Percent means "per hundred"
A percentage is a fraction with 100 as the denominator: 15% is 15 ÷ 100 = 0.15. Almost every percentage question becomes simple once you turn the percentage into a decimal (divide by 100) or turn a fraction into a percentage (multiply by 100).
The four everyday questions
1. What is X% of Y?
Result = X ÷ 100 × Y
15% of 80 = 0.15 × 80 = 12. Handy for tips, tax and commission.
2. X is what percent of Y?
Percent = X ÷ Y × 100
12 is 12 ÷ 80 × 100 = 15% of 80. Use it for test scores, budgets and survey results.
3. Percentage change (increase or decrease)
Change = (new − old) ÷ old × 100
A price rising from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. Falling back from 100 to 80 is (80 − 100) ÷ 100 × 100 = −20%. The two are not the same size, because each is measured against a different starting value.
4. Percentage difference
Difference = |X − Y| ÷ ((X + Y) ÷ 2) × 100
When neither value is the "original", for example comparing two shops' prices, compare the gap with their average. For 80 and 100: 20 ÷ 90 × 100 = 22.2%.
Percentage points versus percent
If an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, but by 25 percent (1 ÷ 4 × 100). News reports and financial documents mix these up often. Percentage points describe the arithmetic gap between two percentages; percent describes the relative change.
Mental shortcuts
- 10%: move the decimal point one place left. 10% of 80 is 8.
- 5%: half of 10%. 15%: 10% plus 5% (8 + 4 = 12).
- X% of Y = Y% of X: 8% of 50 is the same as 50% of 8, which is 4.
- 25%, 50%, 75%: a quarter, a half, three quarters.
Reversing a percentage
If a price after a 20% increase is 120, the original was 120 ÷ 1.20 = 100, not 120 − 20% (96). Divide by (1 + rate) to undo an increase and by (1 − rate) to undo a decrease. The discount calculator finds the original price from a sale price this way.
Common mistakes
- Adding successive percentage changes. +10% then −10% leaves you 1% below where you started (1.1 × 0.9 = 0.99).
- Using the wrong base for percentage change: always divide by the starting value.
- Confusing percent with percentage points when comparing rates.
Reverse percentages
To find the original value before a percentage change, divide by the multiplier rather than subtracting the percentage:
- After a 25% increase the value is 100: the original was 100 ÷ 1.25 = 80.
- After a 20% decrease the value is 80: the original was 80 ÷ 0.80 = 100.
- A price of 120 includes 20% tax: before tax it was 120 ÷ 1.20 = 100.
Successive changes
Multiply the factors rather than adding the percentages:
| Changes | Combined factor | Overall change |
|---|---|---|
| +10%, then −10% | 1.10 × 0.90 = 0.99 | −1% |
| +20%, then +20% | 1.20 × 1.20 = 1.44 | +44% |
| −50%, then +50% | 0.50 × 1.50 = 0.75 | −25% |
| −50%, then +100% | 0.50 × 2.00 = 1.00 | 0% (back to start) |
The last line explains why an investment that halves needs to double, a 100% gain, to recover.
Percentages in everyday life
- Tips: 15% of a bill of 48 is 7.20; 20% is 9.60.
- Exam scores: 42 out of 60 is 42 ÷ 60 × 100 = 70%.
- Salary rises: a raise from 3,000 to 3,150 is a 5% increase.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 = 0.15 × 80 = 12.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. 12 out of 80 is 12 ÷ 80 × 100 = 15%.
How do I calculate percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100 is a 25% increase.
Why is a 20% decrease not undone by a 20% increase?
Because the second percentage is taken from a smaller number. 100 − 20% = 80, and 80 + 20% = 96.
How do I reverse a percentage increase?
Divide by 1 plus the percentage as a decimal. If 100 is the value after a 25% rise, the original was 100 ÷ 1.25 = 80.
If a price falls 50%, how much must it rise to recover?
100%. Half of the original must double to get back to the starting value.
What is 42 out of 60 as a percentage?
42 ÷ 60 × 100 = 70%.
Sources
- UK Government Analysis Function. Style guide: percentages and percentage points.
Last reviewed 5 October 2026. Results are estimates; see our disclaimer.