How to use the percentage calculator
Type into any of the three boxes above. The answer updates as you type – no button needed.
- What is X% of Y? – a discount, a tip, tax or a share of a total.
- X is what % of Y? – a test score, a completion rate or a market share.
- % change from X to Y – a price rise, salary increase or drop in sales.
Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | \frac{X}{100} \times Y | 15% of 1,200 = 180 |
| X is what % of Y? | \frac{X}{Y} \times 100 | 45 of 180 = 25% |
| % change from X to Y | \frac{Y - X}{|X|} \times 100 | 80 → 100 = +25% |
| Y after an X% increase | Y \times \left(1 + \frac{X}{100}\right) | 1,200 + 18% = 1,416 |
| Y after an X% decrease | Y \times \left(1 - \frac{X}{100}\right) | 1,200 − 15% = 1,020 |
| Original before an X% increase | \frac{\text{final}}{1 + \frac{X}{100}} | 1,416 ÷ 1.18 = 1,200 |
Worked examples
\text{Discount} = \frac{15}{100} \times 1{,}200 = 180\text{Sale price} = 1{,}200 - 180 = 1{,}020\frac{45}{60} \times 100 = 75\%\frac{46{,}000 - 40{,}000}{40{,}000} \times 100 = \frac{6{,}000}{40{,}000} \times 100 = 15\%A 15% increase.
\text{Before tax} = \frac{1{,}416}{1.18} = 1{,}200Taking 18% off 1,416 would be wrong (1,161.12), because the tax was added to the smaller amount.
Percentage change, difference and points
| Term | Meaning | 4% → 5% |
|---|---|---|
| Percentage change | Change relative to the starting value | +25% |
| Percentage points | Simple difference between two percentages | +1 point |
| Percentage difference | Difference relative to the average of the two values | 22.2% |
News reports often mix these up. An interest rate rising from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate.
Mental math shortcuts
- 10%: move the decimal point one place left – 10% of 350 is 35.
- 5%: half of 10% – 5% of 350 is 17.5.
- 1%: move the decimal point two places – 1% of 350 is 3.5.
- Swap trick: X% of Y equals Y% of X – 8% of 50 is the same as 50% of 8, which is 4.
Common percentages as fractions
| Percent | Fraction | Decimal |
|---|---|---|
| 10% | \tfrac{1}{10} | 0.1 |
| 12.5% | \tfrac{1}{8} | 0.125 |
| 20% | \tfrac{1}{5} | 0.2 |
| 25% | \tfrac{1}{4} | 0.25 |
| 33.3% | \tfrac{1}{3} | 0.333 |
| 50% | \tfrac{1}{2} | 0.5 |
| 66.7% | \tfrac{2}{3} | 0.667 |
| 75% | \tfrac{3}{4} | 0.75 |
| 80% | \tfrac{4}{5} | 0.8 |
| 100% | 1 | 1 |
Increases and decreases don't cancel out
A 20% rise followed by a 20% fall does not bring you back to the start: 100 → 120 → 96, a 4% loss overall. The fall is worked out on the bigger number, so it takes away more than the rise added.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 1,200 = 0.15 × 1,200 = 180.
How do I work out a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100: 20 ÷ 80 × 100 = 25%.
How do I add a percentage to a number?
Multiply by 1 plus the percentage as a decimal. 1,200 plus 18% tax is 1,200 × 1.18 = 1,416.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount. If 1,020 is the price after 15% off: 1,020 ÷ 0.85 = 1,200.
Why can’t the starting value be zero for percentage change?
Percentage change divides by the starting value, and dividing by zero is undefined.