How to calculate a percentage: four formulas with worked examples
To work out a percentage of a number, multiply the number by the percentage and divide by 100. To find what percentage one number is of another, divide the part by the whole and multiply by 100. Most percentage questions are one of four forms, and each has its own formula and a quick check.
Percentage calculatorWhat percent is it, really?Do it freeThe four formulas at a glance
| Question | Formula | Worked example | Answer |
|---|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 80 | 12 |
| X is what % of Y? | X ÷ Y × 100 | 30 is what % of 120 | 25% |
| What is the % change from A to B? | (B − A) ÷ A × 100 | 50 to 65 | +30% |
| What is Y plus or minus X%? | Y × (1 ± X ÷ 100) | 200 plus 18% | 236 |
The first two are the building blocks. The last two need care about which number is the base, meaning the number the percentage is taken from.
How do I find X% of a number?
Multiply the number by the percentage, then divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12. The same sum in decimals is 0.15 × 80 = 12, which is the form most calculators use. To check any of these sums, the percentage calculator has a row for each of the four questions.
The mental shortcut is to split the percentage into parts you know. 10% of any number is that number divided by 10, so 10% of 80 is 8. Half of 10% is 5%, which is 4, so 15% is 8 + 4 = 12.
A percentage can also be swapped round. 8% of 50 and 50% of 8 are both 4, because 8 × 50 ÷ 100 and 50 × 8 ÷ 100 are the same product. If the second version is easier to picture, use it. Half of 8 is 4 at a glance.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100: X ÷ Y × 100. For example, 30 is what percent of 120? Since 30 ÷ 120 = 0.25, the answer is 25%. Check it by taking 25% of 120, which gives 30 again.
The common mistake is to divide the whole by the part. 120 ÷ 30 = 4 gives 400%, which says that 120 is four times 30. The question asks what share 30 is of 120, so 120 goes on the bottom.
Familiar fractions help. A half is 50%, a quarter is 25%, a fifth is 20% and a tenth is 10%. Since 120 ÷ 4 = 30, 30 is a quarter of 120, which is 25%.
How do I calculate a percentage change?
Subtract the starting value A from the new value B, divide by A and multiply by 100. From 50 to 65, the change is 65 − 50 = 15, and 15 ÷ 50 × 100 = 30%. A fall works the same way: from 120 to 96 the change is −24, and −24 ÷ 120 × 100 = −20%.
The mental shortcut is to find 10% of the starting value first. 10% of 50 is 5. The change of 15 is three lots of 5, so it is 30%. This works for any starting value, because a tenth is easy to find.
Always divide by the starting value, not the new one. From 80 to 100 is a rise of 20 over 80, which is 25%, not 20%. The percentage change mistakes post explains why the base matters when two changes are chained.
How do I add or take off a percentage?
Multiply by 1 plus the percentage to add it, or by 1 minus the percentage to take it off. 200 plus 18% is 200 × 1.18 = 236. 200 less 18% is 200 × 0.82 = 164. The percentage calculator has a switch for adding or taking off, so you can check both.
The mental shortcut is to find the percentage first and then add or subtract it. 10% of 200 is 20 and 8% is 16, so 18% is 36. Then 200 + 36 = 236. The same method gives sale prices, which are covered in how to calculate a discount, and the discount calculator works them out in one step.
Steps for any percentage question
- Say what the question is: a share of a number, a comparison of two numbers, a change over time, or an adjustment.
- Name the base, which is the whole or the starting value.
- Apply the formula from the table, and keep the base on the bottom of any division.
- Check the answer by reversing it. Take the percentage of the result, or apply the change in the other direction.
How to do it with fixmint
- Find the row that matches your question: what is X% of Y, X as a percent of Y, the change from A to B, or Y plus or minus X%.
- Type the two numbers you know into that row.
- Read the highlighted answer and the working under it.
- Check the answer by reversing it: take the percentage of the result, or apply the change the other way.
Edge cases and mistakes
- Percentages above 100. When the part is bigger than the whole, the percentage is above 100. 120 is 150% of 80, since 120 ÷ 80 × 100 = 150, and 80 × 1.5 = 120.
- A starting value of zero. A percentage change from zero cannot be worked out, because the formula divides by the starting value. The percentage calculator says so.
- Percentage points. A rise from 5% to 8% is 3 percentage points, and a 60% increase in the rate. Both are right, so say which one you mean.
- Rounding. Keep full precision through the sum and round the answer once, at the end.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For 15% of 80, that is 80 × 15 ÷ 100 = 12.
What percent is 30 of 120?
30 ÷ 120 × 100 = 25%. Divide the part by the whole first, then multiply by 100.
How do I calculate a percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100, which is 30%.
Why does 20% off followed by 20% on not get me back to the start?
Each change uses a different base. 100 less 20% is 80, and 80 plus 20% is 96, not 100. The second change is taken from 80, not from 100.
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