Guide · Updated 2026-10-08
Percentage Change, Increase and Decrease Explained with Examples
How to work out a percentage change, why going up 25% and back down is not 25%, how to reverse a percentage and what a percentage point is.
Percentages are easy to calculate and easy to misread. Most mistakes come from using the wrong starting value. The Percentage Calculator answers five common questions at once, and this guide explains what each answer means.
The formula for percentage change
Percentage change = (new value − old value) ÷ old value × 100. The old value is always the base. A price that goes from 200 to 250 rose by 50, and 50 ÷ 200 = 0.25, so the change is +25%.
Why up 25% and down 25% do not cancel out
The same 50 difference measured from a different base gives a different percentage. Going from 250 back to 200 is a fall of 50 ÷ 250 = 20%, not 25%. That is why a stock that gains 25% needs only a 20% fall to return to where it started. The Percentage Increase Calculator shows both directions: 200 to 250 is +25% with a multiplier of 1.25, and 250 to 200 is −20% with a multiplier of 0.8.
Increasing and decreasing by a percentage
| Question | Working | Answer |
|---|---|---|
| Increase 100 by 10% | 100 × 1.10 | 110 |
| Decrease 110 by 10% | 110 × 0.90 | 99 |
| What is 20% of 150? | 150 × 0.20 | 30 |
| 20 is what percentage of 150? | 20 ÷ 150 × 100 | 13.3333% |
Notice the second row: increasing 100 by 10% and then decreasing the result by 10% gives 99, not 100. Each percentage applies to the number it is applied to.
Discounts
A 25% discount on £80 saves £20 and leaves £60, which the Discount Calculator shows. Two discounts in a row do not add up: 20% off and then a further 10% off is a total of 28% off (0.8 × 0.9 = 0.72), not 30%.
Percentage points versus percent
If an interest rate goes from 4% to 5%, it has risen by one percentage point, but it has risen by 25% in relative terms (1 ÷ 4). News stories mix the two up, so check which one is meant. The calculator works in relative percentages, as in the formula above.
Common mistakes
- Using the new value as the base instead of the old one.
- Adding percentages from different bases.
- Treating a starting value of zero as a percentage change. Going from 0 to 5 has no percentage change, because there is nothing to divide by.
Frequently asked questions
How do I calculate a percentage increase? Subtract the old value from the new one, divide by the old value and multiply by 100.
How do I reverse a percentage increase? Divide by 1 plus the rate. To remove a 20% increase from 120, divide by 1.20 to get 100.