How to calculate percentages
A percentage is just a fraction of 100. The three most common everyday questions each have a simple formula:
- X% of Y = (X ÷ 100) × Y — e.g. 20% of 150 = 30
- X is what % of Y = (X ÷ Y) × 100 — e.g. 30 is 20% of 150
- % change = ((New − Old) ÷ Old) × 100 — e.g. 80 → 100 is a 25% increase
Working out percentages of money
Most everyday percentage questions are really money questions. The method never changes — convert the percent to a decimal and multiply — but it helps to recognise the shape of each one:
- A discount: 25% off a 80 item → 80 × 0.25 = 20 off, so you pay 60
- A tip: 15% on a 60 bill → 60 × 0.15 = 9
- Sales tax added: 8% on 50 → 50 × 1.08 = 54
- Tax removed from a total: 54 including 8% → 54 ÷ 1.08 = 50
- A pay rise: 40,000 up 5% → 40,000 × 1.05 = 42,000
- Share of a total: 300 spent on rent out of 1,200 income → (300 ÷ 1,200) × 100 = 25%
The one that trips people up is removing a percentage. To strip tax out of a gross figure you must divide by 1 + the rate, not subtract the percentage — subtracting 8% from 54 gives 49.68, which is wrong.
Percentage shortcuts you can do in your head
| Percent | Mental shortcut | Example on 240 |
|---|---|---|
| 1% | Move the decimal two places left | 2.40 |
| 5% | Find 10%, then halve it | 12.00 |
| 10% | Move the decimal one place left | 24.00 |
| 15% | 10% plus half of that again | 36.00 |
| 20% | Find 10%, then double it | 48.00 |
| 25% | Divide by 4 | 60.00 |
| 33⅓% | Divide by 3 | 80.00 |
| 50% | Halve it | 120.00 |
| 75% | Halve it, then add half again | 180.00 |
A useful trick: X% of Y always equals Y% of X. If 18% of 50 looks awkward, flip it — 50% of 18 is just 9.
Percentage points vs percent
These are not the same, and mixing them up is one of the most common errors in news reporting. If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate itself. Use "percentage points" when comparing two percentages directly, and "percent" when describing relative change.
How to do percentages on a calculator
You don't need a % key at all. To find a percentage of a number, multiply by the decimal: for 20% of 150, type 150 × 0.2. To add a percentage, multiply by 1 + the rate (150 × 1.2); to remove one, divide by it (180 ÷ 1.2). On calculators that do have a % key, the behaviour varies by model — the decimal method always works and is worth learning instead.
How do I calculate a percentage of an amount of money?
Multiply the amount by the percentage divided by 100. For 15% of 60, that's 60 × 0.15 = 9. Use the "% of" mode above and it works it out as you type.
How do I find what percent one number is of another?
Divide the part by the whole, then multiply by 100: (30 ÷ 150) × 100 = 20%. That's the "X is what % of Y" mode above.
What's the difference between percentage points and percent?
Going from 10% to 15% is a 5 percentage-point rise, but a 50% increase. They're different things — percentage points compare two percentages, percent describes relative change.
How do I remove a percentage (like tax)?
To find the pre-tax price from a total, divide by (1 + rate). e.g. 120 including 20% tax = 120 ÷ 1.2 = 100. Don't subtract the percentage — that gives the wrong answer.
How do I calculate percentage change?
Subtract the old value from the new, divide by the old value, then multiply by 100: ((100 − 80) ÷ 80) × 100 = a 25% increase. A negative result is a decrease.
What is a percentage of a percentage?
Multiply the two decimals. 50% of 20% is 0.5 × 0.2 = 0.1, which is 10%. This comes up with stacked discounts — two 20% discounts are not 40% off, they're 36% off.