How to Calculate a Percentage (With Examples)

Here's the whole thing in one line: a percentage is just the part divided by the whole, times 100. If you got 18 out of 20 on a quiz, that's 18 / 20 = 0.9, and 0.9 x 100 = 90%. Once that single idea clicks, every percentage question is just a rearrangement of it. You can check any of these in a second with our free percentage calculator.

The one formula behind every percentage

The word percent literally means "per hundred," so a percentage tells you how many parts out of 100 you have. The formula is part / whole x 100. A percent like 20% is the same as the decimal 0.20 or the fraction 20/100. Moving between those three forms — percent, decimal, fraction — is most of the battle, and it's worth getting comfortable with.

Three question types you'll actually see

Almost every percentage problem is one of these three. The numbers change, but the moves don't.

1. What is X% of a number?

Convert the percent to a decimal and multiply. "What is 20% of 80?" becomes 0.20 x 80 = 16. So 20% of 80 is 16. That's it.

2. X is what percent of Y?

Divide the part by the whole, then multiply by 100. "30 is what percent of 120?" becomes 30 / 120 = 0.25, and 0.25 x 100 = 25%. So 30 is 25% of 120.

3. Reverse: X is Y% of what number?

Here you know the part and the percent but need the whole. Divide the part by the decimal form of the percent. "15 is 25% of what number?" becomes 15 / 0.25 = 60. So 15 is 25% of 60.

A quick mental-math trick

To find 10% of any number, just move the decimal one place left: 10% of 80 is 8. From there, 20% is double that (16), 5% is half (4), and 1% is 10% of the 10% (0.8). Stacking those pieces lets you estimate most percentages in your head before you ever reach for a calculator.

Check your work in seconds

Percentages run through grades, tips, discounts, and test scores, so they're worth nailing down. When you want to confirm an answer or see the steps laid out, use the percentage calculator, and if you need to track how a value grew or shrank over time, try the percentage change calculator. To talk through any problem out loud, COSMIQ's free voice tutor is free for every learner.

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