurements Choose the unit system before typing. In metric mode, enter weight in kilograms and height in centimetres: 70 and 175 are a valid example. In US mode, enter pounds and total inches. A height of 5 feet 9 inches is 69 inches, not 5.9. Enter age in completed years so the tool can reject use of adult categories below age 20. Check the measurements rather than copying an old value without its unit. A weight in pounds entered into the kilograms field produces a different index even when the arithmetic is correct. If comparing results over time, keep the measurement method and units consistent. The calculator cannot tell whether an entered measurement was taken accurately or whether a short-term change has clinical meaning. ## BMI formula and adult categories BMI = weight in kilograms / height in metres squared. For 70 kg and 1.75 m, the calculation is 70 / (1.75 * 1.75), approximately 22.86 kg/m². The US-unit calculation first converts pounds to kilograms and inches to metres, then uses the same formula. This avoids changing the definition between unit systems. The [CDC adult BMI categories](https://www.cdc.gov/bmi/adult-calculator/bmi-categories.html) use the following boundaries for adults 20 and older. The category is chosen from the unrounded value, while the displayed index rounds to two decimal places. Adult screening category | BMI in kg/m² | Underweight | below 18.5 | Healthy weight | 18.5 to below 25 | Overweight | 25 to below 30 | Obesity, class 1 | 30 to below 35 | Obesity, class 2 | 35 to below 40 | Obesity, class 3 | 40 or above | These labels summarize the adult classification system. They are not personal judgments or a substitute for a clinical assessment. A result close to a boundary should be read with the original measurements and the rounding note, rather than treated as a sudden change in health. ## Worked BMI examples ### Metric measurements An adult weighing 70 kg at a height of 175 cm has a height of 1.75 m. Squaring it gives 3.0625 m². Dividing 70 by 3.0625 gives approximately 22.86, within the adult healthy-weight category. Enter age 30 to reproduce the example. The arithmetic describes this pair of measurements; it does not establish fitness, nutritional status or a recommended body weight. ### US measurements An adult weighing 180 lb and measuring 70 inches has a BMI of approximately 25.83. The tool converts 180 lb to 81.6466266 kg and 70 inches to 1.778 m before dividing. This falls in the adult overweight category. If you compare this with a metric calculation, use the converted measurements without rounding them heavily first; otherwise a small difference in the displayed index is expected. ### A value at a classification boundary At 100 kg and 200 cm, BMI is 100 / 2² = 25 exactly. That belongs to the category beginning at 25, rather than the range below 25. At 99.98 kg and the same height, BMI is 24.995, which may display as 25.00 after rounding but remains below 25 for classification. The category uses the unrounded calculation to avoid moving a value across a boundary solely because of display rounding. ## When to use BMI, and when it is insufficient Use the calculator to understand a screening number, check a stated formula or prepare questions for a health professional. Keep weight, height, units and the date of measurement with any result you record. A number detached from its measurements is harder to review and can give a false impression of precision. Do not use adult cutoffs for children and teenagers. Their interpretation needs age- and sex-specific growth references; the [CDC adult calculator](https://www.cdc.gov/bmi/adult-calculator/) directs ages 2–19 to a separate child and teen calculator. This tool also excludes pregnancy from its intended screening use. Seek an appropriate clinical assessment rather than trying to force a special situation into an adult table. BMI cannot distinguish muscle, fat and bone or show where body fat is located. The [CDC BMI FAQ](https://www.cdc.gov/bmi/faq/index.html) explains why a muscular person may fall into a higher BMI category without the index identifying body composition. Medical history, physical findings and other information can change how a professional interprets the same number. This page does not prescribe weight change, medication, calorie restriction or treatment. A BMI category can be a starting point for a conversation, but it does not establish a personal goal. Keep your questions focused on your own circumstances rather than comparing one screening number with another person’s result. ## FAQ ### Is a healthy-weight BMI proof that I am healthy? No. It describes the category for a weight-to-height ratio. Health depends on more than that relationship, and a screening table does not evaluate symptoms, laboratory findings or medical history. Discuss concerns with a qualified professional rather than relying on one index to confirm or dismiss them. ### Why does the form require age when age is not in the formula? The formula itself uses weight and height. Age is requested to prevent applying adult categories to people under 20. Once that adult scope is satisfied, changing age does not change the arithmetic result. This is different from child BMI interpretation, where age affects the relevant growth reference. ### Can BMI estimate my body-fat percentage? No. The result is measured in kilograms per square metre, not percent. Two adults with the same BMI can have different body composition. Do not label the index as a body-fat measurement or subtract it from 100 to derive another quantity. A different assessment is needed for that question. ### Why does a rounded value appear beside a different category? A value just below a boundary can round up in the two-decimal display. Classification uses the underlying value, so 24.995 remains below 25 even if displayed as 25.00. Check the input precision and avoid interpreting a tiny numerical difference as a clinical finding. ### Do I need to upload a photo or create an account? No. Only the measurements entered in the form are needed, and the arithmetic runs in your browser. No photograph, identity document or public profile is required. You can test the examples with invented measurements and leave optional site services disabled. ## Related tools and guides - [Health calculators](https://calcr.app/categories/health) - [Calorie calculator](https://calcr.app/tools/calorie-calculator) - [Age calculator](https://calcr.app/tools/age-calculator) For reference only. BMI is a screening measure and this page does not provide medical advice, diagnosis or treatment. ### Snake URL: https://calcr.app/games/snake Last publication: 2026-11-10T14:30:57.641Z Guide a snake across a twenty-by-twenty board, collect food and avoid walls and its own body. Pause whenever you need a break. ## How to play Snake Start a round and steer with the arrow keys or on-screen direction buttons. The snake moves across a twenty-by-twenty board. Collect food to grow and increase your score while leaving space for the next turn. ## Movement rules You can turn at right angles, but cannot reverse directly into the snake's neck. If the snake is moving right, a left command does not reverse it; turn up or down first. Reaching a wall or colliding with the body ends the round. For example, after collecting food near the right edge, turn before reaching the boundary. A growing body needs a wider safe route than the initial short snake. Empty space is often more useful than the shortest line to the next food item. ## Pausing and restarting Use pause when you need to stop. Time-sensitive play pauses when the page goes into the background. Return to the visible game before continuing. Restart begins a new round rather than restoring a previous board. ## FAQ ### Why did my reverse command do nothing? A direct reversal would move the head into the body, so it is not a valid turn. ### Can the snake pass through a wall? No. This version uses solid boundaries rather than wrapping to the opposite side. ### Does my best score follow me to another device? No. It is saved in local browser storage and is not a synced account record. The game works without registration or payment. There are no game advertisements in the launch configuration. A browser can throttle inactive tabs, so an active visible page is the intended place to play. ## Related tools and guides - [All games](https://calcr.app/games) - [Code Mode](https://calcr.app/code-mode) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) - [About Calcr](https://calcr.app/about) ### Calorie calculator URL: https://calcr.app/tools/calorie-calculator Last publication: 2026-11-11T03:01:16.052Z Free calorie calculator for adult maintenance energy. Estimate resting calories and activity-adjusted kcal per day with clear formulas and limitations. ## Free calorie calculator for adult maintenance energy Estimate resting energy expenditure and an activity-adjusted maintenance scenario in kilocalories per day. This free calorie calculator uses the Mifflin–St Jeor equation with your age, weight, height and selected equation coefficient, then multiplies by an assumed activity factor. It does not prescribe food intake, calculate a weight-loss deficit or promise a future body weight. ## Enter measurements and choose assumptions Choose metric kilograms and centimetres or US pounds and total inches. Enter age in completed years. This implementation supports ages 19–78, the range studied in the original paper, rather than extending the equation to children or an unlimited age range. A valid number inside that range still does not prove that the estimate suits your individual circumstances. The original model has male and female coefficients. The form names those coefficients explicitly rather than treating them as a complete description of a person's physiology or identity. If neither model is appropriate to your clinical situation, a health professional can help choose a suitable assessment. You do not need to enter your name, date of birth or contact details. ## Calorie calculator formula For weight W in kilograms, height H in centimetres and age A in years, the simplified resting-energy equations are: - Male coefficient: 10W + 6.25H - 5A + 5. - Female coefficient: 10W + 6.25H - 5A - 161. - Activity-adjusted scenario: resting estimate * selected multiplier. The equations come from [Mifflin and colleagues' original 1990 study](https://pubmed.ncbi.nlm.nih.gov/2305711/?dopt=Abstract). They predict resting expenditure from measurements; they are not a direct measurement of your metabolism. The activity multipliers below are additional assumptions used by this calculator and were not derived as personalized activity measurements in that paper. Selected activity assumption | Multiplier | Mostly seated | 1.2 | Light activity | 1.375 | Moderate activity | 1.55 | High activity | 1.725 | Very high activity | 1.9 | These labels help compare scenarios. They are not a validated questionnaire that identifies your exact multiplier from a workout count. Daily movement, occupation and training can vary, and an activity estimate can be the largest source of uncertainty in the final number. Avoid choosing the highest factor simply because one demanding session occurred. ## Worked maintenance-calorie examples ### Resting and mostly seated estimates For a 30-year-old using the male coefficient at 70 kg and 175 cm, the resting equation is 700 + 1093.75 - 150 + 5 = 1648.75 kcal/day. Multiplying by 1.2 gives 1978.5, displayed as 1979 kcal/day. The resting and activity-adjusted numbers answer different questions; the smaller one is not a recommended eating target. ### A different coefficient and body size For age 40, weight 60 kg, height 165 cm and the female coefficient, resting expenditure is 600 + 1031.25 - 200 - 161 = 1270.25 kcal/day. With the light-activity assumption of 1.375, the scenario is 1746.59375, displayed as 1,747 kcal/day. Keep the unrounded resting value during multiplication; rounding it first can slightly change the final display. ### Comparing activity assumptions Return to the first example and change only the multiplier from 1.2 to 1.55. The resting estimate remains 1648.75, while the activity-adjusted result becomes 2555.5625, displayed as 2,556 kcal/day. This difference comes entirely from an assumption. It is not evidence that the person's actual expenditure changed or that a specific exercise burned the difference. ## When to use this calculator, and when not to use it Use it to learn how a resting-energy equation works or to compare transparent maintenance scenarios before discussing them with a qualified professional. Write down the selected coefficient, multiplier and measurement units along with any saved result. A bare number of calories hides assumptions that are necessary to interpret it. Do not use this estimate for pregnancy, breastfeeding, childhood, medical nutrition therapy or eating-disorder management. This page also does not assess symptoms, medication effects, recovery from illness or unusual energy needs. The [NIDDK Body Weight Planner's scope information](https://www.niddk.nih.gov/health-information/weight-management/body-weight-planner) likewise distinguishes adult planning from use during pregnancy or breastfeeding; its dynamic model is different from this simple equation. Maintenance expenditure and a weight-change plan are different tasks. Subtracting an arbitrary amount from the result does not make a safe or individually appropriate diet. Changes in body weight are not modeled here, and the calculator does not forecast a timeline. A repeat calculation with the same measurements simply repeats the same assumptions. It is not a follow-up assessment and cannot show whether a food plan or treatment has worked. If food or weight tracking is distressing, you can stop using the tool and seek support suited to your circumstances. ## FAQ ### Does the result tell me exactly how much to eat? No. It is an equation-based scenario with an assumed activity level. Actual needs may differ, and a recommended intake requires individual context. The display is rounded to a whole kilocalorie for readability, but that arithmetic precision should not be mistaken for certainty about a person's daily requirements. ### Is resting energy the same as total daily energy? No. The resting estimate is the starting value predicted by the equation. The larger activity-adjusted estimate applies a selected multiplier to approximate a broader daily scenario. This tool labels the two separately. It does not measure either quantity directly, and it does not ask you to use the resting number as a food limit. ### Which activity multiplier should I choose? Choose an assumption that represents the scenario you are examining, and compare nearby factors if you are uncertain. A single workout does not fully describe a typical day or week. The form's labels are broad guides rather than a personal assessment. A dietitian or clinician can help interpret activity and energy needs in a relevant context. ### Can I use this for weight loss or muscle gain? The tool supplies maintenance scenarios only. It does not set a deficit, surplus, target weight or treatment plan. Training, medical history and nutritional needs require more context than the form collects. Do not infer that following the displayed number guarantees a particular change in weight or body composition. ### Why does switching units change my result slightly? Equivalent measurements produce the same underlying calculation after conversion. Rounding a converted weight or height can alter the inputs, which may change the displayed result by a small amount. Check that US height is entered in total inches, not a feet-and-inches decimal. A large difference usually calls for reviewing units before interpreting the energy estimate. ## Related tools and guides - [Health calculators](https://calcr.app/categories/health) - [BMI calculator](https://calcr.app/tools/bmi-calculator) - [Age calculator](https://calcr.app/tools/age-calculator) For reference only. This page does not provide medical or nutritional advice, diagnosis, treatment or an individualized calorie prescription. ### Minesweeper URL: https://calcr.app/games/minesweeper Last publication: 2026-11-10T14:31:03.034Z Reveal a nine-by-nine board containing ten mines. Use neighboring counts and flags, with a safe first reveal and a touch-friendly flag mode. ## How to play Minesweeper Reveal cells on a nine-by-nine board containing ten mines. A number tells you how many mines occupy the surrounding cells, including diagonals. An interior cell has up to eight neighbors. Use a right-click to flag a suspected mine. On touch devices, switch to flag mode before selecting the cell. Switch back to reveal mode when you want to uncover cells again. ## Read the clues If a revealed 1 has exactly one unopened neighbor, that neighbor must contain a mine. If a revealed 2 already has two correctly identified mine neighbors, its other unopened neighbors are safe. A flag is your own hypothesis; placing it does not verify the cell. For example, two adjacent numbered cells can share the same hidden neighbors. Compare both clues rather than treating each number as a separate set of mines. This helps avoid counting one hidden mine twice. ## First move and win condition The first revealed cell and its immediate neighbors are safe. This does not promise a board that can always be solved without guessing. Reveal every non-mine cell to win. Revealing a mine ends the round; flags alone do not complete it. ## FAQ ### Do diagonals count? Yes. The eight surrounding positions count, reduced at edges and corners. ### Is a flag guaranteed to mark a mine? No. It records your deduction and can be wrong. ### Which cells are safe on the first reveal? The selected first cell and its immediate neighbors contain no mines. Beyond that opening, use the revealed clues rather than assuming further cells are safe. Records are local to your browser, without a public leaderboard. The launch version does not show game advertisements or require an account. ## Related tools and guides - [All games](https://calcr.app/games) - [Code Mode](https://calcr.app/code-mode) - [Scientific calculator](https://calcr.app/tools/scientific-calculator) - [About Calcr](https://calcr.app/about) ### Mortgage calculator URL: https://calcr.app/tools/mortgage-calculator Last publication: 2026-11-11T03:01:22.505Z Free mortgage calculator for a fixed-rate loan. Estimate monthly principal and interest, add your property tax and insurance, and review total interest. ## Free mortgage calculator for fixed-rate monthly payments Estimate a fixed-rate loan's monthly principal and interest, then add your entered property tax and home insurance amounts. This free mortgage calculator also shows scheduled interest over the full term. Enter the amount borrowed after the down payment, rather than the property's purchase price. The result is an illustrative payment estimate, not a lender quote, approval or affordability decision. ## Set up the loan correctly Use the fixed nominal annual interest rate stated for the loan, not an APR that also reflects certain borrowing costs. Select a whole number of years from 1 to 50. The model assumes twelve equal payment periods per year, a fixed rate throughout and payments at the end of each month. It does not model adjustable rates, interest-only periods, balloon payments or a different day-count convention. Enter annual property tax and annual home insurance separately. The tool divides each by twelve for a monthly estimate. Enter zero if you want to examine principal and interest alone, but remember that zero in a field means excluded from this scenario, not necessarily absent from real homeownership. Taxes and insurance can change even when a fixed-rate loan's principal-and-interest payment stays the same. ## Mortgage payment formula Let P be the loan amount, r the nominal annual rate divided by 12 and expressed as a decimal, and n the number of monthly payments. Monthly principal and interest is P * r / (1 - (1 + r)^(-n)). At a zero interest rate, use P / n instead, avoiding division by zero in the standard formula. Scheduled interest equals the unrounded monthly principal-and-interest payment multiplied by n, minus P. The displayed monthly amount rounds to cents. A lender's final payment can differ slightly because real schedules may round each payment or handle partial periods differently. The total-interest figure does not include property tax, insurance, fees or the down payment. The [CFPB explanation of PITI](https://www.consumerfinance.gov/ask-cfpb/what-is-piti-en-152/) separates principal, interest, taxes and insurance. Its [payment comparison guidance](https://www.consumerfinance.gov/ask-cfpb/on-a-mortgage-whats-the-difference-between-my-principal-and-interest-payment-and-my-total-monthly-payment-en-1941/) also explains that mortgage insurance and other costs may be additional. This calculator does not infer PMI or HOA fees, so add those separately when examining a real budget. ## Worked mortgage examples ### A thirty-year fixed-rate scenario For a $300,000 loan at 6% over 30 years, r is 0.005 and n is 360. Monthly principal and interest is approximately $1,798.65. Annual property tax of $3,600 adds $300 per month, and insurance of $1,200 adds $100. The displayed monthly estimate including those entered amounts is $2,198.65. Scheduled interest over the loan term is approximately $347,514.57, using unrounded payments. This example assumes the $300,000 is the loan balance after any down payment. If a home costs $375,000 and the down payment is $75,000, that loan amount follows by subtraction. Entering the full home price would calculate a larger loan and a different payment. The form does not subtract a down payment a second time. ### Comparing a shorter term Keeping the same $300,000 balance and 6% rate but choosing 15 years gives 180 monthly payments. Principal and interest is approximately $2,531.57 per month. The monthly payment rises, but scheduled interest falls to approximately $155,682.14. This is a comparison with the same assumed rate; actual offers for different terms can have different rates and fees. Do not judge affordability from the lower lifetime interest alone. A larger monthly commitment can affect cash flow, and the calculator does not know your other obligations. Compare full written loan offers under consistent assumptions, including costs excluded from this simplified model. ### Checking the zero-rate branch A $120,000 balance at 0% over ten years is repaid through 120 payments of $1,000 before tax or insurance. Scheduled interest is zero. This is a mathematical check of the amortization formula, not a claim that such a mortgage is available. Adding $2,400 annual tax and $1,200 annual insurance would raise the monthly estimate to $1,300 without creating loan interest. ## When to use this estimate, and when not to Use it to compare fixed-rate scenarios, understand a payment breakdown or check how term length changes the scheduled payment. Change one input at a time so the comparison remains interpretable. Keep the loan amount, rate, term and entered annual costs with any saved result. Do not use it to establish loan eligibility, choose an investment, calculate a binding payoff or replace a Loan Estimate. It does not include closing costs, escrow shortages, mortgage insurance, association dues, maintenance, utilities, extra principal payments or missed payments. A monthly figure without those costs is only one part of a household budget. Verify the terms and totals with the lender before making a financial commitment. ## FAQ ### Is APR the rate I should enter? Use the nominal note rate for this monthly amortization formula. APR serves a broader comparison purpose and may include certain fees. Substituting it can change the payment estimate without correctly modeling those fees. Check the loan documents if the two rates differ or the offer does not clearly identify the note rate. ### Does the result include the down payment? No. Enter the loan amount after subtracting the down payment from the financed purchase amount. The down payment is an upfront contribution, not part of the scheduled monthly principal-and-interest payment here. Closing costs financed into the balance need to be reflected in the entered loan amount if applicable. ### Why can my actual monthly bill change on a fixed-rate loan? The fixed part is generally principal and interest under the assumed schedule. Property taxes, insurance and escrow adjustments can change. This tool spreads your entered annual costs evenly across twelve months; it does not forecast future assessments or premiums. Compare the individual components on a mortgage statement rather than only the total. ### Are PMI and HOA included? No. They are excluded and are not estimated from your down payment or location. If either applies, add the appropriate amount separately when reviewing a budget. The absence of a field does not mean the charge is zero or that a particular loan avoids mortgage insurance. ### Can I model additional monthly principal payments? This version assumes only the scheduled payment. Extra principal changes the balance path and payoff date, so subtracting an arbitrary amount from total interest would be incorrect. Use an amortization model that explicitly applies extra payments and verify any prepayment conditions in the loan documents. ## Related tools and guides - [Finance calculators](https://calcr.app/categories/finance) - [Paycheck calculator](https://calcr.app/tools/paycheck-calculator) - [Compound interest calculator](https://calcr.app/tools/compound-interest-calculator) For reference only. This page does not provide financial advice, a loan offer or a guarantee of borrowing terms. ### Compound interest calculator URL: https://calcr.app/tools/compound-interest-calculator Last publication: 2026-11-11T03:01:27.131Z Free compound interest calculator with monthly deposits. Compare a fixed-rate growth scenario, total contributions and interest, with explicit assumptions. ## Free compound interest calculator with monthly contributions Project a balance using an initial amount, a fixed monthly contribution, a nominal annual interest rate and a time period. This free compound interest calculator separates money contributed from modeled interest. It assumes monthly compounding and deposits at each month-end. The result describes a fixed-rate scenario; it does not predict market returns, recommend an investment or guarantee that a balance will be available. ## Choose the inputs for one consistent scenario The initial balance is present at the start. The monthly contribution is added after that month's interest calculation. Enter zero contributions to examine one lump sum, or zero initial balance to examine deposits alone. This form accepts nonnegative balances, deposits and rates; it does not model withdrawals, negative returns or an account that can become overdrawn. Enter the nominal annual rate, not APY. A nominal rate of 6% becomes a monthly rate of 0.5% in this model. APY already reflects compounding, so dividing an APY by twelve is a different assumption. Check the account or scenario's rate definition before comparing the result with another calculator. The time must equal a whole number of months; half a year represents six months. ## Compound interest formula Let P be the initial balance, C the contribution at each month-end, i the nominal annual rate divided by twelve in decimal form, and N the number of months. The final balance is P * (1 + i)^N + C * ((1 + i)^N - 1) / i. The first term grows the initial balance; the second accumulates the later deposits over their remaining months. When i is zero, final balance is P + C * N. Total contributed is also P + C * N, and modeled interest is final balance minus that contributed amount. Keeping these quantities separate prevents deposits from being mistaken for investment gains. Calculations retain decimal precision until display rounding to cents. The [SEC's Investor.gov compound interest calculator](https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator) similarly distinguishes an initial investment, recurring contributions, time, a rate assumption and compounding frequency. This page deliberately fixes the frequency to monthly and the deposit timing to month-end so those assumptions are visible rather than hidden behind one large final number. ## Worked compound-interest examples ### One starting balance and no deposits Start with $1,000 at a nominal annual rate of 12% for one year, with no monthly contributions. The monthly rate is 1%, so the final balance is 1000 * 1.01^12, approximately $1,126.83. Modeled interest is $126.83. Simple interest of 12% on the original $1,000 would be $120; the difference arises because monthly interest also earns interest in later months. The rate in this example is chosen to make the monthly arithmetic easy to inspect. It is not a current account offer or an expected market return. Changing the rate changes the scenario, and the tool does not assess whether any entered rate is realistically available or appropriate for a particular investment. ### Regular month-end deposits Start with zero and deposit $100 at each month-end for one year at the same nominal 12% rate. The result is approximately $1,268.25. Contributions total $1,200 and modeled interest is $68.25. The final deposit arrives at the end of month twelve and earns no interest within this period, while earlier deposits have more time to compound. If deposits arrived at the beginning of each month instead, each would earn one additional month's interest and the result would differ. This calculator uses month-end timing consistently. Do not compare its output with a beginning-of-period model without accounting for that difference, especially when the contribution is large relative to the starting balance. ### A zero-rate savings scenario An initial $500 plus $50 deposited monthly for two years gives 24 deposits. At 0%, the final balance is 500 + 50 * 24 = $1,700. Total contributions are $1,700 and interest is zero. This check is useful for seeing how much of a future balance comes from saving rather than growth. A zero-year scenario returns the initial balance with no deposits or interest. ## When to use this calculator, and when not to Use it to understand compounding, compare contribution amounts or test how time affects a clearly stated fixed-rate scenario. Change one assumption at a time and save the inputs with the result. If you compare several rates, label them as scenarios rather than choosing the largest output as though it were a forecast. Do not use it as a prediction of stocks, funds, cryptocurrency or another investment with variable returns. Losses, fees, taxes, contribution limits and inflation are not modeled. The [SEC's introduction to investing](https://www.investor.gov/introduction-investing) provides broader context for evaluating investments; a growth formula alone does not assess suitability or risk. A future dollar balance also does not state its future purchasing power. Inflation can change what the same amount buys. Withdrawals and fees change the balance path, and a tax paid each year can affect later compounding. These cannot always be corrected by subtracting one amount from the final result. Use a model that explicitly includes the relevant cash flows when those details matter. ## FAQ ### What is the difference between nominal rate and APY? A nominal annual rate states the rate before compounding under a specified frequency. APY expresses an annual yield including compounding. This tool divides the nominal annual rate by twelve. Entering an APY into that field changes the intended rate assumption, so verify the label on a real account before using its advertised figure. ### Are monthly deposits included in the interest figure? No. Total contributed includes the starting balance and every scheduled deposit. Interest is the modeled final balance minus that total. Looking at both values helps distinguish saving more money from earning more growth. Neither value represents a verified statement from an actual account. ### Can I use a negative rate or a withdrawal? This version does not support them. Negative returns and withdrawals need a model that handles the resulting cash flows and any balance constraints. Entering a positive number instead would describe a different scenario. A rejected input should prompt a suitable calculation rather than changing its sign to force an answer. ### Does more frequent compounding always explain a different result? It can explain a difference when the nominal rate and other assumptions are identical, but deposit timing, rate definition, term and fees may also differ. This tool fixes monthly compounding. Compare all inputs before attributing a discrepancy to frequency alone, and avoid comparing a nominal rate with an APY as though they were the same input. ### Is the projected balance guaranteed? No. It follows mathematically from a constant rate and scheduled deposits. The calculator does not evaluate an account's terms, an issuer's reliability or an investment's future performance. Treat the output as an illustration and obtain appropriate advice before making a financial decision. ## Related tools and guides - [Finance calculators](https://calcr.app/categories/finance) - [Mortgage calculator](https://calcr.app/tools/mortgage-calculator) - [Paycheck calculator](https://calcr.app/tools/paycheck-calculator) For reference only. This page does not provide financial or investment advice, an offer or a guarantee of returns.