Percentages — guides, formulae and calculator
A percentage is simply "part of a hundred", and almost every percentage question is one of a few types. Here you will find a separate guide for each — with the formula, step-by-step worked examples and frequently asked questions — plus a calculator that shows the full working.
How to calculate percentages in the three types of question: a percentage of an amount, one number as a percentage of another, and finding the whole. Formulae, worked examples and a free calculator.
How to find a percentage of an amount: the formula, mental shortcuts for quick calculation (10%, 1%, combined percentages) and real-life worked examples — discounts, tips and VAT at 20%.
How to work out a percentage discount in a sale, including the trap of stacked discounts (20% then another 10% is not 30%). Formulae and worked examples with prices in pounds.
How to work out a percentage increase and a percentage decrease, including the classic trap: a 50% rise followed by a 50% fall does not return to the original price. Formulae and worked examples.
How to find the original amount after a percentage increase or decrease: divide by the multiplier, never subtract the percentage. Worked examples with sale prices, VAT and salaries, and the common mistake to avoid.
How to calculate compound interest: multiply by the same multiplier once for every year, using the formula P × (1 + r)ⁿ. Worked examples with savings, depreciation and finding the number of years, plus the difference from simple interest.
How to convert a fraction to a percentage, a percentage to a decimal and back — the useful table (1/2 = 50%, 1/4 = 25% and more), the formulae and step-by-step worked examples.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: