Ratio and proportion calculator

Divide every term by the greatest common divisor of the terms. For 12 : 18 the GCD is 6, giving 2 : 3. Decimals and fractions are cleared first by multiplying every term by the same number: 1.5 : 2.5 × 2 = 3 : 5, and 1/2 : 3/4 : 5/6 × 12 = 6 : 9 : 10, which is already in simplest form because its GCD is 1.

Cross-multiply, then divide. In 3 : 4 = 9 : x the products of the diagonal terms are equal, so 3x = 4 × 9 = 36 and x = 12. The unknown can sit in any position: in x : 5 = 6 : 15, 15x = 5 × 6 = 30, so x = 2. If the term diagonally opposite x is 0, there is no single answer.

Add the ratio terms, divide the amount by that total to get one share, then multiply each term by the share. For 1,000 split 2 : 3 : 5 the terms add to 10, one share is 100, and the parts are 200, 300 and 500. The parts always add back to the amount; 100 split 1 : 2 gives 100/3 and 200/3, about 33.33 and 66.67.

A ratio compares parts with each other; a fraction compares a part with the whole. In a class of 12 girls and 18 boys the ratio of girls to boys is 12 : 18 = 2 : 3, but girls make up 12/30 = 2/5 of the class. A two-term ratio a : b becomes the fraction a/(a + b) of the whole.

Multiply or divide every term by the same factor. To make the first term of 2 : 3 equal 30, the factor is 30 ÷ 2 = 15, so the scaled ratio is 30 : 45. Scaling a recipe works the same way: a 2 : 3 mix made 15 times larger needs 30 and 45 units of the two ingredients, and the proportions stay 40% and 60%.

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 8 worked examples whose answers come from independent sources; for example, “Simplify 12 : 18” is checked against gcd(12, 18) = 6 (Python math.gcd).

Khan Academy — Ratios, rates and proportions; Wolfram MathWorld — Proportional.