Ratio Calculator

Simplify a ratio to its lowest terms, or solve a proportion for a missing value — with every reduction and cross-multiplication step shown.

Simplify a Ratio

Enter two numbers to reduce a:b to lowest terms.

Simplified ratio —

Solve for x

Enter the three known numbers in a:b = c:x to solve the proportion for x.

x — a:b = c:x

How to Simplify a Ratio

Enter two numbers to see the simplified ratio and the reduction working, or solve a proportion for a missing value.

1

Enter your two numbers

Type the two sides of the ratio, like 8 and 12, into the A and B fields.

2

The calculator finds the largest shared divisor

It finds the largest whole number that divides both numbers evenly and divides each side by it, reducing the ratio to the smallest whole-number pair that means the same thing.

3

Read the result, or solve for x

The simplified ratio appears at the top with the working below it. Need to scale a ratio up or down instead? Use the "Solve for x" card, or try the Proportion Calculator for more proportion problems.

Frequently Asked Questions

What is a ratio and how do you simplify one?
A ratio compares two quantities, written a:b, showing how many units of one thing there are for every unit of another. To simplify a ratio to lowest terms, divide both numbers by the largest whole number that divides them evenly: the ratio 8:12 shares a largest common divisor of 4, so dividing both sides gives 2:3, the smallest whole-number pair that expresses the same relationship. This calculator finds that shared divisor automatically and shows each division step.
How do you solve a proportion for a missing number?
A proportion sets two ratios equal, a:b = c:d, and solving for a missing term uses cross-multiplication: a × d = b × c. If you know a, b, and c, the missing d equals (b × c) / a. For example, in 1:2 = 3:x, x = (2 × 3) / 1 = 6. Enter the three known numbers in the "solve for x" fields and the calculator fills in the fourth.
What is the difference between a ratio and a proportion?
A ratio is a single comparison between two quantities, like 2:3, while a proportion is a statement that two ratios are equal, like 2:3 = 4:6. Ratios describe one relationship; proportions let you scale that relationship up or down to find an equivalent one, which is how this calculator's "solve for x" tool finds a missing value that keeps the same ratio.
Can a ratio calculator handle negative or decimal numbers?
This calculator works with whole numbers for simplifying a ratio (decimals are truncated) and rejects zero on the side that would cause a division by zero, since a ratio or proportion with a zero term is undefined. For the proportion solver, any non-zero value for the first term (a) is accepted, including negatives, since the cross-multiplication formula d = (b × c) / a still holds.