Appears in: Functional Skills Level 2 · GCSE foundation
Percentage change: how to work out a percentage increase or decrease
Percentage change questions come in two directions. Either you're given the percentage and asked to apply it — a 20% pay rise, 15% off — or you're given two amounts and asked what the percentage change was. Multipliers handle the first; one formula handles the second.
The method
- To increase by a percentage, multiply by (1 + the decimal). Up 20% is × 1.2. Up 4% is × 1.04.
- To decrease by a percentage, multiply by (1 − the decimal). Down 20% is × 0.8. Down 35% is × 0.65.
- To find the percentage change between two amounts: change ÷ original × 100. The original is the amount before the change — always.
Worked examples
Example 1
A salary of £350 a week goes up by 20%. What is the new weekly pay?
- Up 20% is a multiplier of 1.2.
- £350 × 1.2 = £420.
Example 2
A £350 coat is reduced by 20% in a sale. What is the sale price?
- Down 20% is a multiplier of 0.8.
- £350 × 0.8 = £280.
Example 3
A ticket cost £80 last year and costs £92 this year. What is the percentage increase?
- Change = £92 − £80 = £12.
- Change ÷ original = 12 ÷ 80 = 0.15.
- × 100 = 15% increase.
Example 4
A phone's price falls from £250 to £210. What is the percentage decrease?
- Change = £250 − £210 = £40.
- 40 ÷ 250 = 0.16.
- × 100 = 16% decrease.
Where the marks go missing
- Dividing by the new amount instead of the original. Percentage change is always measured against where you started.
- Working out the percentage and then forgetting to add it on or take it off. Multipliers avoid this: one multiplication, done.
- Assuming a 20% rise followed by a 20% fall gets you back to the start. It doesn't: × 1.2 × 0.8 = × 0.96, a 4% drop overall.
Frequently asked questions
What is the formula for percentage change?
Percentage change = (new amount − original amount) ÷ original amount × 100. A positive result is an increase, a negative one a decrease.
How do I increase a number by a percentage on a calculator?
Multiply by 1 plus the percentage as a decimal. To increase by 12%, multiply by 1.12. To decrease by 12%, multiply by 0.88.