Percents are fractions with a fixed denominator of 100. Converting a percent to a fraction is a matter of writing that denominator down and then reducing the result to lowest terms. The only wrinkles are decimal percents, which need an extra step to clear the decimal point, and fractional percents like 66⅔%, which hide an exact fraction behind a mixed number. This calculator handles all of them and shows how each reduction was made.
How to use the percent to fraction calculator
- Type the percent. The % sign is optional, and inputs like
40,37.5%,0.8%,175%and66 2/3%all work. - The tape shows the simplified fraction, the decimal and, for values above 100%, the mixed number.
- Follow the steps to see the fraction over 100, the scaling used to remove decimals and the greatest common factor that reduced it.
How the conversion works
If p has decimal places, multiply the top and bottom by 10 for each decimal place first, so both are whole numbers. Then find the greatest common factor and divide it out. The GCF calculator shows several ways to find it if you want to check by hand.
Worked example: 37.5%
Over 100: 37.5% = 37.5/100
Clear the decimal (×10 top and bottom): 375/1,000
Greatest common factor: GCF(375, 1,000) = 125
Simplify: 375 ÷ 125 = 3 and 1,000 ÷ 125 = 8, so 37.5% = 3/8
Check by dividing: 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%.
Percent and fraction equivalents worth memorizing
| Percent | Fraction | Percent | Fraction |
|---|---|---|---|
| 5% | 1/20 | 37.5% | 3/8 |
| 10% | 1/10 | 40% | 2/5 |
| 12.5% | 1/8 | 60% | 3/5 |
| 16⅔% | 1/6 | 62.5% | 5/8 |
| 20% | 1/5 | 66⅔% | 2/3 |
| 25% | 1/4 | 75% | 3/4 |
| 33⅓% | 1/3 | 87.5% | 7/8 |
Knowing these makes estimating quick: a 37.5% share of 64 is three-eighths of 64, or 24.
Rounded percents and “nice” fractions
Percents you read in reports are often rounded. If a survey says 33.3% of people agreed, the exact fraction of what was printed is 333/1,000, but the real share was almost certainly one third. When the exact fraction has a large denominator, the calculator also suggests the nearest simple fraction (denominator 16 or less) so you can tell which one was probably intended. Use the exact result when you are converting a precise value, such as a tax rate set by law.
Percents over 100% and negative percents
A percent above 100 converts to an improper fraction. 175% is 7/4, or 1¾ — the quantity plus three quarters more. Negative percents, used for decreases and losses, convert the same way with a minus sign: −12.5% = −1/8.
Where this conversion helps
- Cooking and crafts: scaling a recipe by 62.5% is the same as using 5/8 of each ingredient, which is easier to measure with cups and spoons.
- Construction: a 12.5% slope is a rise of 1 for every 8 units of run.
- Probability: a 20% chance is a 1-in-5 chance, which is easier to picture.
- Test prep: standardized tests often expect fraction answers in lowest terms.
To reverse the process, use the fraction to percent calculator. If you need a decimal instead of a fraction, the percent to decimal calculator is the faster route.
Frequently asked questions
How do you convert a percent to a fraction?
Write the percent as a number over 100, then simplify. 40% = 40/100, and dividing the top and bottom by their greatest common factor, 20, gives 2/5.
How do I convert a percent with a decimal, like 37.5%?
Write it over 100 (37.5/100), then multiply the top and bottom by 10 to clear the decimal: 375/1,000. The greatest common factor is 125, so the fraction simplifies to 3/8.
What is 33 1/3% as a fraction?
33 1/3 = 100/3, and 100/3 ÷ 100 = 100/300 = 1/3. Writing it as 33.3% instead would give 333/1,000, which is close to but not exactly one third.
How do I write a percent over 100% as a fraction?
Use the same steps; you'll get an improper fraction. 175% = 175/100 = 7/4, which is the mixed number 1 3/4.
What fraction is 12.5%?
12.5% = 125/1,000 = 1/8. Eighths are common in measurements and appear as 12.5%, 25%, 37.5%, 50%, 62.5%, 75% and 87.5%.