Ratio Calculator

What is a ratio calculator?

A ratio calculator works with comparisons of two quantities written in the form a : b. It does three jobs students need every day: it simplifies a ratio to its lowest terms, it solves a proportion when one of four terms is missing, and it checks whether two ratios are equivalent. Ratios appear in recipes, maps and scale drawings, mixing paint or concrete, currency conversion, gear ratios and probability, so being able to handle them confidently is a core skill. Rather than just printing an answer, this tool shows the full method — finding the greatest common divisor, dividing both terms, or cross-multiplying — so you learn how the result is reached.

How to use it

Pick a mode. In Simplify, enter the two terms of your ratio and read the reduced form plus its decimal value. In Solve proportion, type three of the four terms of a : b = c : d, tap the letter of the term you do not know, and the calculator solves for x by cross-multiplication. In Compare, enter both ratios and the tool tells you whether they are equivalent and shows the cross products. Decimals are allowed everywhere; for simplifying they are scaled to whole numbers first.

The formulas

To simplify, divide both terms by their greatest common divisor g: a : b = (a ÷ g) : (b ÷ g). To solve a proportion, cross-multiply: a : b = c : d means a × d = b × c, so a missing term is found by rearranging, for example x = (b × c) ÷ a. Two ratios are equivalent exactly when their cross products are equal, a × d = b × c.

Reading the result

A simplified ratio is the same comparison written with the smallest whole numbers, which makes it easier to picture and compare. The decimal value tells you how many of the first quantity there are per single unit of the second. When solving a proportion, x is the value that keeps both sides in the same proportion. In Compare mode, equivalent means the two ratios describe the same relationship even if the numbers look different, like 2 : 3 and 6 : 9.

Frequently asked questions