Percent to Fraction Converter
This converter turns any percentage into its simplest fraction form and also shows the exact decimal equivalent and the greatest common divisor (GCD) used to reduce the fraction. Percentages and fractions are two ways of expressing the same idea: a portion of a whole. Being able to move between the two forms is useful in mathematics, cooking, finance, statistics and everyday problem solving. The conversion process starts by writing the percentage value over 100, creating an initial fraction. For whole number percentages this is straightforward; for decimal percentages such as 62.5%, the numerator contains a decimal so both the numerator and denominator must first be multiplied by the appropriate power of 10 to produce whole numbers (625 and 1000 in this case) before simplification. The resulting integer fraction is then reduced to lowest terms using the Euclidean algorithm to find the GCD, and both numerator and denominator are divided by it. The simplified fraction is shown as the main result, with the GCD and decimal as supporting figures. To use the converter, type any percentage into the input field, including decimals such as 12.5 or 66.67. The result updates immediately. You do not need to type the percent symbol. This tool is useful for students converting between fraction and percentage forms, teachers preparing worked examples, and anyone checking whether a percentage such as a discount or interest rate can be expressed as a simple fraction. Results are as precise as the number of decimal places in your input allows.
How it works
The calculator reads the percentage value and counts the number of decimal places in it. It multiplies the percentage by 10 raised to that count to produce a whole number, and multiplies 100 by the same factor for the denominator. This produces an equivalent integer fraction. The Euclidean algorithm then finds the GCD of the numerator and denominator, and both are divided by the GCD to give the lowest terms fraction. A GCD of 1 means the fraction was already in its simplest form after scaling.
Worked example
Convert 62.5% to a fraction. The decimal has one decimal place, so multiply both parts by 10: numerator = 625, denominator = 1000. The initial fraction is 625/1000. Find the GCD: GCD(625, 1000) = 125. Divide both by 125: numerator = 625 ÷ 125 = 5, denominator = 1000 ÷ 125 = 8. The simplified fraction is 5/8. As a decimal: 5 ÷ 8 = 0.625, which confirms the result matches the original percentage.
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