How to calculate percentages
“Per cent” means “per hundred”, so 25% is 25 out of 100, or 0.25. Almost every percentage question is one of a handful of patterns. Here are the formulas this calculator uses.
1. X% of Y
Example: 20% of 150 = 150 × 20 ÷ 100 = 30. This is how you work out a discount, a tip or a tax amount.
2. X is what percent of Y
Example: 30 out of 120 = 30 ÷ 120 × 100 = 25%. Useful for exam marks: 72 out of 90 is 80%.
3. Percentage increase or decrease
Example: a price rising from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase. Falling from 100 to 80 is a 20% decrease, which is why a 25% rise followed by a 20% fall brings you back to where you started.
4. Adding or subtracting a percentage
Example: 500 plus 18% GST = 500 × 1.18 = 590. A 30% discount on 2,000 = 2,000 × 0.70 = 1,400.
5. Percentage difference
Use this when neither number is the “starting” value, for example when comparing two prices. 40 and 60 differ by 20 ÷ 50 × 100 = 40%.
6. Reverse percentage (finding the original)
Example: if 90 is 75% of a number, the number is 90 ÷ 0.75 = 120. Handy for working out a price before a discount or before tax.
Quick percentage reference
| Percent | Fraction | Decimal | Of 200 |
|---|---|---|---|
| 1% | 1/100 | 0.01 | 2 |
| 5% | 1/20 | 0.05 | 10 |
| 10% | 1/10 | 0.1 | 20 |
| 12.5% | 1/8 | 0.125 | 25 |
| 20% | 1/5 | 0.2 | 40 |
| 25% | 1/4 | 0.25 | 50 |
| 33.33% | 1/3 | 0.333… | 66.67 |
| 50% | 1/2 | 0.5 | 100 |
| 75% | 3/4 | 0.75 | 150 |
Mental-maths tip: X% of Y is always the same as Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 80 is 80 × 15 ÷ 100 = 12.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100 = 30% increase.
How do I work out my exam percentage?
Divide the marks you scored by the total marks and multiply by 100. For example, 432 out of 500 is 432 ÷ 500 × 100 = 86.4%.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with an old one, so the direction matters. Percentage difference compares two values with neither as the starting point, using their average as the base.
How do I remove a percentage from a price that already includes it?
Divide by 1 plus the rate. A price of 590 including 18% tax is 590 ÷ 1.18 = 500 before tax. Use calculator 6 with 118% for the same result.