How to calculate a percentage increase
A percentage increase tells you how much a value has grown compared with where it started. The formula is:
Percentage increase = (New value − Old value) ÷ Old value × 100
- Subtract the old value from the new value to get the difference.
- Divide the difference by the old value.
- Multiply by 100 to turn it into a percentage.
Example: rent goes from $1,200 to $1,320. The difference is $120, and 120 ÷ 1,200 = 0.10, so the rent rose by 10%.
Percentage decrease
The same formula works for a fall in value: the result is simply negative. A price dropping from 50 to 40 gives (40 − 50) ÷ 50 × 100 = −20%, a 20% decrease.
Increase or decrease a number by a percentage
- To increase X by P%: X × (1 + P/100). 250 increased by 15% = 250 × 1.15 = 287.5.
- To decrease X by P%: X × (1 − P/100). 250 decreased by 15% = 250 × 0.85 = 212.5.
A common mistake
A 20% increase followed by a 20% decrease does not bring you back to the start: 100 → 120 → 96. The second percentage is applied to a bigger number. For other percentage questions, use the main percentage calculator; for prices on sale, try the discount calculator.
Percentage increase in everyday life
| Situation | Old | New | Change |
|---|---|---|---|
| Salary raise | $52,000 | $55,120 | +6% |
| Rent increase | $1,400 | $1,470 | +5% |
| Website traffic | 12,000 visits | 15,600 visits | +30% |
| Price drop on sale | $250 | $200 | −20% |
Reverse percentage: finding the original value
If you know the value after an increase and the percentage, divide instead of multiplying: original = new ÷ (1 + P/100). A price of $115 after a 15% increase was 115 ÷ 1.15 = $100 before. After a decrease, divide by (1 − P/100): $80 after a 20% discount was 80 ÷ 0.8 = $100.
Compound increases over several periods
Repeated increases multiply. Three yearly increases of 5% give 1.05 × 1.05 × 1.05 = 1.1576, a total of 15.76%, not 15%. To find the average yearly rate from a total change, use (new ÷ old)1/n − 1, where n is the number of periods.
Need other percentage operations, such as “what is X% of Y”? Use the main percentage calculator. For an advertising budget, see the CPM calculator.