Percentage Calculator
Find a percentage of a number, what percent one number is of another, or the whole from a part and its percentage.
Result
Percentage of the number: 36
Plain arithmetic on the numbers you entered, with nothing added or estimated.
- Decimal rate
- 0.15
- Whole minus the part
- 204
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How to use the Percentage Calculator
- Choose the question that matches yours. Each one knows two of the three numbers and finds the third.
- For a percentage of a number, enter the percentage P and the number X.
- For what percent one number is of another, enter the part X and the whole Y. The whole can be any number except 0.
- For the whole, enter the part X and the percentage P it represents. The percentage can be any number except 0.
- Read the answer, its decimal rate, and the whole minus the part. Use Percentage Change instead when comparing an old value with a new one.
One equation, three questions
OpenStax defines n% as n/100, so a percentage is a rate per hundred. Every
everyday percentage question uses the same relation between a part, a whole
and that rate:
part = (percentage ÷ 100) × wholeTwo of the three numbers are known and the third is missing. The question you pick decides which one:
What is P% of X? part = P ÷ 100 × XX is what percent of Y? percentage = X ÷ Y × 100X is P% of what? whole = X ÷ (P ÷ 100)The second and third rearrange the first. Dividing both sides by the whole leaves the rate; dividing both sides by the rate leaves the whole. That is also a way to check an answer: put it back into the first line and the part should come out as entered.
Which number goes where
The word “of” marks the whole, the number that stands for 100%. In “what is 15% of 240” the whole is 240. In “15 is what percent of 60” it is 60, and 15 is the part. In “30 is 20% of what” the whole is the unknown and 30 is the part.
The whole and the percentage are divisors in the last two questions, so the page asks for a value other than 0 there. Negative values are accepted; the answer takes the sign the arithmetic gives it.
The page also shows the rate as a decimal and the whole minus the part, which is what is left after a discount or how far a total still has to go.
The arithmetic follows OpenStax Contemporary Mathematics, and the three forms of the percent equation follow OpenStax Prealgebra 2e, section 6.2.
With your numbers
- Percentage as a decimal = 15% = 0.15.
- Result = 240 × 0.15 = 36.
Quick reference
Plain arithmetic on the numbers you entered, with nothing added or estimated.
| Example | Result |
|---|---|
| What is 15% of 240 | Percentage of the number: 36 |
| What is 20% of 80 | Percentage of the number: 16 |
| What is 7.5% of 320 | Percentage of the number: 24 |
| What is 125% of 40 | Percentage of the number: 50 |
| 15 is what percent of 60 | Part as a percentage of the whole: 25% |
| 3 is what percent of 8 | Part as a percentage of the whole: 37.5% |
| 120 is what percent of 80 | Part as a percentage of the whole: 150% |
| 30 is 20% of what | The whole: 150 |
| 12 is 40% of what | The whole: 30 |
| 45 is 15% of what | The whole: 300 |
Common questions about the Percentage Calculator
- What does percent mean?
- Percent means per hundred. Fifteen percent is 15 divided by 100, or 0.15.
- How are the three questions related?
- They are one equation, part = percentage × whole, with a different number missing each time. Multiply to find the part, divide the part by the whole to find the percentage, and divide the part by the percentage to find the whole.
- Which number is the whole in "X is what percent of Y"?
- The number after "of". It is the one that counts as 100%, so it goes on the bottom of the division.
- Can a percentage be greater than 100?
- Yes. A part bigger than the whole gives more than 100%, and 125% of a number is one and a quarter times that number.
- Why can the whole or the percentage not be 0?
- Both questions divide by that number, and dividing by zero has no answer. Zero percent of any whole is zero, so it cannot point back to a single whole.
- What happens with negative numbers?
- The same arithmetic applies and the signs follow the usual rules. A negative part of a positive whole gives a negative percentage, which usually means a loss or a shortfall.
- Is this a percentage-change calculator?
- No. Percentage change compares an old value with a new one and divides by the old value. Use Percentage Change for that.