Percentages Made Easy: Formulas and Examples
Percentages appear everywhere: discounts, exam marks, salary raises, interest rates, tips and price changes. "Per cent" simply means "per hundred", so 15% means 15 out of every 100. Once you know the handful of formulas below, almost any percentage question becomes simple.
1. How to calculate the percentage of a number
To find a percentage of a number, multiply the number by the percentage and divide by 100:
Examples: 15% of 200 = 15 × 200 ÷ 100 = 30. 25% of 80 = 20. 18% of 1,500 = 270. A quick mental trick: 10% of any number is the number ÷ 10, so 20% is double that and 5% is half of it.
2. How to calculate what percentage a number is of another number
To find what percentage one number (the part) is of another number (the whole), use:
- Divide the first number by the second number.
- Multiply the result by 100.
- Add the % sign.
| Question | Working | Answer |
|---|---|---|
| 30 is what % of 200? | 30 ÷ 200 × 100 | 15% |
| 45 is what % of 60? | 45 ÷ 60 × 100 | 75% |
| 8 is what % of 32? | 8 ÷ 32 × 100 | 25% |
| Scored 72 out of 90? | 72 ÷ 90 × 100 | 80% |
This is exactly how exam marks are turned into percentages. Choose "A is what % of B?" in the calculator above to get the answer instantly.
3. How to calculate percentage increase between two numbers
Change = (B − A) ÷ A × 100. A positive result is an increase; a negative one is a decrease. Example: a price rising from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase, and a salary going from 250 to 300 is a 20% increase. Choose "% change from A to B" in the calculator to get it instantly.
4. Increase or decrease a number by a percentage
Increase: B × (1 + A ÷ 100) and Decrease: B × (1 − A ÷ 100). Example: 200 increased by 15% is 230; decreased by 15% is 170.
A common trap
A 20% decrease followed by a 20% increase does not bring you back to where you started. 100 down 20% is 80, and 80 up 20% is 96. That's because the second percentage is applied to a smaller number. Keep this in mind when reading about prices or investments that fall and then recover.
Percent vs percentage points
If an interest rate goes from 5% to 6%, it has risen by one percentage point, but by 20% in relative terms. News and financial reports often mix these up, so it's worth checking which one is meant.
Planning further? You may also find our Basic Calculator, Scientific Calculator useful, or explore all calculators.
Further reading: Percentage (Wikipedia)