Percentage change — increase and decrease
How do you work out a percentage change?
A percentage change describes how much a value has grown or shrunk, relative to its starting value — a share price, the number of pupils in a school, or the kilometres you ran this week compared with last week. There is a famous trap here: a rise followed by a fall of the same percentage does not bring you back to the original number.
Worked examples, step by step
The price of a flight rises from £800 to £880. By what percentage did the price rise?
- The difference: 880 − 800 = 80
- The percentage: (80 ÷ 800) × 100
- 80 ÷ 800 = 0.1
- 0.1 × 100 = 10
- Answer: the price rose by 10%
The number of pupils in a class falls from 32 to 28. By what percentage did it fall?
- The difference: 32 − 28 = 4
- The percentage: (4 ÷ 32) × 100
- 4 ÷ 32 = 0.125
- 0.125 × 100 = 12.5
- Answer: the number of pupils fell by 12.5%
A price rises by 50%, then falls by 50%. Is it back to the original price?
- Suppose the original price is £100
- After a 50% rise: 100 × 1.5 = £150
- After a 50% fall from 150: 150 × 0.5 = £75
- £75 is less than the original £100
- Answer: no — the price does not return to the original. 50% of 150 is more pounds than 50% of 100, so the fall "takes away" more than the rise "built"
A salary of £28 000 rises by 6%. What is the new salary?
- The size of the rise: (28 000 × 6) ÷ 100 = £1680
- The new salary: 28 000 + 1680 = 29 680
- Or directly: 28 000 × 1.06 = 29 680
- Answer: the new salary is £29 680
Now try it yourself
Frequently asked questions
What is the formula for percentage change?
Percentage change = ((new value − original value) ÷ original value) × 100. A positive result is an increase, a negative result is a decrease.
Why does a 50% rise followed by a 50% fall not return to the original price?
Because a percentage is always worked out on the current value, not on the original value. A 50% rise on 100 gives 150; a 50% fall on 150 (not on 100!) gives 75, not 100. The base for the percentage changed between the two steps.
How do you know whether it is an increase or a decrease?
Compare the new value with the original: if the new value is bigger it is an increase, and if it is smaller it is a decrease. The sign of the difference (new value minus original value) decides: positive = increase, negative = decrease.
What is the difference between a percentage change and percentage points?
If an interest rate rises from 4% to 5%, that is a rise of one percentage point, but the relative percentage change is 25% (because (5 − 4) ÷ 4 × 100 = 25). The two ideas are different and are often confused in financial reporting.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: