How to calculate percentages: discounts, increases and VAT
The four most common percentage operations, with formulas and worked examples.
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The basic idea
“Per cent” means “out of a hundred”. 15% of something is 15 parts out of 100, i.e. multiplying by 0.15. Almost every percentage calculation comes down to turning the percentage into a decimal by dividing by 100.
1. Find X% of an amount
Formula: result = amount × X / 100.
Example: 20% of £80 is 80 × 20 / 100 = £16.
2. What percentage one amount is of another
Formula: percentage = part / total × 100.
Example: if you get 42 out of 60 questions right, you scored 42 / 60 × 100 = 70%.
3. Percentage change between two values
Formula: change = (final value − initial value) / initial value × 100.
Example: if rent goes from 750 to 810, it rises (810 − 750) / 750 × 100 = 8%. A negative result is a decrease. Note: it cannot be calculated when the initial value is zero.
4. Apply a discount or an increase
Discount: final price = price × (1 − X / 100). Increase: final price = price × (1 + X / 100).
Example: 60 with a 25% discount becomes 60 × 0.75 = 45.
Common mistakes
- Adding up chained discounts: 20% followed by 10% is not 30% but 28% (0.8 × 0.9 = 0.72).
- Removing VAT by subtracting the percentage: to go from 121 including 21% VAT to the net price, divide by 1.21 (100), don't subtract 21% (95.59).
- Confusing percentage points with percentages: going from 10% to 12% is a rise of 2 points, but 20% in relative terms.