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1. X percent of a number2. What percent is A of B?3. Percentage change4. Add or take off a percentage5. Find the original after a percentage was appliedTwo traps to avoidPercentages appear in shopping, salaries, tax, exam results and interest rates, and a handful of formulas cover almost all of them. Keep these five and you can check any figure yourself, then confirm it with the Percentage Calculator.
1. X percent of a number
Multiply the number by X and divide by 100. 15% of 200 is 200 × 15 ÷ 100 = 30.
2. What percent is A of B?
Divide A by B and multiply by 100. If you scored 42 out of 60, that is 42 ÷ 60 × 100 = 70%.
3. Percentage change
(new − old) ÷ old × 100. A rise from 50 to 75 is (75 − 50) ÷ 50 × 100 = +50%. A fall from 80 to 60 is −25%. Always divide by the old value.
4. Add or take off a percentage
To add 20%, multiply by 1.20. To take off 20%, multiply by 0.80. A 120 price with 25% off is 120 × 0.75 = 90. For discounts, the Discount Calculator does this and shows the saving, and for tax the VAT Calculator adds or removes it.
5. Find the original after a percentage was applied
This is the one people get wrong. If a price is 90 after a 25% discount, divide by 0.75, not add 25%: 90 ÷ 0.75 = 120. Likewise, a total of 115 that includes 15% tax is 115 ÷ 1.15 = 100 before tax.
Two traps to avoid
- Up then down does not return you to the start. +50% and then −50% leaves you at 75% of where you began.
- Stacked discounts are not added. 20% off and then 10% off is 28% off in total, not 30%.
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