The percentage increase formula
To measure an increase, take the gap between the new and old values and divide it by the old value: (new − old) ÷ old × 100. If rent goes from 1,200 to 1,290, the change is 90, and 90 ÷ 1,200 = 0.075, so the rise is 7.5%.
To apply an increase, multiply by 1 plus the percentage as a decimal: new = old × (1 + percent ÷ 100). A 7.5% rise on 1,200 is 1,200 × 1.075 = 1,290. The same idea works for a 4% pay rise on 52,000: 52,000 × 1.04 = 54,080.
Rises that follow each other add up to more than their sum
Each rise applies to the number as it now stands, not to the original. Two 10% rises in a row make 100 × 1.1 × 1.1 = 121, a 21% rise, not 20%. Five yearly 3% raises give 1.03 to the power of 5, about 1.1593, so a 15.93% rise overall.
This is also why you cannot undo a rise by taking the same percentage off. A 20% rise takes 100 to 120, and taking 20% off 120 leaves 96. To get back to 100 you need a fall of about 16.67%. The line under each answer on this page tells you that figure. The percentage decrease calculator explains the effect in the other direction.
Things to watch for
- Doubling is a 100% increase, not 200%. Tripling is 200%. From 50 to 150 is a 200% increase because 100 was added to a starting value of 50.
- There is no percentage increase from zero. Anything compared to nothing is an infinite multiple, so the calculator says so instead of printing a number.
- Percent is not percentage points. A rate rising from 4% to 5% is up 1 point, which is a 25% increase.
- Tiny starting values mislead. From 2 to 20 is a 900% increase, which sounds huge for a rise of 18.
For the general case, including every other percentage question, use the percentage calculator.