ToolCalcu

Ratio Calculator

Reduce a ratio to its simplest form, see it as a fraction and as percentages, or find the missing number in a proportion.

Your ratio

Result

Please correct the highlighted fields.
Simplified ratio
2 : 3
As a fraction
2 / 3
A ÷ B
0.666667
Share of A
40%
Share of B
60%

How ratios are simplified and solved

A ratio A : B keeps its meaning when both terms are divided by the same number. Dividing by their greatest common divisor gives the simplest whole-number form. Decimals are first scaled to whole numbers.

A proportion says two ratios are equal: A : B = C : D. Because the ratios are equal, D is B multiplied by the same factor that takes A to C.

Formulas used

Simplified = (A ÷ gcd, B ÷ gcd)
Share of A = A ÷ (A + B)
D = B × C ÷ A

Worked example

Simplify the ratio 24 : 36:

  1. Greatest common divisor of 24 and 36: 12
  2. Divide both terms: 24 ÷ 12 = 2 and 36 ÷ 12 = 3

24 : 36 simplifies to 2 : 3.

Assumptions and limits

  • Values must be zero or positive; both cannot be zero.
  • Values up to one billion are accepted.
  • When a term is 0 the ratio reduces to 0 : 1 or 1 : 0.

Common questions

How do I know if two ratios are equal?

Simplify both. If they reduce to the same terms they are equal; for example 4:6 and 10:15 both reduce to 2:3. You can also compare A ÷ B for each one, because equal ratios give the same result.

Can a ratio contain zero?

A term of zero is allowed in a simple ratio such as 0:5, but A cannot be zero when you solve a proportion, because the scale factor would need a division by zero. A ratio in which both terms are zero has no meaning.

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