Ratio calculator
Free ratio calculator to simplify ratios or solve a missing proportion. Use fractions or decimals, check units and follow examples for scaling and shares.
By Calcr · Updated
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.