Percentage pitfalls
- An increase then a decrease of the same rate don't cancel out: +20% then −20% gives 1.2 × 0.8 = 0.96, a 4% fall.
- To find a price before an increase, divide by the multiplier: £138 after a 15% rise was 138 / 1.15 = £120, not 138 minus 15%.
- Discounts don't add up: −30% then −10% is −37%, not −40%.
- Points or percent? A rate going from 5% to 6% rises by one percentage point, but by 20%.
Markup or margin?
Markup compares profit with the cost price; margin compares it with the selling price. An item bought for 40 and sold for 65 has a 62.5% markup and a 38.5% margin.
Formulas worth knowing
- t% of a number: number × t / 100. 15% of 80 = 12.
- Proportion: part / total × 100. 18 out of 24 = 75%.
- Percentage change: (final − start) / start × 100. From 250 to 290: +16%.
- Multiplier: 1 + t / 100 for an increase, 1 − t / 100 for a decrease. A 15% rise means multiplying by 1.15; a 15% fall by 0.85.
- Original value: final / multiplier. After +15%, a price of 138 was 138 / 1.15 = 120.
- Successive changes: multiply the multipliers. +10%, −5%, +3% give 1.1 × 0.95 × 1.03 = 1.0764, i.e. +7.64% (not +8%).
Everyday examples
- A pay rise from 2,000 to 2,060: +3%. If inflation is 2% that year, real purchasing power rises by about 1% (1.03 / 1.02 = 1.0098).
- Sales: −30% then a further −10% at the till on an 80 item: 80 × 0.7 × 0.9 = 50.40, a real 37% discount.
- A builder's invoice of 1,500 excluding VAT at 20%: 1,800 including VAT, of which 300 is VAT.
- A shop price of 59.99 including 20% VAT: 49.99 excluding VAT.
- An interest rate going from 3% to 4%: +1 percentage point, but +33% in relative terms.
For students
These calculations come up throughout secondary school (multipliers, repeated percentage change, average rate). The “Successive changes” block also gives the average rate per period, found by taking the n-th root of the overall multiplier. Every result shows its formula: copy it to show your working.
For a weighted average of grades, see the grade average calculator; for a mortgage and its interest, the mortgage simulator.
Guide written and checked by Erwan Hautot · updated 6 November 2026.