How it works
The four percentage calculations you'll ever need
Almost every real-world percentage question is one of four shapes. Once you spot which shape a problem is, the calculation is the same each time.
1. Find X% of Y
Turn the percentage into a decimal (÷ 100) and multiply.
20% of £65 → 0.20 × 65 = £13.
7.5% of £1,200 → 0.075 × 1,200 = £90.
2. What percentage is A of B?
Divide A by B, multiply by 100.
£34 out of £200 → 34 / 200 × 100 = 17%.
45 out of 60 questions → 45 / 60 × 100 = 75%.
3. Percentage increase or decrease
((new − old) / old) × 100. Positive = rise, negative = fall.
Price goes from £80 to £92: (92 − 80) / 80 × 100 = +15%.
Price goes from £80 to £68: (68 − 80) / 80 × 100 = −15%.
4. Increase or decrease a number by X%
Multiply by (1 ± X/100).
Increase £200 by 12% → 200 × 1.12 = £224.
Decrease £200 by 12% → 200 × 0.88 = £176.
A common shortcut: to add VAT (20%) to a net price, multiply by 1.20.
Reverse percentage: the one that trips everyone up
If something has already been increased or decreased, you can't just subtract the percentage. Example: the sale price is £68 after a 15% discount — what was the original?
Sale price = original × (1 − 0.15) = original × 0.85. So original = 68 / 0.85 = £80.
Same idea with VAT: £240 gross at 20% → net = 240 / 1.20 = £200. People often wrongly subtract 20% of £240 (= £48) to get £192 — which is incorrect by £8.
Percentage vs percentage points
A small but important distinction. If an interest rate rises from 4% to 5%, that's a 1 percentage point rise — but a 25% relative increase (because 1 is 25% of 4). Financial commentators use both, and mixing them up inflates or deflates stories by orders of magnitude.
Everyday British uses
- Sales and discounts — "30% off" means new price = old × 0.70.
- Tips in restaurants — discretionary service is usually 10–12.5%. Some add it automatically to the bill.
- Mortgage rate movements — expressed in basis points (1 bp = 0.01%); a 25 bp cut is a 0.25 percentage point cut.
- NHS waiting-list statistics — often expressed as percentage of patients seen within 18 weeks.
- Wage rises — compare annual rises against CPI inflation to see real-terms change.
Quick mental-maths shortcuts
- 10% — shift the decimal one place left. 10% of £47.50 = £4.75.
- 5% — take 10% and halve it. 5% of £47.50 = £2.375.
- 1% — shift the decimal two places left. 1% of £47.50 = £0.475.
- 15% — 10% + 5%. 15% of £47.50 = £4.75 + £2.375 = £7.125.
- 20% — double 10%. 20% of £47.50 = £9.50.
- Percentages reverse: X% of Y equals Y% of X. 18% of 50 is the same as 50% of 18 = 9.