What Percentage Is X of Y? Formula and 12 Worked Examples

To find what percentage X is of Y, divide X by Y and multiply the result by 100. For example, 18 out of 24 is 18 divided by 24, which is 0.75, times 100, which equals 75%. That single rule covers test scores, discounts, tips, survey results, and almost every other "what percentage" question you will meet.

The formula never changes, but it helps to see it applied across different situations so the wording stops tripping you up. Below is the rule in plain terms, followed by 12 one line examples grouped by the kind of problem they solve. If you just want a quick answer for your own numbers, the percentage calculator on Quialo does the division and multiplication for you.

The Formula

percentage = (X / Y) * 100

Here X is the part (the smaller "of which" quantity) and Y is the whole (the total you are measuring against). Read the question carefully: "what percentage is X of Y" always means X is the part and Y is the whole. So "what percentage is 30 of 120" is (30 / 120) times 100, which is 25%.

Two quick checks keep you honest. First, if X is smaller than Y, the answer is under 100%. Second, if X equals Y, the answer is exactly 100%. If you ever get a result above 100% for a part of a whole, you have probably swapped X and Y.

12 Worked Examples

Test scores and grades

1. 18 out of 24 on a quiz: (18 / 24) times 100 equals 75%.
2. 42 out of 50 on an exam: (42 / 50) times 100 equals 84%.
3. 7 correct out of 8 questions: (7 / 8) times 100 equals 87.5%.

Discounts and savings

4. Saving 15 on a 60 item: (15 / 60) times 100 equals 25% off.
5. A 200 jacket marked down by 50: (50 / 200) times 100 equals 25% off.
6. Paying 90 on a 120 original price means you saved 30, so (30 / 120) times 100 equals 25% off.

Tips and gratuity

7. A 12 tip on an 80 bill: (12 / 80) times 100 equals 15%.
8. A 9 tip on a 45 meal: (9 / 45) times 100 equals 20%.
9. A 5 tip on a 50 total: (5 / 50) times 100 equals 10%.

Statistics and proportions

10. 36 of 200 survey respondents said yes: (36 / 200) times 100 equals 18%.
11. 480 of 600 seats filled: (480 / 600) times 100 equals 80%.
12. 3 defective parts out of 250: (3 / 250) times 100 equals 1.2%.

How to Sanity Check Your Answer

A fast way to confirm a result is to work backward. If you calculated that 42 of 50 is 84%, take 84% of 50 (that is 0.84 times 50) and you should land back on 42. When the two sides match, your percentage is right. This reverse check catches the most common error, which is dividing the whole by the part instead of the part by the whole.

It also helps to estimate before you compute. For 18 of 24, you know 18 is three quarters of 24, and three quarters is 75%, so a final answer near 75% looks correct. An estimate that is far from your calculated figure is a signal to recheck which number is X and which is Y.

A Related Question: Percentage Change

"What percentage is X of Y" measures a part against a whole. A different but easily confused question is "by what percentage did a value change," which compares a new figure to an old one. If your prices went from 80 to 100, that is a percentage change, not a part of a whole. For those problems, use the percentage change calculator, which divides the difference by the original value and multiplies by 100.

FAQ

What is the formula for what percentage X is of Y?

Divide X by Y, then multiply by 100. In symbols, percentage equals (X divided by Y) times 100. X is the part and Y is the whole.

What percentage is 30 of 120?

(30 / 120) times 100 equals 25%. Thirty is one quarter of one hundred and twenty, and one quarter is 25%.

How do I avoid mixing up X and Y?

Read the phrase "X of Y" literally: X is the part you are measuring, Y is the total. Dividing the larger number by the smaller one gives a figure above 100%, which is a clear sign the two were swapped.

Is "what percentage is X of Y" the same as percentage change?

No. This question compares a part to a whole. Percentage change compares a new value to an old one and can be positive or negative. They use different formulas, so pick the one that matches your situation.