What is a Percentage to Fraction Calculator?
This tool converts any percentage into its equivalent fraction, fully simplified to lowest terms. A percentage literally means "per hundred," so 45% is just 45 out of 100. This calculator handles that conversion for you, reduces the fraction using the greatest common divisor (GCD), and also gives you the mixed-number form and the decimal value. It works with whole-number percentages like 25% as well as decimals like 12.5%.
How to use it
Enter the percentage you want to convert in the input box and submit. You will instantly see the simplified fraction (numerator over denominator), the equivalent mixed number when the value is greater than 100%, and the decimal equivalent. No need to do any manual reduction.
The formula explained
To convert a percent to a fraction, write the percentage over 100: \(p / 100\). If the percentage has decimal places, multiply both numerator and denominator by a power of ten to clear them — for example 12.5% becomes \(125/1000\). Then divide both parts by their greatest common divisor to simplify. The GCD of 125 and 1000 is 125, so \(125/1000\) reduces to \(1/8\).
$$\text{Fraction} = \frac{\text{Percentage}}{100} \;\xrightarrow{\;\div\gcd\;}\; \frac{a}{b}$$
Worked example
Convert 75% to a fraction. Start with \(75/100\). The GCD of 75 and 100 is 25. Dividing both gives \(3/4\). Since 75% is less than 100%, the whole part is 0 and the fraction stays \(3/4\). The decimal value is 0.75.
$$\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} = 0.75$$
FAQ
How do I convert a decimal percentage like 33.33%? The calculator multiplies by enough powers of ten to remove the decimal, then reduces. Repeating decimals are approximated to the digits you type.
What is a mixed number? For percentages over 100%, the fraction is improper (numerator larger than denominator). A mixed number expresses this as a whole number plus a proper fraction, e.g. \(150\% = 3/2 = 1\tfrac{1}{2}\).
Can I convert back from a fraction to a percentage? Yes — divide the numerator by the denominator and multiply by 100. For \(3/4\) that is \(0.75 \times 100 = 75\%\).
