Pick the question you are stuck on, type in the two numbers and get the answer with every step shown. It handles the four things students get asked most: a percent of a number, what percent one number is of another, a reverse percentage, and a percent of a percent.
Pick a question and enter the numbers
Everything is worked out in your browser. Nothing you type is sent anywhere.
Your answer
Your answer shows up here once you fill in both numbers.
What to enter
- A percent of a number
- Enter the percent and the number. The page shows the answer and the steps. Use it for discounts, tax and shares of a total.
- What percent is one number of another
- Enter the part first and the whole second. Use it to turn 18 out of 24 into a percent.
- Reverse percentage
- Enter the number you have and the percent it represents. The page works back to the original. It is the one that trips people up in exams.
- A percent of a percent
- Enter two percents. It is useful when one share is taken from another, like the pass rate of a group that sat the test.
Worked examples
A percent of a number
What is 15% of 80? A made-up example: a 80 jacket is 15% off, and you want to know how much comes off.
- Turn the percent into a decimal: 15 ÷ 100 = 0.15.
- Multiply by the number: 0.15 × 80 = 12.
So 12 comes off, and the jacket costs 68.
What percent is one number of another
You got 18 out of 24 on a quiz. What percent is that?
- Divide the first number by the second: 18 ÷ 24 = 0.75.
- Multiply by 100 to get a percent: 0.75 × 100 = 75%.
That is 75%.
A reverse percentage
After a 20% rise, a price is 60. What was it before? The new price is 120% of the original, so the original is the unknown.
- Turn the percent into a multiplier: 120 ÷ 100 = 1.2.
- Divide the number you have by the multiplier to get back to the original: 60 ÷ 1.2 = 50.
So the original price was 50. Check it: 50 plus 20% of 50 is 60.
A percent of a percent
Half of a class passed a test, and 20% of those who passed got a distinction. What share of the whole class got a distinction?
- Multiply the two percents: 20 × 50 = 1,000.
- Divide by 100: 1,000 ÷ 100 = 10%.
So 10% of the class got a distinction.
Reverse percentages and multipliers
A multiplier does an increase or a decrease in one step. Add the percent to 100, then divide by 100. Taking off a percent works the same way from 100 downward.
| What you want | Multiply by |
|---|---|
| Add 10% | 1.1 |
| Add 20% | 1.2 |
| Add 50% | 1.5 |
| Take off 10% | 0.9 |
| Take off 20% | 0.8 |
| Take off 50% | 0.5 |
Reverse percentages go the other way. If a price is 60 after a 20% increase, you divide by 1.2, and you do not take 20% off. That is why 60 ÷ 1.2 = 50.
Working out percentages without a calculator
Percentages are quick to do in your head if you build from 10%.
- Find 10% by moving the decimal point one place left: 10% of 80 is 8.
- Halve it to get 5%: 4.
- Add the pieces. 15% is 10% plus 5%, so 8 + 4 = 12.
A few more that help: 50% is half, 25% is half of a half, 1% is moving the decimal two places, and 20% is double 10%.
How each answer is calculated
- A percent of a number: turn the percent into a decimal by dividing by 100, then multiply by the number.
- What percent is X of Y: divide X by Y, then multiply by 100.
- Reverse percentage: turn the percent into a multiplier by dividing by 100, then divide the number you have by that multiplier.
- A percent of a percent: multiply the two percents and divide by 100.
Assumptions to keep in mind
- The page reads a number you type with commas, spaces and a percent sign, and ignores them.
- It works with any size of number, including percents over 100, because a share can be more than the whole.
- The big answer is shown to up to four decimal places and the working to six, with trailing zeros removed. Round to what your homework asks for.
- It does not know the context. A tax rate, a discount and an exam mark all use the same sums, so check that you put each number in the right box.
Mistakes that give the wrong answer
Putting the numbers in the wrong boxes
18 out of 24 is 75%, but 24 out of 18 is 133.33%. For "what percent", the part goes first and the whole goes second.
Using the new price as the original
If a price went up 20% to 60, the original is not 60 minus 20%. It is 60 ÷ 1.2 = 50. A reverse percentage needs a division.
Adding percents of different things
10% of one number and 10% of another cannot just be added to make 20% of anything, because they are percents of different amounts.
Forgetting to divide by 100
Writing 15% as 15 instead of 0.15 gives an answer 100 times too big. The page does the conversion and shows it.
Rounding too early
Round only at the end. Rounding a middle step can change the last digit of the answer.
Questions students ask
How do I calculate a percentage of a number?
Divide the percent by 100 to get a decimal, then multiply by the number. For 15% of 80, that is 0.15 × 80 = 12. The first mode above does it and shows the steps.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For 18 out of 24, it is 18 ÷ 24 × 100 = 75%. If you are turning a test score into a percent, the test grade calculator also gives the letter grade.
What is a reverse percentage?
It is when you know the result after a percentage change and want the original. If something costs 60 after a 20% rise, divide by the multiplier 1.2 to get the original of 50. The reverse mode does this.
How do I work out percentages without a calculator?
Find 10% by moving the decimal point one place, then build from there. 10% of 80 is 8, 5% is half of that (4), so 15% is 12. Halving gives 50%, halving again gives 25%, and 1% is moving the decimal two places.
Is it percent or per cent?
Both mean the same thing. Percent is the usual spelling in the US and Canada, and per cent is common in the UK and Australia. In exams, use the spelling your course uses. If you want the percent change between two numbers, the percentage change calculator does that.
