Math · Ratio

Ratio Calculator

Simplify a ratio to lowest terms, or solve a proportion for a missing value — free and private, with no sign-in.

Ratio Calculator

Choose what to do, leave exactly one field blank when solving a proportion, then select Calculate.

What do you want to do?

First term (a)

Second term (b)

Third term (c)

Fourth term (d)

How these calculations work

Simplifying a:b divides both terms by their greatest common divisor, the same way a fraction is reduced to lowest terms. Solving a:b = c:d works for any one missing term — leave exactly one of the four fields blank and the others are used to find it, via the cross-multiplication rule a × d = b × c. Scaling a:b by a factor n gives (a × n):(b × n) — the same ratio, just written with larger or smaller numbers.

Examples

4:8 simplifies to 1:2. 10:15 simplifies to 2:3. In 1:2 = 5:d, d = 10. In a:2 = 5:10, a = 1. 2:3 scaled by 4 is 8:12.

About these calculations

These are standard ratio and proportion rules from elementary mathematics — no external source citation is needed for them.

Related tools

More calculators are on the way — browse everything planned on the Home page.

Frequently asked questions

Can the terms be negative or zero?

When simplifying, both terms must be whole numbers and can't both be zero at once (one of them being zero, like 0:5, is fine). When solving a proportion, any one term can be blank, and zero is allowed unless it is the divisor for the missing term being solved. Scaling accepts any real multiplier, including zero and negative numbers.

Why does the calculator say my input is invalid?

A required field is empty or not a number. When simplifying, both terms must also be whole numbers, not decimals.