Percent to Fraction Calculator

The math behind the conversion

Any percent is already a fraction out of 100 by definition — "37.5%" literally means 37.5 out of 100. The work is in clearing the decimal and reducing to lowest terms, which this tool does with the Euclidean algorithm (repeatedly dividing and taking remainders until the remainder hits zero) rather than trial division, so it stays fast even on fractions with large denominators.

Worked example: a decimal percentage

Enter 37.5. The digits after the decimal point tell the calculator how far to scale: "5" is one digit long, so it multiplies both the percent and 100 by 10, turning 37.5/100 into 375/1000. The Euclidean algorithm finds gcd(375, 1000) = 125 (375 = 3 × 125, and 1000 = 8 × 125). Dividing both by 125 gives 3/8. So 37.5% = 3/8 — you can check this by dividing 3 ÷ 8 = 0.375.

Why the decimal-scaling step matters

Without first clearing the decimal, a straight "percent/100" fraction like 37.5/100 has a non-integer numerator, which breaks the GCD algorithm — GCD is only defined for integers. Scaling both the numerator and denominator by the same power of 10 preserves the fraction's value while making both parts whole numbers, which is why the number of decimal places in your input determines the scaling factor (10 for one decimal place, 100 for two, and so on).

Where this is used

Converting a percent to a fraction shows up in probability problems (a 25% chance is more useful as 1/4 when computing combined odds), in recipe scaling, and in basic algebra courses that require expressing percentages, decimals, and fractions as three equivalent representations of the same number.