Ratio Calculator

Simplify ratios to lowest terms or solve a proportion for the missing value.

Simplified ratio

Simplifying works best with whole numbers. Proportions need a non-zero first term.

Ratios and proportions

A ratio compares two quantities — parts of a mix, a map scale, ingredients in a recipe. Simplifying expresses it in the smallest whole numbers that keep the same relationship, which makes ratios easy to compare and scale.

A : B = C : D ⟹ A × D = B × C

A proportion says two ratios are equal. That cross-multiplication rule lets you find a missing term: if three of the four values are known, the fourth is fixed. It is the everyday maths behind scaling drawings, converting units and adjusting recipes.

Worked example

The ratio 4 : 6 simplifies to 2 : 3. As a proportion, 2 : 3 = 10 : 15, because cross-multiplying gives 3 × 10 ÷ 2 = 15.

Why ratios are so handy

Ratios travel well. A 2 : 3 mix is the same whether you are working in millilitres or gallons, so a recipe or formula scales cleanly to any size. Reading a ratio as "1 : n" or as a decimal often makes the practical step — how much of each — obvious.

Things to watch

  • Keep the order. 2 : 3 and 3 : 2 are different relationships.
  • Same units. Compare like with like before forming a ratio.
  • Cross-multiply to solve. Three known terms always fix the fourth.

Frequently asked questions

How is a ratio simplified?
Divide both sides by their greatest common divisor. For 4 : 6 that divisor is 2, giving 2 : 3 — the smallest whole-number form of the same relationship.
How does solving a proportion work?
A proportion sets two ratios equal: A : B = C : D. Cross-multiplying gives A × D = B × C, so the missing term D is B × C ÷ A.
What does "1 : n" tell me?
It rescales the ratio so the first part is one, making the relationship easy to read — for example a map scale or a mixing ratio expressed per single unit.
Can ratios use decimals?
They can, though simplifying works best with whole numbers. For mixing and scaling, the decimal and "1 : n" forms are often the most practical.