% of · % change · + %
Percentage calculator
20% of 150 is 30, and 30 is 20% of 150. Four everyday percentage questions sit below, and each one is answered as you type.
- 20% × 150 = 30
- 30 ÷ 150 = 20%
- 120 → 150 = +25%
- 150 + 20% = 180
Every block works on its own. Results are shown to ten significant digits; a decimal comma is accepted as well as a point.
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At a glance
- Price
- No charge
- Account
- None needed
- Upload
- Not applicable — you type numbers, nothing is sent anywhere
- Questions
- Percent of a number, what percent, percent change, raise or lower by a percent
- Precision
- Double-precision arithmetic, shown to ten significant digits
- Limit
- Percent change from a starting value of zero is not defined
Common percentages and the fall that undoes a rise
Both tables come from the same functions as the calculator. The second one shows why a rise and an equal fall do not cancel.
| Percent | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| Rise | Fall needed to return to the start |
|---|---|
| +10% | -9.091% |
| +25% | -20% |
| +50% | -33.33% |
| +100% | -50% |
| +200% | -66.67% |
How to work out a percentage
Pick the question you have
Use “What is X% of Y?” for a share of a number, “X is what percent of Y?” for a ratio, “Percent change” for a rise or fall between two values, and “Raise or lower by a percent” for a new total.
Type the two numbers
Each block starts with a worked example. Replace the numbers and the result changes straight away, with no button to press.
Read and copy the answer
A rise shows a plus sign and a fall a minus sign. In the last block you see the number raised and the number lowered by the same percent side by side.
How percentages are calculated
Percent means per hundred. To take a percentage of a number, divide the percentage by 100 and multiply: 20% of 150 is 0.2 × 150 = 30. To find what percent a part is of a whole, divide the part by the whole and multiply by 100: 30 ÷ 150 × 100 = 20%. Percent change is the new value minus the old one, divided by the old one: from 120 to 150 that is (150 − 120) ÷ 120 = +25%.
Percent change always uses the starting value as the base, which is why a rise and the same fall do not cancel. Raise 100 by 25% and you get 125; lower 125 by 25% and you get 93.75, not 100. To get back you need a fall of 20%, because 25 is 20% of 125. A change from 10% to 12% is 2 percentage points, but it is a 20% increase of the rate itself. Percent change from a start of zero is undefined, and the calculator says so.
Percentage questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 20% of 150 is 0.2 × 150 = 30, and 12.5% of 80 is 0.125 × 80 = 10.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 150 is 30 ÷ 150 × 100 = 20%, and 45 out of 60 is 75%. The whole is the number after “of”.
How do I calculate percent change?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 120 to 150 the change is +25%; from 150 back to 120 it is −20%. The two differ because each uses its own starting value as the base.
Why does +25% followed by −25% not return to the start?
The second percentage is taken of the larger number. 100 + 25% = 125, and 25% of 125 is 31.25, so the result is 93.75. The fall that undoes a rise of p% is p ÷ (100 + p) × 100%, so +25% needs −20%, +50% needs −33.33% and +100% needs −50%.
What is the difference between percent and percentage points?
Percentage points subtract two percentages; percent change compares them. If an interest rate goes from 4% to 5%, it rises by 1 percentage point, which is a 25% increase of the rate. Use the percent change block for the second figure.
Does this calculator send my numbers anywhere?
No. It does arithmetic in your browser tab and sends nothing, so it also works offline once the page has loaded.