Percentage change and reverse percentage calculator
Percentage questions carry marks on every GCSE and IGCSE paper, and most lost marks come from using the wrong base value or forgetting the multiplier. This calculator shows the change, the percentage, the multiplier and the reverse calculation, so you can see which number the percentage is actually taken from.
30% increase
Difference: 12
Working: (52 − 40) ÷ 40 × 100
Multiplier: × 1.3
The method behind it
- Percentage change = (new − original) ÷ original × 100.
- Increase by p%: × (1 + p/100). Decrease by p%: × (1 − p/100).
- Reverse percentage: divide the new amount by the multiplier, never subtract.
How to use this tool
1. Pick the calculation you need
Percentage change compares an old and a new value. Apply a percentage increases or decreases a number. Reverse percentage finds the original amount before a change.
2. Enter your two numbers
Type the values from the question. Decimals and negative changes are handled, and money amounts can be entered without a currency symbol.
3. Copy the multiplier into your working
Examiners award method marks for the multiplier, for example × 1.15 or ÷ 0.82, so write it down rather than jumping to the answer.
Frequently asked questions
How do you calculate percentage change?
Percentage change = (new value − original value) ÷ original value × 100. The original value always goes on the bottom; using the new value is the single most common error in GCSE percentage questions.
What is a reverse percentage?
A reverse percentage finds the amount before a change. If a price is £84 after a 20% discount, divide by the multiplier 0.8 to get the original £105. Never subtract 20% from the new price.
What multiplier do I use for a percentage increase?
Add the percentage to 100% and convert to a decimal. A 15% increase is × 1.15, a 7.5% increase is × 1.075, and a 15% decrease is × 0.85.
How do I handle repeated percentage change?
Multiply the multipliers together. Three years of 4% growth is × 1.04³ = × 1.124864, which is more than 12% — compound change is never the same as adding the percentages.
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.