Three questions, one idea
A percentage is a number out of 100. "20%" means 20 for every 100, which is the same as the decimal 0.20 or the fraction 1/5. Almost every percentage problem is one of three questions about the same relationship between a part, a whole and a percentage. If you know any two, you can find the third.
| You know | You want | Formula | Example |
|---|---|---|---|
| percentage and whole | part | whole × p ÷ 100 | 20% of 150 = 30 |
| part and whole | percentage | part ÷ whole × 100 | 30 of 150 = 20% |
| part and percentage | whole | part ÷ p × 100 | 30 is 20% of 150 |
Worked examples
Tip on a restaurant bill
The bill is $64 and you want to leave 18%. That is 0.18 × 64 = $11.52. A quick check in your head: 10% of $64 is $6.40, so 20% is $12.80, and 18% should land a little under that.
Score on a test
You answered 42 of 48 questions correctly. 42 ÷ 48 = 0.875, and 0.875 × 100 = 87.5%.
Working back from a deposit
A landlord asks for a $450 deposit, which they say is 25% of the first month's rent. The full rent is 450 ÷ 0.25 = $1,800.
Shortcuts for doing it in your head
- 10%: move the decimal point one place left. 10% of 340 is 34. From there, 5% is half of that (17) and 20% is double (68).
- 1%: move the decimal two places. 1% of 2,500 is 25, so 3% is 75.
- Swap the numbers: 4% of 75 is awkward, but 75% of 4 is easy: 3. They are always equal.
- Halves and quarters: 50% is half, 25% is a quarter, 75% is three quarters, 12.5% is an eighth.
Mistakes to watch for
Adding percentages of different wholes. A 20% discount followed by another 10% off is not 30% off. The second discount applies to the already reduced price, so the total saving is 28%. Our percentage increase and decrease calculator handles repeated changes.
Mixing up which number is the whole. "What percent of 150 is 30?" and "What percent of 30 is 150?" give 20% and 500%. The whole is the number that comes after "of".
Calling a change in a rate a percent change. If unemployment goes from 5% to 6%, it rose by one percentage point, but by 20% in relative terms. Both are correct; say which one you mean.
Questions people ask
How do I calculate a percentage of a number?
Turn the percentage into a decimal by dividing it by 100, then multiply. 15% of 80 is 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 18 out of 24 is 18 ÷ 24 × 100 = 75%.
Is 8% of 50 the same as 50% of 8?
Yes. Multiplication works in either order, so x% of y always equals y% of x. Both are 4. Use whichever is easier to do in your head.
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages by subtraction: a rate moving from 4% to 6% rose by 2 percentage points. In percent terms that same move is a 50% increase. The percentage difference calculator shows both.
Can a percentage be more than 100%?
Yes. 150% of 40 is 60, and 60 is 150% of 40. Percentages above 100 simply mean more than the whole you started with.