Percent To Fraction Calculator

What this calculator does

So, you have a percentage like 50% and you want it as a fraction, 1/2. This tool takes the percent, turns it into a fraction over 100, and reduces that to lowest terms.

There is one box, for the percent. Type the number and it returns the fraction.

How to use it

1. Type the percent (just the number, without the % sign).
2. Press Calculate.

It takes zero and positive percentages, which covers the usual job of turning a rate like 35% into a fraction.

A percent is already a fraction over 100

The word percent comes from the Latin per centum, meaning by the hundred. So a percentage is not really a separate kind of number at all, it is a fraction whose denominator is always 100. 50% is 50/100. 7% is 7/100. 35% is 35/100. That is the starting fraction, and reducing it is all that is left to do.

The method it uses

Two moves. First, divide the percent by 100 to get its plain value: 50% becomes 0.5. Then write that as a fraction over the right power of 10 and reduce it by the greatest common divisor, which the tool finds with the Euclidean algorithm. For 50%, dividing by 100 gives 0.5, which is 5/10, and reducing by 5 gives 1/2. For 35%, that is 35/100, and the greatest common divisor of 35 and 100 is 5, giving 7/20.

A worked example, step by step

Take 24%.

• Over 100 that is 24/100.
• The greatest common divisor of 24 and 100 is 4.
• Divide both by 4: the answer is 6/25.

The same route takes 80% to 80/100, which reduces to 4/5.

What happens above 100 percent

A percentage can be more than 100, and this tool handles that honestly. 150% is 150/100, which reduces to 3/2. Rather than dress that up as the mixed number 1 1/2, the tool leaves it as the top-heavy fraction 3/2, the single-fraction form. If you would prefer to see it as a mixed number, the fraction to mixed number converter will make that swap. Either way, 150% and 3/2 are the same amount.

The reverse trip: fraction to percent

This tool goes from a percent to a fraction. To go the other way, you divide the fraction out and multiply by 100, which the fraction to percent calculator does. A fraction, a decimal, and a percent are three ways of writing the same value, so each conversion is just a step between two of them.

Questions people ask

Why divide by 100?

Because percent means by the hundred. A percentage is a fraction with 100 on the bottom, so dividing by 100 recovers its plain value before reducing.

Does it reduce the fraction?

Yes. After writing the percent over 100, it divides top and bottom by their greatest common divisor to reach lowest terms.

What about a percentage over 100?

It gives a top-heavy fraction, so 150% comes back as 3/2. To see that as a mixed number, use the fraction to mixed number converter.

What if my percent has a decimal, like 12.5%?

It still works: 12.5% is 0.125, which becomes 125/1000 and reduces to 1/8.

How do I turn a fraction back into a percent?

Use the fraction to percent calculator, which divides the fraction out and multiplies by 100. It is the inverse of this tool.

References

On percent as a hundredth and the reducing step. A percentage is a fraction over 100, so converting it means writing that fraction and putting it in lowest terms with Euclid's greatest common divisor.

1. Eric W. Weisstein, "Percent," from MathWorld, a Wolfram resource, on percentages as ratios expressed per hundred.
2. Euclid, Elements, Book VII, Proposition 2 (c. 300 BC), the Euclidean algorithm for the greatest common divisor, in David E. Joyce's online edition: Euclid's Elements, Book VII, Proposition 2.