What this percentage calculator answers
Most percentage questions are one of three shapes. You know the percent and the number and want the part: what is 18% of 2,450? You know two numbers and want the percent: 42 out of 56 is what percent? Or you know a part and its percent and want the whole: 36 is 15% of what?
Pick the shape that matches your question, type the two numbers you have, and the third appears straight away. The working is shown underneath, so you can copy the method into a spreadsheet or check a figure someone gave you.
Step by step
- Choose the question: X% of a number, X is what % of Y, or X is P% of what.
- Type the two numbers you know. Commas for thousands are fine, so 2,450 and 2450 both work.
- Read the answer on the right, or under the form on a phone. For X% of a number you also see the number with the percent added and taken away.
- Use Copy result to paste the answer into a message, or Copy link to send someone the same sum.
The percentage formula, three ways
A percent is a fraction out of 100. Every percentage sum is the same relationship turned around to find whichever piece is missing.
part = percent ÷ 100 × whole
percent = part ÷ whole × 100
whole = part ÷ (percent ÷ 100)If you remember only the first line you can get the other two by rearranging it. The calculator shows the decimal step, like 18 ÷ 100 = 0.18, because that is the step most people skip when they do it in their head.
Worked example: 18% of 2,450
A client asks for an 18% deposit on a 2,450 job. How much is the deposit?
- Turn the percent into a decimal: 18 ÷ 100 = 0.18
- Multiply by the whole: 0.18 × 2,450 = 441
The deposit is 441. The calculator also shows that 2,450 plus 18% is 2,891, and 2,450 minus 18% is 2,009, which helps when you need a price with a percentage added or taken off.
Now turn it round. If 441 has been paid out of 2,450, choose X is what % of Y: 441 ÷ 2,450 × 100 = 18%. And if you only know that 441 was an 18% deposit, X is P% of what gives 441 ÷ 0.18 = 2,450.
Quick reference: common percentages
| Percent | Fraction | Shortcut |
|---|---|---|
| 10% | 1/10 | Move the decimal point one place left |
| 20% | 1/5 | Find 10% and double it |
| 25% | 1/4 | Halve, then halve again |
| 33.33% | 1/3 | Divide by 3 |
| 50% | 1/2 | Halve it |
| 75% | 3/4 | Take away a quarter |
The 10% trick is the one worth remembering. 10% of 2,450 is 245, so 5% is 122.5 and 15% is 367.5. Most mental percentage maths is built from those pieces.
Where people slip
- Using the wrong whole. "What percent of the class passed?" divides by everyone in the class, not by the number who failed.
- Adding a percent and then taking the same percent off. 100 plus 10% is 110, but 110 minus 10% is 99, not 100. The second 10% is worked out on a bigger number.
- Mixing up percent and percentage points. A rate that moves from 4% to 6% has risen by 2 percentage points, which is a 50% increase. The percentage change calculator handles that second kind of question.
- Averaging percentages from groups of different sizes. 50% of 10 people and 90% of 100 people is not 70% overall; it is 95 out of 110, about 86%.
Frequently asked questions
How do I work out a percentage of a number?
Divide the percent by 100 and multiply by the number. For 15% of 80, that is 0.15 × 80 = 12. On a phone calculator you can also type 80 × 15 and press the % key. Choose X% of a number above and the answer appears as you type, along with the number plus and minus that percent.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you scored 42 out of 56, that is 42 ÷ 56 = 0.75, so 75%. The order matters: the number you are asking about goes on top, and the total it belongs to goes underneath. Choose X is what % of Y to do this.
How do I find the original number from a percentage?
Divide the part by the percent written as a decimal. If 36 is 15% of a total, the total is 36 ÷ 0.15 = 240. This is the sum to use when you know a deposit, a share or a tip and want the full amount it came from. The X is P% of what option does it for you.
How do I calculate an average percentage?
Add up the parts and the wholes separately, then divide. If one test was 18 out of 20 and another was 30 out of 50, that is 48 out of 70, which is 68.6%. Averaging the two percentages, 90% and 60%, would give 75%, which overstates the result because the second test was bigger.
How do I work out a loss percentage?
Take the selling price from what you paid, divide by what you paid, and multiply by 100. Buying for 250 and selling for 200 is a loss of 50, and 50 ÷ 250 × 100 = 20%. The profit margin calculator shows profit and loss against both cost and price.
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