Percentage calculator
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.
By Calcr · Updated
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.