Percent to Fraction Calculator

What is a percent to fraction calculator?

A percent to fraction calculator turns a percentage into an equivalent fraction expressed in its lowest terms. A percent is simply a number out of one hundred, so every percentage already hides a fraction inside it. This tool makes that fraction explicit: it takes a value such as 50% or 12.5% and returns a clean numerator and denominator, splitting off any whole-number part when the percentage is 100% or more.

Percentages are convenient for comparison and reporting, but fractions are often easier to work with in exact arithmetic, recipes, measurements, probability, and classroom problems. Converting between the two forms lets you choose whichever representation fits the task.

How does it work?

The conversion rests on the definition of a percent. The word “percent” means “per hundred”, so a value $p\%$ is the same as dividing $p$ by 100:

$p\% = \frac{p}{100}$

The calculator then reduces that fraction to lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD):

$\frac{p}{100} = \frac{p \div \gcd(p,\,100)}{100 \div \gcd(p,\,100)}$

If the percentage is not a whole number, it is first scaled so both parts are integers before reducing. When the result is greater than or equal to 100%, the calculator pulls out the whole-number part and leaves the remaining proper fraction beside it, giving a mixed number.

Worked examples

• 50%: $\frac{50}{100} = \frac{50 \div 50}{100 \div 50} = \frac{1}{2}$
• 25%: $\frac{25}{100} = \frac{1}{4}$
• 75%: $\frac{75}{100} = \frac{3}{4}$
• 12.5%: scaling by 10 gives $\frac{125}{1000} = \frac{1}{8}$
• 150%: $\frac{150}{100} = \frac{3}{2} = 1\frac{1}{2}$, shown as a whole number 1 next to $\frac{1}{2}$

Practical notes

Whole-number percentages always reduce against a denominator of 100, so the largest possible starting denominator is 100 before simplification. Decimal percentages like 12.5% or 33.33% are handled by scaling first, which is why a value such as 12.5% lands neatly on $\frac{1}{8}$.

Repeating decimals such as 33.33% are treated as the exact figure you enter, not as the true repeating value $\frac{1}{3}$. If you need the exact thirds, enter enough decimal places or convert from the underlying decimal directly. To go the other way, use the fraction to percent calculator at https://www.mega-calculator.com/math/fraction-to-percent/, and to obtain the plain decimal form instead of a fraction, use the percent to decimal calculator at https://www.mega-calculator.com/math/percent-to-decimal/. If you already have a decimal value rather than a percent, the decimal to fraction calculator at https://www.mega-calculator.com/math/decimal-to-fraction/ produces the same reduced result.