How to calculate percentages
Almost every percentage question is one of three sums: what is X percent of a number, what percent is one number of another, or how much did a value go up or down. Learn those three shapes and you can handle discounts, marks, tips, tax and growth without second-guessing yourself.
A percentage is just a fraction out of 100. The percentage calculator covers the three common cases in one place; this guide explains each so you know which to use and can check the maths yourself.
1. Percent of a number
To find a percentage of a value, convert the percent to a decimal and multiply:
$$\text{result} = \frac{P}{100} \times N$$
For example, 15% of 240 is 0.15 × 240 = 36. This is the sum behind tips, VAT and "20% off" offers.
2. What percent one number is of another
To express one number as a percentage of another, divide and multiply by 100:
$$\text{percent} = \frac{\text{part}}{\text{whole}} \times 100$$
For example, scoring 42 out of 60 on a test is 42 ÷ 60 × 100 = 70%. This is how marks, completion rates and shares of a total are worked out.
3. Percentage increase or decrease
To measure how much a value changed, compare the difference to the original:
$$\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$$
For example, a price rising from 200 to 250 is (250 − 200) ÷ 200 × 100 = 25% increase. A negative result means a decrease. Note that the base is always the original value — a 25% rise followed by a 25% fall does not return you to where you started.
Where each one shows up
- Percent of — discounts, tips, tax, interest on a balance.
- What percent — exam scores, progress, market share.
- Percentage change — price rises, growth, drops over time.
For shop discounts specifically, the discount calculator and VAT calculator are purpose-built and show the final price directly.
Frequently asked questions
How do I turn a percentage into a decimal?
Divide by 100 — so 15% becomes 0.15. Multiply by 100 to go the other way.
Why is a 25% rise then a 25% fall not break-even?
Because the two percentages are taken from different bases. The fall is calculated on the higher amount, so it removes more than the rise added.
How do I add a percentage to a number?
Work out the percent of the number and add it on, or multiply by (1 + P/100). Adding 15% to 240 gives 240 × 1.15 = 276.
Calculate a percentage
Open the percentage calculator and pick the case you need. For related everyday tools, see our guide to online calculators.
