Ratio Calculator

What is a ratio?

A ratio compares two quantities, showing how much of one there is for every amount of the other. We write it with a colon, like 3:2, which reads as "three to two." Ratios turn up constantly in cooking, mixing, maps, finance, and design, anywhere proportions matter.

To simplify a ratio you divide both sides by their greatest common divisor, the same way you reduce a fraction. That keeps the proportion identical while using the smallest whole numbers.

How to use this calculator

1. Enter the two numbers in the ratio, such as 12 and 18.
2. Click calculate to simplify the ratio to lowest terms.
3. Read the equivalent ratio in both colon form and fraction form if shown.
4. Use the result to compare quantities or scale the ratio up or down by the same factor.

The formula explained

To simplify a ratio, divide both parts by their greatest common divisor, or GCD. The formula turns \(a:b\) into \(\frac{a}{\gcd(a,b)} : \frac{b}{\gcd(a,b)}\).

• a = the first number in the ratio
• b = the second number in the ratio
• gcd(a,b) = the greatest common divisor of the two numbers

Step by step method

1. Find the greatest common divisor of the two numbers.
2. Divide each part of the ratio by that same divisor.
3. Write the simplified ratio in colon form.
4. If you need an equivalent ratio, multiply both parts by the same number.

Worked example

Problem. Simplify the ratio 12:18 and find an equivalent ratio with a total of 30 parts.

1. The greatest common divisor of 12 and 18 is 6, so divide both numbers by 6.
2. 12 \div 6 = 2 and 18 \div 6 = 3, so the simplified ratio is 2:3.
3. To make an equivalent ratio with 30 parts, multiply 2:3 by 6 to get 12:18, which already totals 30.

Tips and common mistakes

• Always divide both parts by the same number, never just one part.
• If the numbers have no common factor greater than 1, the ratio is already in simplest form.

Frequently asked questions