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Ratio Calculator

Find the missing value in a proportion A : B = C : D, or reduce a ratio such as 12 : 18 : 24 to its simplest form, with the cross-multiplication shown.

Formulas last reviewed: September 2026

Disclaimer: Results are calculated with standard formulas and are meant for learning and quick checks. Please double-check important work, especially anything used for exams, engineering, finance or safety.

Comparing quantities

A ratio compares two or more quantities, such as 3 : 4. Two ratios that are equal form a proportion, written A : B = C : D. Ratios are used in recipes, maps, mixing paints and concrete, currency conversion and scaling drawings.

This calculator solves a proportion when one value is missing and simplifies any ratio to its lowest whole-number terms.

How it is calculated

A : B = C : D → A × D = B × C
Missing D = (B × C) ÷ A

Worked example

3 : 4 = 9 : ?

Cross-multiply
3 × D = 4 × 9
Solve
D = 36 ÷ 3
Answer
12

Simplifying 12 : 18 : 24 gives 2 : 3 : 4 (divide each part by 6).

Everyday uses

  • Scale a recipe: if 2 cups of rice serve 3, how many cups serve 12?
  • Map scales such as 1 : 50,000 turn a distance on paper into a distance on the ground.
  • Share an amount in a ratio by adding the parts and dividing the total.

Frequently asked questions

What is the difference between a ratio and a fraction?

A ratio compares parts to each other (3 boys to 4 girls), while a fraction compares a part to the whole (3 out of 7 are boys).

How do I simplify a ratio?

Divide every part by their greatest common factor. 12 : 18 has a GCF of 6, so it simplifies to 2 : 3.

How do I split an amount in a given ratio?

Add the parts, divide the total by that sum to get the value of one part, then multiply by each ratio number.

Can I leave more than one box empty?

No. A proportion needs exactly one unknown, so leave just one of the four boxes blank.