Fraction To Percent Calculator

What this calculator does

So, you have a fraction like 3/4 and you want it as a percentage, 75%. This tool divides the fraction out and multiplies by 100, giving the percent to two decimal places.

There are two boxes, a numerator and a denominator. Type the fraction and read off the percentage.

How to use it

1. Type the numerator, the top number.
2. Type the denominator, the bottom number.
3. Press Calculate.

The denominator cannot be zero. Otherwise any fraction, proper or top-heavy, will convert.

Rescaling a fraction so the bottom is 100

A percentage is just a fraction with its denominator fixed at 100. So turning 3/4 into a percent is really asking: how many hundredths is 3/4? The answer is 75 hundredths, which we write as 75%. Every fraction has such a per-hundred version, and finding it is the whole task. That is why the same fraction can wear three outfits: 3/4 as a fraction, 0.75 as a decimal, and 75% as a percentage, all the same amount.

The method it uses

Divide the numerator by the denominator to get the fraction's plain value, then multiply by 100 and add the percent sign. For 3/4, dividing gives 0.75, and multiplying by 100 gives 75%. For 1/5, dividing gives 0.2, and 0.2 times 100 is 20%. The tool rounds to two decimal places, so a fraction like 1/3, whose value never ends, comes out as 33.33%.

A worked example, step by step

Take 5/8.

• Divide top by bottom: 5 ÷ 8 = 0.625.
• Multiply by 100: 0.625 × 100 = 62.5.
• So 5/8 is 62.50%.

The same two steps turn 7/10 into 70% and 9/4 into 225%.

Why bother turning it into a percent

Percentages exist because they make different fractions easy to compare at a glance. Is 5/8 bigger than 3/5? Hard to say as fractions. As 62.5% against 60%, the answer is obvious. Putting everything on the same per-hundred scale is exactly why merchants started quoting rates this way centuries ago, and why we still read interest, discounts, and results as percentages today. The fraction carries the exact value; the percent makes it quick to read.

The reverse trip: percent to fraction

This tool goes from a fraction to a percent. To go back, you write the percent over 100 and reduce, which the percent to fraction calculator does. Fraction, decimal, and percent are three ways of writing the same value, so each conversion is a move between two of those forms.

Questions people ask

How does it turn a fraction into a percent?

It divides the numerator by the denominator, then multiplies by 100. That gives the number of hundredths, which is the percentage.

How many decimal places does it show?

Two. A fraction with an endless value, such as 1/3, is rounded and shown as 33.33%.

Can the percent be more than 100?

Yes. A top-heavy fraction like 9/4 is more than a whole, so it converts to 225%.

Why multiply by 100?

Because a percent is a count of hundredths. Multiplying the fraction's value by 100 expresses it out of 100, which is what percent means.

How do I turn a percent back into a fraction?

Use the percent to fraction calculator, which writes the percent over 100 and reduces. It is the inverse of this tool.

References

On expressing a fraction per hundred. Multiplying a fraction's value by 100 and appending the sign is the standard route to a percentage, and the notation itself grew out of the Italian per cento, by the hundred.

1. Eric W. Weisstein, "Percent," from MathWorld, a Wolfram resource, which notes that a fraction is converted to a percentage by multiplying by 100 and appending the % sign.
2. "Percentage," Wikipedia, on percent from the Latin per centum and the % sign's origin in the Italian per cento.