How to calculate percentages
By M Alamgir Saeed · Updated
Percentages show up in shopping discounts, restaurant tips, exam scores, pay rises and price increases. Almost every percentage question is one of three simple calculations. Learn those three and you can handle nearly anything, with or without a calculator.
What "percent" means
Percent means "per hundred". 25 percent is 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25. To turn a percentage into a decimal, divide it by 100; to turn a decimal into a percentage, multiply by 100.
1. What is X% of a number?
Multiply the number by the percentage and divide by 100. 20% of 80 is 80 x 20 / 100 = 16. A quick mental trick: 10% is the number divided by 10, so 20% is twice that, and 5% is half of it.
| Question | Calculation | Answer |
|---|---|---|
| 20% of 80 | 80 x 20 / 100 | 16 |
| 15% tip on 42 | 42 x 15 / 100 | 6.30 |
| 8% of 1,250 | 1,250 x 8 / 100 | 100 |
2. X is what percent of Y?
Divide the part by the whole and multiply by 100. If you scored 42 out of 50 on a test, your score is 42 / 50 x 100 = 84%. The same formula tells you what share of a budget went on rent, or what fraction of a task is finished.
3. Percentage increase or decrease
Subtract the old value from the new value, divide by the old value and multiply by 100. A price that goes from 50 to 60 has risen by (60 - 50) / 50 x 100 = 20%. A price that falls from 60 to 45 has dropped by (45 - 60) / 60 x 100 = -25%, a 25% decrease.
Common mistakes
- A rise and a fall of the same percentage do not cancel out: 100 up 10% is 110, and 110 down 10% is 99.
- Always divide by the original value when working out a change, not the new one.
- Two discounts multiply, they do not add: 20% off then another 10% off is 28% off in total, not 30%.
- Percentage points are not percent: an interest rate moving from 3% to 4% is a rise of 1 percentage point, but 33% in relative terms.
Let the calculator do it
The Percentage Calculator on this site has a box for each of these three questions and shows the formula it used, so you can check the working. For splitting a bill, the Tip Calculator does the percentage and the division in one go.
Try the free Percentage Calculator
Frequently asked questions
How do I work out 15% of a number in my head?
Find 10% by dividing by 10, then add half of that again. For 60: 10% is 6, half of 6 is 3, so 15% is 9.
How do I calculate a discount price?
Multiply the price by (100 - discount) / 100. A 25% discount on 80 is 80 x 0.75 = 60.
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages (3% to 4% is 1 point). Percent change measures it relative to the start (a 33% increase).