Ratio Calculator

What It Does

This calculator reads a ratio three ways. In the simplify reading it divides the terms you enter by their greatest common divisor and shows both the reduced ratio and the divisor that produced it. In the solve reading it finds the missing term of a proportion, a : b = c : x, from the cross-product a × x = b × c. In the scale reading it multiplies every term by a factor and shows the scaled ratio beside its reduced form.

Real-World Usage

Use it to put a ratio into its simplest form before writing it down, to find the missing term when a proportion is stated in three parts — recipe quantities, map scales, screen aspect ratios, mix ratios, currency rates — or to scale a known ratio up or down to the quantities you actually have.

Local Context

A ratio and a proportion are country-neutral arithmetic: the terms are your own input and the result depends on them alone. The same reading applies whether you write decimals with a point or a comma, and every number on the page is formatted in its own language.

How do I simplify a ratio?

Divide every term by the greatest common divisor of the terms. For 8 : 12 the greatest common divisor is 4, so the ratio reduces to 2 : 3. The reduced ratio describes the same relationship between the quantities, written in the smallest whole numbers.

How do I solve a proportion?

Write the two equal ratios as a : b = c : x and cross-multiply: a × x = b × c. Rearranged for the missing term, x = b × c ÷ a. For 3 : 4 = 6 : x that gives x = 4 × 6 ÷ 3 = 8. The same rearrangement works for any of the four positions.

Can a proportion contain a zero?

A zero is fine as a term of the ratio, but not as the term the missing value is divided by, because that division is undefined. This calculator checks that divisor and refuses the calculation rather than returning infinity. In 3 : 4 = 6 : x the divisor is the first term, a, so a must not be 0.

What does scaling a ratio do?

Scaling multiplies every term by the same factor, so the ratio between the quantities does not change. 8 : 12 scaled by 3 is 24 : 36, which reduces back to 2 : 3. Use it to size a recipe, a mix or a drawing to the quantities you actually have.