Ratio and Proportion Solver

How to use the ratio calculator

The tool has two parts that work independently.

Solve a proportion A : B = C : D

1. Fill in three of the four boxes A, B, C and D, and leave the unknown one empty (you can also type x or ?). The unknown can be in any position.
2. The answer appears as you type, as x = …; the Solve button does the same. The box that was solved is outlined.
3. The step-by-step panel shows the proportion, the cross-multiplication, how x is isolated and a check that both ratios are equal. Copy copies the value of x, Clear empties the four boxes.

Whole numbers, decimals (2.5) and fractions (1/2) are all accepted.

Simplify a ratio

1. Type the ratio in Ratio (terms separated by :), for example 12 : 18 : 24. Two or more terms are accepted, including decimals and fractions.
2. The simplest whole-number ratio is shown immediately (2 : 3 : 4), followed by the unit ratio (1 : 1.5 : 2). The steps show how decimals were cleared, the greatest common divisor and each term divided by it, plus the share of the total for each term.

How a proportion is solved

A proportion states that two ratios are equal: A : B = C : D, which also means A ÷ B = C ÷ D. Multiplying both sides by B × D gives the cross-multiplication rule:

A × D = B × C

The product of the outer terms (A and D) equals the product of the inner terms (B and C). To find the unknown, divide the product of the two terms on the other diagonal by its partner:

• D = B × C ÷ A
• C = A × D ÷ B
• B = A × D ÷ C
• A = B × C ÷ D

Example. A recipe uses 3 eggs for 4 people. How many eggs for 6 people? Write 3 : 4 = x : 6. Then 3 × 6 = 4 × x, so x = 18 ÷ 4 = 4.5 eggs.

This is the same method as the “rule of three” used for unit prices, recipe scaling, map scales, currency conversion and dosage calculations, as long as the two quantities are directly proportional.

How a ratio is simplified

A ratio keeps the same meaning when all its terms are multiplied or divided by the same nonzero number. To write it with the smallest whole numbers:

1. If any term is a decimal or a fraction, multiply every term by the lowest common denominator. For 1.5 : 2, multiply by 2 to get 3 : 4.
2. Divide every term by their greatest common divisor (GCD). For 12 : 18 : 24, the GCD is 6, which gives 2 : 3 : 4.

The unit ratio divides every term by the first one, so that the first term is 1. It is handy for comparisons: a screen of 16 : 9 is 1 : 0.5625, one of 4 : 3 is 1 : 0.75.