What is a percentage?
A percentage is a number expressed as a share of 100. 25% means 25 out of every 100, which is 0.25 as a decimal or 1/4 as a fraction. Percentages make it easy to compare parts of different-sized wholes, like a discount on two prices or growth in two budgets.
Most everyday percentage questions come down to one of the five rows above: finding a part, finding the whole, finding a rate, measuring a change, or applying a change.
Use the second row when you know a part and the percent it stands for, and need the whole. Type the number and the percent. If 30 is 15% of a number, that number is 30 ÷ 15 × 100 = 200.
Percentage formulas
Worked examples for each question
Three numbers for every row of the calculator, with the arithmetic written out. Pick the row that looks like your problem and swap in your own numbers.
| Question | Calculation | Answer |
|---|---|---|
| What is 15% of 80? | 0.15 × 80 | 12 |
| What is 7.5% of 240? | 0.075 × 240 | 18 |
| What is 120% of 50? | 1.2 × 50 | 60 |
| 30 is what percent of 120? | 30 ÷ 120 × 100 | 25% |
| 45 is what percent of 60? | 45 ÷ 60 × 100 | 75% |
| 9 is what percent of 8? | 9 ÷ 8 × 100 | 112.5% |
| 30 is 15% of what? | 30 ÷ 0.15 | 200 |
| 18 is 7.5% of what? | 18 ÷ 0.075 | 240 |
| 60 is 120% of what? | 60 ÷ 1.2 | 50 |
| Change from 80 to 100 | (100 − 80) ÷ 80 × 100 | +25% |
| Change from 250 to 200 | (200 − 250) ÷ 250 × 100 | −20% |
| Change from 40 to 130 | (130 − 40) ÷ 40 × 100 | +225% |
| 80 plus 25% | 80 × 1.25 | 100 |
| 200 minus 20% | 200 × 0.8 | 160 |
| 1,250 plus 7% | 1,250 × 1.07 | 1,337.5 |
Notice how the first three groups are the same equation solved for a different unknown. Part = Percent × Whole. Know the percent and the whole, and you get the part (15% of 80). Know the part and the whole, and you get the percent (30 of 120). Know the part and the percent, and you get the whole (30 is 15% of 200). If you remember that one line, you can check any answer the calculator gives you.
Percentages in your head
A few habits make most everyday percentage math quick without a calculator:
- Start from 10%. Move the decimal point one place to the left: 10% of 240 is 24. Then 5% is half of that (12), 20% is double (48) and 15% is 10% plus 5% (36).
- 1% is the number divided by 100. 1% of 240 is 2.4, so 3% is 7.2 and 7.5% is 18.
- Swap the two numbers. X% of Y is the same as Y% of X. 8% of 50 feels hard, 50% of 8 is 4, and both are 4.
- Turn a fraction into a percent by dividing. 3/8 is 3 ÷ 8 = 0.375, which is 37.5%. The other way, 37.5% is 0.375, or 375 out of 1,000, which cancels down to 3/8.
- Successive changes multiply, they do not add. Up 20% then down 20% is × 1.2 × 0.8 = × 0.96, a 4% drop overall. Two increases of 10% are × 1.21, not 20%.
Reverse percentages: the price before tax or discount
The most common mistake is to take the percentage off the final number. A $119 price that already includes 19% tax did not have $22.61 of tax in it (19% of 119). The tax was added to the price before tax, so divide by 1.19: 119 ÷ 1.19 = $100 before tax and $19 of tax. In the same way, if a jacket costs $128 after a 20% discount, the original price was 128 ÷ 0.8 = $160, not 128 × 1.2 = $153.60. Use the "X is P% of what?" row, where the percent is 119 or 80, or the discount calculator for sale prices.
How to use the percentage calculator
- 1Find the row that matches your question, for example "What is the percentage change from X to Y?".
- 2Type your two numbers. The answer and a sentence explaining it update as you type.
- 3Copy one answer with the button next to it, or copy all answers or a link that keeps every number.
Percent change vs. percentage points
When the numbers you compare are already percentages, say which change you mean. If an interest rate goes from 4% to 5%, it rose by 1 percentage point. Measured with the percentage change formula, the rate itself grew by 25%. Both statements are correct, but they answer different questions.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12. For mental math, take 10% first and build from there: 10% of 80 is 8, half of that is 4, and 8 + 4 = 12.
How do I find a number when I know a percentage of it?
Divide the part by the percentage as a decimal. If 30 is 15% of a number, the number is 30 ÷ 0.15 = 200. Check it backward: 15% of 200 is 30.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. 45 out of 60 is 45 ÷ 60 × 100 = 75%. The answer can be over 100%: 9 is 112.5% of 8.
How do I calculate a percentage increase or decrease?
Subtract the old value from the new value, divide by the old value and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%, an increase. Going from 250 to 200 is (200 − 250) ÷ 250 × 100 = −20%, a decrease.
How do I take a percentage off a price, or add one?
Multiply by 1 minus the percentage as a decimal to take it off, or by 1 plus it to add. 20% off $160 is 160 × 0.8 = $128. Adding 7% tax to $1,250 is 1,250 × 1.07 = $1,337.50. To remove a percentage that is already included, divide instead: $119 including 19% tax is 119 ÷ 1.19 = $100 before tax.
Why does a 10% increase followed by a 10% decrease not give the original number?
The second percentage is taken from a different base. 100 plus 10% is 110, and 110 minus 10% is 99, because 10% of 110 is 11.
What is the difference between percent and percentage points?
Percentage points describe the gap between two percentages. A rate that moves from 4% to 5% rises by 1 percentage point, which is a 25% increase in the rate itself.
Is my data stored anywhere?
No. Every calculation runs in your browser. Your numbers only end up in a link if you choose to copy one.