gizmobench

Ratio Calculator

Simplify a ratio of any number of terms, or solve a proportion for a missing value. Decimal ratios are scaled to whole numbers before reducing, which is the step that decides whether 1.5:2 comes back as 3:4 or unchanged.

Simplified · divided by 63 : 40.75 as a decimal · 42.86% : 57.14% · scale factor 6
Ratio
Mode
Separator

Separate the terms with a colon, a slash, a space or the word “to”, so 18:24, 18/24 and 18 to 24 are the same ratio. Two terms or twenty, decimals and percentages included.

  • Simplifiedgreatest common divisor 6
    3 : 4
  • As a decimalfirst term ÷ second, exact
    0.75
  • As a percentage spliteach term's share of the total, adding to exactly 100%
    42.86% : 57.14%
  • Scale factormultiply the simplified form by this to get back what you typed
    6
  • Greatest common divisorthe number every term was divided by, once the decimals were cleared
    6

The working

Clear the decimals, then divide through by what every term shares, on paper, and only the steps this ratio actually needed.

  • Divide every term by their greatest common divisor, 6: 3:4

Ratios worth a try

1.5 : 2 is 3 : 4, not 1.5 : 2. A ratio with decimals has to be scaled to whole numbers before a common divisor means anything. Calculators that run the GCD straight on the decimals hand back the input unchanged and look like they worked. The same goes at the other end of the scale: above about 9 × 1015 a computer can no longer tell two whole numbers apart as decimals, and 1000000000000000002 : 1000000000000000004 quietly “simplifies” to 1 : 1. Everything here is big-integer arithmetic, so both answers come out right, and where a decimal readout had to be cut short, the row it sits on says so.

Common questions

How do I simplify a ratio?
Divide every term by the greatest common divisor of all of them. For 18:24 the GCD is 6, giving 3:4. The tool shows the divisor it used and the scale factor to get back, so you can check the reduction rather than trust it. Ratios of three or more terms reduce the same way, so 12:18:30 becomes 2:3:5.
What about ratios with decimals?
They are scaled to integers first. 1.5:2 is multiplied by 10 to give 15:20, which reduces to 3:4. This matters because a greatest common divisor is only defined for integers: a calculator that runs GCD directly on 1.5 and 2 returns the input unchanged and looks like it worked, which is the most common wrong answer in this category.
How do I solve a proportion?
Enter three known terms and mark the fourth unknown, as in 3:4 = 9:x. The tool cross-multiplies to get x = 4 × 9 ÷ 3 = 12, and shows that arithmetic. Where the answer is not a whole number it is given as an exact fraction as well as a decimal, since rounding a proportion early is how mixing and scaling errors start.
Can I use / or the word 'to' instead of a colon?
Yes. 16:9, 16/9 and "16 to 9" are all read the same way, and spacing does not matter. That means you can paste a ratio in whatever form you already have it rather than reformatting it first.
What does the percentage split mean?
Each term expressed as a share of the whole. For 3:4 that is 42.86% and 57.14%, which is the form you want when the ratio describes how something is divided rather than how two quantities compare. The decimal reading, 0.75, is the first term divided by the second, which is what you want when comparing.
Is 0:5 a valid ratio?
Yes, and it reduces to 0:1. A ratio with a zero term is meaningful as long as they are not all zero. An all-zero ratio has no defined reduction, since every number divides zero, and the tool says that rather than returning 0:0 or dividing by zero.

Exact. Every term is parsed into a BigInt fraction and reduced with integer arithmetic, so simplification, the scale factor and the solved proportion are correct at any size, including values past 2^53, where a floating-point greatest common divisor is silently wrong. Only the decimal and percentage readouts are rounded, and each one that was cut short is marked.