Percent to Fraction Calculator

How to convert a percent to a fraction

A percent is a fraction whose denominator is 100, so the conversion is mostly a matter of writing the number over 100 and then cancelling common factors.

1. Write the percentage as the numerator and put 100 underneath: 35% becomes 35/100.
2. If the percentage has decimals, multiply the top and bottom by 10, 100, 1,000 and so on until the numerator is a whole number: 12.5/100 becomes 125/1,000.
3. Divide both numbers by their greatest common divisor to reach lowest terms: 35/100 ÷ 5 gives 7/20.
4. If the numerator ends up larger than the denominator (any percent above 100%), you can leave it as an improper fraction or split it into a whole number and a proper fraction.

p% = p ÷ 100Then reduce by dividing the numerator and denominator by their greatest common divisor.

The greatest common divisor is easiest to find with the GCD calculator or by trial division, and the simplify fractions calculator will reduce any fraction you end up with.

Worked examples

35% as a fraction. 35/100 shares the factor 5, and 35 ÷ 5 = 7 while 100 ÷ 5 = 20, so 35% = 7/20.

12.5% as a fraction. Shift the decimal point three places to clear it: 12.5/100 = 125/1,000. Both numbers divide by 125, giving 1/8. That matches the decimal check, because 1 ÷ 8 = 0.125.

0.4% as a fraction. Under one percent the fraction is very small. 0.4/100 = 4/1,000 = 1/250, which is 0.004 as a decimal.

225% as a fraction. 225/100 reduces by 25 to 9/4. As a mixed number that is 2 1/4, since 9 = 2 × 4 + 1. The result is above 1 because 225% is more than the whole.

6.25% as a fraction. Multiply by 100 to remove the decimals: 6.25/100 = 625/10,000. Dividing both by 625 gives 1/16.

How this calculator chooses its fraction

The calculator does not simply write your digits over a power of ten. It expands the value as a continued fraction and stops at the first fraction that lands within one part per million of your number. That keeps the answer short and readable: 66.66667% comes back as 2/3 instead of 6,666,667/10,000,000.

The side effect is that a rounded repeating decimal needs enough digits to be recognised. Entering 33.33333 returns 1/3, and 16.66667 returns 1/6. A shorter entry such as 33.3333 does not quite clear the threshold and returns the long fraction 333332/999997 instead. If you expect a simple answer such as a third or a sixth, type the repeating digits out to seven or more places.

Results above 100% are shown as mixed numbers, for example 150% gives 1 1/2. Negative inputs keep their sign, and 0% returns 0.

Percent to fraction conversion table

These are the percentages that come up most often, already reduced to lowest terms.

Thirds are the classic exception, because they cannot be written exactly with a finite decimal. 33 1/3% is exactly 1/3 and 66 2/3% is exactly 2/3, but their decimal forms repeat forever.

Common mistakes

• Forgetting to reduce. 50/100 is correct but incomplete; the lowest-terms form is 1/2.
• Dividing by 10 instead of 100. Percent always means per hundred, so 5% is 5/100 = 1/20, not 5/10.
• Misplacing the decimal point in small percents. 0.5% is 1/200, not 1/2. Half a percent is a tiny share.
• Reading a mixed number as a product. In 2 1/4 the whole number and the fraction are added, so it equals 2 + 1/4 = 9/4.

To go the other way, use the fraction to percent calculator. For a percent written as a plain decimal, the percent to decimal calculator shows the intermediate step, and the decimal to fraction calculator handles values that are already decimals. For other percent questions, such as change or percentage of a total, try the percentage calculator.