Simplify Ratio Calculator

How it is calculated

The tool reduces the ratio a : b with the Euclidean algorithm. First, if either number has decimals (up to 6 places are read), both are multiplied by the same power of 10 to become whole numbers, so 2.5 : 4 becomes 25 : 40. It then repeatedly replaces the pair (x, y) with (y, x mod y) until the remainder is zero; the last non-zero value is the greatest common divisor, g. The simplified ratio is (a ÷ g) : (b ÷ g). It also shows the decimal value a ÷ b to two places and the divisor g it used, which is the divisor on the scaled whole numbers. Both numbers must be above zero; zero, negative or empty entries and extremely large or tiny values give no result.

Common mistakes

• Believing that decimals are rounded first. They are not: 2.5 : 4 correctly gives 5:8, because the tool scales both sides to whole numbers. Only digits beyond the sixth decimal place are ignored.
• Swapping the two sides. 9:16 and 16:9 are different ratios, and the decimal shown is a ÷ b, so it changes from 1.78 to 0.56.
• Thinking a result such as 7:13 means an error. When the divisor shows 1, the two numbers share no common factor and the ratio is already in lowest terms.
• Entering a zero or negative side. The tool needs both numbers above zero and shows no result otherwise.
• Confusing the divisor with the scale. For 0.125 : 0.5 the tool shows a divisor of 125 because it works on 125 : 500, and the answer is 1:4.