Guide · updated 12 August 2026
Percentage calculator: learn to work out discounts and increases easily
A percentage is a simple idea, but applying it often goes wrong in the same places. This guide covers the basic formulas, mental-maths tricks and the five mistakes that recur in the shop, at work and in dissertations.
A percentage is a multiplier – this settles almost everything
If you have to think about whether to multiply or divide, turn the percentage into a factor first. 25% is 0.25. A 25% discount means you pay 75%, so the factor is 0.75. A 25% increase means a factor of 1.25. Once the factor is clear, the sum is an ordinary multiplication – and the reverse an ordinary division.
A practical example: a coat costs £149 and the discount is 35%. The factor is 0.65, so the price is
149 × 0.65 = £96.85. One calculation, not two.
Mental maths: build everything from ten per cent
Ten per cent is always easy: move the decimal point one step left. £68 → £6.80. The other percentages are built from that in pieces.
- 5% = half of ten → £3.40
- 15% = 10% + 5% → 6.80 + 3.40 = £10.20
- 20% = 10% twice → £13.60
- 25% = a quarter → divide by four → £17.00
- 30% = 10% three times → £20.40
This is enough to size up a restaurant bill, a tip or a sale sign in seconds. For an exact result it's still worth using the percentage calculator, especially when decimals are involved.
The five most common mistakes
1. Undoing a discount by adding the same percentage back. If the price is £84 and the discount was
30%, the original price isn't 84 × 1.3 = £109.20 but 84 / 0.7 = £120. When you go backwards,
you divide.
2. Adding successive discounts together. −30% and −20% isn't −50% but −44%. The factors are multiplied: 0.7 × 0.8 = 0.56, so you pay 56%. The same goes for increases: two 10% increases are 21%, not 20%.
3. The wrong reference number in a change. A change is always worked out from the starting value. 100 → 120 is +20%, but 120 → 100 is −16.67%. The same amount, a different percentage, because the divisor changes.
4. Confusing per cent and percentage point. A rate of 2% → 3% is one percentage point but 50% more interest cost. The news uses both – read carefully which one is meant.
5. Rounding too early. If you round mid-way, the error compounds in the next step. Round only the final result, and with money to the nearest penny.
Increases: pay, rent and prices
An increase is worked out with the same logic as a discount, the factor is just larger than one. A salary of £2,850
and a 3.5% rise gives 2,850 × 1.035 = £2,949.75, i.e. £99.75 more a month. Two things are worth
remembering. First, the rise is gross: the part that reaches your account is smaller, and a rise can even push up your
tax rate. Second, a percentage rise widens the differences in pounds – 3% is £66 on a £2,200 salary and £126 on £4,200.
You can see both figures with the salary calculator.
Basket discounts: work from the whole total, not line by line
At the till, percentages easily get muddled when there are several items. If the basket has three items – £39, £24
and £12 – and 20% is promised off the whole purchase, don't work out each line separately and round in between. Add the
total first, 39 + 24 + 12 = £75, and only then 75 × 0.8 = £60. Working from the total is faster
and less error-prone than tapping in line by line.
Double discounts work with the same logic. If a membership card gives a further 10% at the till off the
already-discounted price, the factor is 0.8 × 0.9 = 0.72, so you pay 72% of the original, not 70%. You'll
see the same logic in the discount calculator, which shows the saving in both pounds
and per cent.
Percentages in a dissertation and in reports
In survey results the most common mistake is reporting a share without the sample size. "68% of respondents" means something different when there are 25 respondents than when there are 2,500. In a small sample a single respondent can change the share by several percentage points, so always report both the percentage and the number, for example as "68% (n = 25)". That way the reader can judge the reliability of the result themselves. Percentage shares and their confidence interval are covered in the percentages in a dissertation page.
When you need an exact figure
Mental maths is enough for an estimate, but for contracts, invoices and reports it's worth using a calculator and saving the formula. The site's calculators show the formula with the numbers filled in, so you can paste it straight into an email or your notes – then the recipient can see what the figure is based on too.