How to use
- Find the card that matches your question, such as “What is X% of Y?” or “Percentage change”.
- Replace the example numbers with your own. The answer updates as you type.
- Check the formula under the answer if you need to show your working.
Percentage formulas
- X% of Y = Y × X ÷ 100
- X as a percent of Y = X ÷ Y × 100
- Percentage change = (new − old) ÷ old × 100
- Price after X% off = price × (1 − X ÷ 100)
- Whole from a part = part ÷ X × 100
Percent vs percentage points
If an interest rate rises from 2% to 3%, it has gone up by 1 percentage point, but by 50 percent. Use the percentage change card for the second figure.
Frequently asked questions
Why doesn’t a 20% rise followed by a 20% fall return to the start?
The fall is 20% of the larger number. 100 → 120 → 96. To get back from 120 to 100 you need a fall of about 16.7%.
How do I work out a percentage of a total?
Use “X is what percent of Y?”. For example, 45 out of 60 is 75%.
How do I find the price before a discount?
Use “Find the whole from a part”. If you paid 70 after 30% off, 70 is 70% of the original price: 70 ÷ 70 × 100 = 100.