How to calculate a percentage
Almost every percentage problem is one of five questions. This guide gives the formula for each, a worked example with real numbers, and the two mistakes that cause most wrong answers.
The short version
- Decide which question you are asking. A share of a number, one number as a percent of another, a change between two values, or a number plus or minus a percent.
- Pick the matching formula. They are listed in the table below.
- Identify the base. The base is the whole you are comparing to, and it is where most mistakes happen.
- Calculate, then sanity-check. Does the answer make sense? 20% of 150 should be less than half of 150.
Skip the arithmetic. The free Percentage Calculator does this for you, shows the formula and the working with your own numbers, and runs in your browser - nothing you type is uploaded. Also useful: Easy Grader.
The five formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X × Y ÷ 100 | 20% of 150 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 ÷ 150 × 100 = 20% |
| % change from A to B | (B − A) ÷ A × 100 | 80 → 100 is +25% |
| Add X% to Y | Y × (1 + X ÷ 100) | 200 + 15% = 230 |
| Subtract X% from Y | Y × (1 − X ÷ 100) | 200 − 15% = 170 |
Worked examples
A discount. A pair of shoes costs 2,400 and is 15% off. The discount is 15 × 2,400 ÷ 100 = 360, so you pay 2,400 − 360 = 2,040. In one step: 2,400 × 0.85 = 2,040.
A test score. You answered 37 of 45 questions correctly: 37 ÷ 45 × 100 = 82.2%.
A change. Monthly sales rose from 80 to 100 units: (100 − 80) ÷ 80 × 100 = +25%. If they fall from 100 back to 80 the change is (80 − 100) ÷ 100 × 100 = −20%. The same 20-unit gap is a different percentage, because the base changed.
Reverse percentages: finding the original
If a price after a 20% discount is 80, the original was not 80 + 20% = 96. After the discount you are paying 80% of the original, so:
The same idea works for tax: a price including 17% tax of 117 had a pre-tax price of 117 ÷ 1.17 = 100.
Percent versus percentage points
If an interest rate goes from 4% to 5%, it rises by 1 percentage point, which is a 25% increase in the rate (1 ÷ 4). Both statements are true; they answer different questions, so be clear about which one you mean.
The two mistakes that cause most errors
- Using the wrong base. A 20% drop followed by a 20% rise does not return to the start: 100 → 80 → 96.
- Adding percentages that have different bases. A 10% discount followed by another 10% is 19% off, not 20%: 100 × 0.9 × 0.9 = 81.