Work out a percent of a number, find what percent one value is of another, or calculate the percentage change between two figures.
Find a percentage of a number.
Result
30
20% of 150 = 30
The three core percentage calculations
Percent of a number
(X ÷ 100) × Y
What percent X is of Y
(X ÷ Y) × 100
Percent change from X to Y
((Y − X) ÷ X) × 100
Round percentages of common reference bases
| Percent | of 100 | of 200 | of 500 | of 1000 |
|---|---|---|---|---|
| 1% | 1 | 2 | 5 | 10 |
| 5% | 5 | 10 | 25 | 50 |
| 10% | 10 | 20 | 50 | 100 |
| 15% | 15 | 30 | 75 | 150 |
| 20% | 20 | 40 | 100 | 200 |
| 25% | 25 | 50 | 125 | 250 |
| 33.33% | 33.33 | 66.66 | 166.65 | 333.3 |
| 50% | 50 | 100 | 250 | 500 |
| 75% | 75 | 150 | 375 | 750 |
A percentage is a way to express a number as a fraction of one hundred. This page works out the three percentage calculations that come up most often: finding a percent of a value, finding what percentage one number is of another, and calculating the percentage change between two values.
The calculator above updates as you type. The same formulas are written out below so you can also work the numbers by hand.
(X ÷ 100) × Y(X ÷ Y) × 100((Y − X) ÷ X) × 100For percent change, a positive result is an increase and a negative result is a decrease.
To work out the discount, calculate 20% of 150:(20 ÷ 100) × 150 = 30
The price drops by £30, so the sale price is £150 − £30 = £120.
To work out the percentage score, divide and multiply by 100:(30 ÷ 120) × 100 = 25%
A score of 30 out of 120 is 25%.
To work out the percentage increase:((100 − 80) ÷ 80) × 100 = 25%
That is a 25% rise. Going back the other way is not symmetrical: a drop from £100 to £80 is ((80 − 100) ÷ 100) × 100 = −20%, not −25%.
The table below shows common percentages of round reference values. It can be useful as a sanity check or for quick mental estimates.
| Percent | of 100 | of 200 | of 500 | of 1000 |
|---|---|---|---|---|
| 1% | 1 | 2 | 5 | 10 |
| 5% | 5 | 10 | 25 | 50 |
| 10% | 10 | 20 | 50 | 100 |
| 15% | 15 | 30 | 75 | 150 |
| 20% | 20 | 40 | 100 | 200 |
| 25% | 25 | 50 | 125 | 250 |
| 33.33% | 33.33 | 66.66 | 166.65 | 333.3 |
| 50% | 50 | 100 | 250 | 500 |
| 75% | 75 | 150 | 375 | 750 |
It is easy to confuse percentage points with percent change. Percentage points are the simple arithmetic difference between two percentages, while percent change measures that difference relative to the starting percentage.
For example, if an interest rate rises from 4% to 6%, that is a rise of 2 percentage points. As a percent change, it is ((6 − 4) ÷ 4) × 100 = 50%. Headlines and reports sometimes mix these up, which can make a change sound larger or smaller than it really is.
A percentage is just a decimal multiplied by one hundred. To convert a decimal to a percent, multiply by 100; to convert a percent back to a decimal, divide by 100.
Divide the percentage by 100 and multiply by the number. For example, 20% of 80 is (20 / 100) × 80 = 16.
Divide the first number by the second, then multiply by 100. For example, 30 is (30 / 120) × 100 = 25% of 120.
Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase; a negative result is a decrease.
A percentage point is the simple arithmetic difference between two percentages, while percent change is that difference expressed relative to the starting percentage. Moving from 10% to 15% is a 5 percentage point rise, which is a 50% relative increase.
Multiply the decimal by 100. For example, 0.075 becomes 7.5%, and 1.2 becomes 120%.
For other everyday number tools, see the Tip Calculator, Loan Calculator, Mortgage Calculator, and BMI Calculator.