How to calculate a percentage increase or decrease
Whether it's a pay rise, a price increase or a sale discount, the sum is the same.
The formula
Percentage change = (new − old) ÷ old × 100
If the answer is positive, it's an increase. If it's negative, it's a decrease.
Worked examples
Pay rise. Your salary goes from £32,000 to £34,000. That's (34,000 − 32,000) ÷ 32,000 × 100 = 6.25%.
Price rise. Your energy direct debit goes from £120 to £138 a month. That's 18 ÷ 120 × 100 = 15%.
Discount. A coat drops from £80 to £56. That's (56 − 80) ÷ 80 × 100 = −30%, so 30% off.
Going the other way
To increase a number by a percentage, multiply by 1 plus the percentage as a decimal. £500 plus 8% is £500 × 1.08 = £540.
To decrease by a percentage, multiply by 1 minus the decimal. £500 less 15% is £500 × 0.85 = £425.
The traps
Percentages don't cancel out. A 50% rise followed by a 50% fall doesn't take you back where you started. £100 up 50% is £150, then down 50% is £75.
Percentage vs percentage points. If an interest rate goes from 4% to 5%, that's a rise of 1 percentage point, but a 25% increase in the rate itself. News reports often mix these up.
Always divide by the starting figure. The change is measured against where you began, not where you ended.
Get the answer instantly
The percentage calculator works out percentage change, a percentage of a number, and what percentage one number is of another. For a pay rise, also check what it's worth after tax in the take-home pay calculator.