CalcArcade.

Ratio Calculator

A ratio problem such as 2 : 3 = 4 : x has three known numbers and one unknown. Enter any three of the four boxes and leave one empty. The calculator works out the missing value.

Your numbers

Result

How we calculate it

Two ratios are equal when a ÷ b = c ÷ d, which gives a × d = b × c. Solving for the empty box: a = b × c ÷ d, b = a × d ÷ c, c = a × d ÷ b and d = b × c ÷ a.

For 2 : 3 = 4 : d, the missing value is d = 3 × 4 ÷ 2 = 6. The calculator also shows the ratio a ÷ b and, for whole numbers, the ratio in its simplest form.

Assumptions and limits

  • Leave exactly one box empty. The empty box is the one that gets solved.
  • The second number of a ratio cannot be zero, and the calculation cannot divide by zero.
  • Decimals and negative numbers are accepted.

Frequently asked questions

How do I solve a proportion?

Cross multiply: a × d = b × c. Then divide both sides by the number that sits next to the unknown. If a : b = c : x, then x = b × c ÷ a.

How do I scale a recipe with a ratio?

Write the amount you have to the amount you want as the first ratio and solve for the missing amount. If 2 cups serve 3 people, 4 cups serve 6 people.

How do I simplify a ratio?

Divide both numbers by their greatest common divisor. 6 : 9 is divided by 3 to give 2 : 3.

Related calculators

Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: a (first number of the first ratio) = 2; b (second number of the first ratio) = 3; c (first number of the second ratio) = 4.

  • Missing value 6
  • Ratio a ÷ b 0.6667
  • Simplified ratio 2 : 3

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.