Percentage calculator
Two questions cover most percentage work: what a percentage of a number comes to, and what one number is as a percentage of another. Both are below.
Result
- 15.00% of 200.00
- 30.00
- 45.00 as a percentage of 180.00
- 25.00%
Worked examples
Finding a percentage of a number
A jacket costs $240. What is 15% of that?
- 15 ÷ 100 = 0.15
- 0.15 × 240 = 36
15% of $240 is $36.
Finding what percentage one number is of another
You scored 45 out of 180 on a test.
- 45 ÷ 180 = 0.25
- 0.25 × 100 = 25
45 is 25% of 180.
What a percentage actually is
A percentage is a fraction with 100 fixed as the denominator. "Per cent" is Latin for "by the hundred", so 25% is simply another way of writing 25/100, or 0.25. Every percentage calculation is therefore a fraction calculation wearing different clothes.
That is worth holding onto, because it explains why the arithmetic works. To find a percentage of something you convert the percentage to a decimal and multiply. To find what percentage one number is of another you divide and then scale by 100. There is no third rule to learn.
Converting between percentages, decimals and fractions
To go from a percentage to a decimal, divide by 100 — move the decimal point two places left. 7.5% becomes 0.075. To go the other way, multiply by 100: 0.4 becomes 40%.
Fractions convert by division. 3/8 is 3 ÷ 8 = 0.375, which is 37.5%. Some fractions do not terminate: 1/3 is 0.3333…, or 33.33% to two decimal places, and rounding it is the reason three shares of a whole sometimes appear to add to 99.99%.
Where percentages mislead
Percentages always describe a base, and the base is easy to lose track of. A 50% fall followed by a 50% rise does not return you to where you started — 100 falls to 50, then rises by 50% of 50, which is 25, leaving 75.
The same trap appears in reporting. A drug that cuts risk from 2 in 1,000 to 1 in 1,000 has reduced relative risk by 50%, but absolute risk by only 0.1 percentage points. Both figures are true; they answer different questions.
Formula
part = (percentage ÷ 100) × whole • percentage = (part ÷ whole) × 100
Percentage, decimal and fraction equivalents
The conversions worth knowing by sight. Anything else can be derived by dividing.
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.3333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 66.67% | 0.6667… | 2/3 |
| 75% | 0.75 | 3/4 |
| 100% | 1.0 | 1/1 |
| 150% | 1.5 | 3/2 |
Mental shortcuts
Percentages are commutative — x% of y always equals y% of x — which is often the fastest route.
| Want | Do this | Example |
|---|---|---|
| 10% | Move the decimal one place left | 10% of 84 = 8.4 |
| 5% | Halve the 10% | 5% of 84 = 4.2 |
| 1% | Move the decimal two places left | 1% of 84 = 0.84 |
| 15% | 10% plus half of it | 8.4 + 4.2 = 12.6 |
| 20% | Double the 10% | 16.8 |
| Awkward pairs | Swap the numbers | 4% of 75 = 75% of 4 = 3 |
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 15% of 200: 15 ÷ 100 = 0.15, then 0.15 × 200 = 30.
How do I work out what percentage one number is of another?
Divide the part by the whole, then multiply by 100. For 45 out of 180: 45 ÷ 180 = 0.25, and 0.25 × 100 = 25%.
What is the difference between percentage and percentage point?
A percentage point is the arithmetic gap between two percentages. If interest rises from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate itself.
Can a percentage be more than 100?
Yes. 100% is the whole, so anything larger is more than the original. A value that triples has grown to 300% of its starting size, which is a 200% increase.
Why do percentages sometimes not add up to 100?
Usually rounding. Three equal shares are 33.33% each, totalling 99.99%. It can also mean the categories overlap or are not exhaustive.
How do I add a percentage to a number?
Multiply by one plus the percentage as a decimal. Adding 15% to 200 is 200 × 1.15 = 230. Adding a percentage and then removing the same percentage does not return you to the start.
What is 10% of a number quickly?
Move the decimal point one place to the left. 10% of 84 is 8.4, and every other percentage can be built from that — 5% is half of it, 20% is double, 15% is 10% plus 5%.
Is x% of y the same as y% of x?
Yes, always, because both are x × y ÷ 100. This is genuinely useful: 4% of 75 is awkward, but 75% of 4 is obviously 3.
How do I remove a percentage that is already included?
Divide rather than subtract. A $120 total including 20% tax has a pre-tax value of 120 ÷ 1.2 = $100, not $96.
How do I calculate a percentage without a calculator?
Break it into 10% and 1% blocks. For 23% of 400: 10% is 40, so 20% is 80; 1% is 4, so 3% is 12; the total is 92.