Ratio Simplifier

How it is calculated

The tool reduces a ratio a : b to its simplest whole-number form by dividing both terms by their greatest common divisor (GCD), found with the Euclidean algorithm: repeatedly replace the pair (x, y) with (y, x mod y) until the remainder is 0. Then simplified = (a / GCD) : (b / GCD).

It also shows the decimal value a / b, rounded to two places, which is useful for comparing ratios or finding a scale factor. Only positive whole numbers are accepted: decimals, zero and negative numbers give no result. If you have decimals, multiply both terms by 10, 100 or 1000 first so they become integers.

Common mistakes

• Entering decimals such as 1.5 : 2 directly; the tool only accepts whole numbers, so use 15 : 20 instead.
• Swapping the terms. 16:9 and 9:16 are different ratios, and the decimal changes from 1.78 to 0.56.
• Dividing only one term by the common factor, which changes the ratio instead of simplifying it.
• Thinking the decimal is a percentage; 1.78 means a is 1.78 times b, not 1.78%.