Ratio calculator

A ratio compares two quantities, such as 2 parts cement to 3 parts sand, or a map scale of 1:50,000. Ratios answer two everyday questions: what is the simplest form of this ratio, and if I scale one side, what does the other side become? This calculator does both.

How to use it

1. To simplify, enter both parts of the ratio, for example 12 and 18.
2. To solve a proportion, enter three known values of a:b = c:x and get the missing value.
3. Copy the result.

Simplifying a ratio

Divide both parts by their greatest common divisor. For 12:18 the GCD is 6, so the ratio simplifies to 2:3. For decimals, first multiply both sides by a power of 10: 1.5:2.5 becomes 15:25, which simplifies to 3:5.

Solving a proportion

For a:b = c:x, cross-multiply: x = b × c / a.

• Recipe: a recipe uses 3 cups of flour for 2 cups of milk. For 7.5 cups of flour: x = 2 × 7.5 / 3 = 5 cups of milk.
• Map scale: at 1:25,000, 4 cm on the map is 4 × 25,000 = 100,000 cm, or 1 km.
• Image size: a 1920:1080 image scaled to 1280 wide needs a height of 1080 × 1280 / 1920 = 720.

Ratios with more than two parts

Mixes such as concrete 1:2:4 work the same way. To split 70 kg in the ratio 1:2:4, add the parts (7), find one part (10 kg) and multiply: 10, 20 and 40 kg.

Common mistakes

• Mixing units: convert both sides to the same unit before comparing.
• Confusing ratio with fraction: a 2:3 ratio means 2 out of 5 parts, not 2/3 of the total.