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.
A common mixing mistake
A 2:3 ratio of two liquids does not mean 2 parts of one to a 3-litre total — it means 2 parts to 3 parts, 5 parts total. To mix 10 litres at 2:3, divide 10 by 5 parts (2 litres per part), so you need 4 litres and 6 litres, not simply 4 and 6 of something else.