Percentage Calculator
This percentage calculator answers the three questions every percentage problem boils down to: what is X% of Y, X is what percent of Y, and X is Y% of what. Pick a mode, type two numbers, and it returns the answer, the formula with your numbers in it, the decimal form and the full working. Below the tool you will find the formulas, worked examples and the mistakes that trip people up.
How to use the percentage calculator
- Choose a mode with the buttons at the top: X% of Y, X is what % of Y, or X is Y% of what.
- Type your two numbers. The calculator opens in X% of Y mode with 15 and 80 filled in, so the first answer you see is
15% of 80 = 12. - Read the answer at the top. Underneath it the formula is written out with your numbers, followed by the decimal form and the numbered working steps.
- Use the copy buttons to grab the result, the working, or a link that reopens the calculator with the same numbers.
In X% of Y mode the calculator also prints a quick table of 5%, 10%, 15%, 20%, 25%, 50% and 75% of your Y value. With the default 80 that table reads 4, 8, 12, 16, 20, 40 and 60, which is handy when you are comparing a few options at once, such as different down payments or tip levels.
The other two modes have their own defaults. 18 is what % of 24 gives 75%, and 12 is 15% of what gives 80. If your question is only ever the second kind, the what percent of calculator opens straight in that mode and spells out the division.
The three percentage questions and their formulas
Every basic percentage problem has three numbers in it: a percent, a whole (the amount you are taking a percentage of) and a part. You always know two of them and want the third. That gives exactly three questions, and each has one formula.
These are not three separate facts to memorize. They are one relationship, part = rate × whole, rearranged three ways, where the rate is the percent written as a decimal. If you know any two of the three, the third follows. The guide to calculating percentages walks through that single relationship from the ground up.
| How the question is worded | What you know | Mode to use | Default example |
|---|---|---|---|
| What is 15% of 80? | percent and whole | X% of Y | 12 |
| 18 is what percent of 24? | part and whole | X is what % of Y | 75% |
| 12 is 15% of what number? | part and percent | X is Y% of what | 80 |
The word of almost always sits right in front of the whole. In “15% of 80” the whole is 80; in “18 is what percent of 24” the whole is 24. Find the of and you have found the number that goes on the bottom of the division.
Worked examples
Example: what is 35% of 240?
Percent and whole are known, so this is the first formula.
35% of 240 is 84. A quick sense check: 25% of 240 is 60 and 50% is 120, so 35% has to land between them, closer to 60. It does.
Example: 27 is what percent of 45?
Part and whole are known. Divide the part by the whole.
27 is 60% of 45. The decimal 0.6 and the percentage 60% are the same quantity written two ways; multiplying by 100 only moves the decimal point two places.
Example: 63 is 35% of what?
Part and percent are known, so you are working back to the whole.
The whole is 180. Check it forwards: 0.35 × 180 = 63. Going backwards is where most errors happen, so the forward check is worth the extra few seconds.
Example: 7.5% of $1,240
A money amount with a decimal percent works exactly the same way.
7.5% of $1,240 is $93. If the 7.5% is a sales tax rate (used here only as an example rate), the sales tax calculator adds it on and can also take tax back out of a total.
Why the decimal form does the work
“Percent” means “per hundred,” so 15% is 15 out of every 100, or 15 ÷ 100 = 0.15. That decimal is the number you actually multiply by. The calculator shows it for every answer because it is the step people skip in their heads and then get wrong.
To convert, move the decimal point two places to the left: 15% becomes 0.15, 7.5% becomes 0.075, 120% becomes 1.2, and 0.4% becomes 0.004. The percent to decimal calculator handles awkward cases and shows the fraction too, and the decimal to percent calculator goes the other way.
Percentages you can do in your head
Three anchor values cover most mental arithmetic. 10% is the number with the decimal point moved one place left. 1% is the point moved two places. 50% is half. Everything else is built from those.
X% of Y equals Y% of X
Because multiplication can be done in either order, X% of Y and Y% of X are always equal. That turns some hard problems into easy ones. 8% of 50 looks awkward, but 50% of 8 is obviously 4, and so is 8% of 50. Likewise 16% of 25 equals 25% of 16, which is 4.
Percentages over 100%, under 1%, and other edge cases
Nothing in the formulas limits a percent to between 0 and 100. The calculator accepts any number and the arithmetic stays the same.
- Over 100%. 250% of 40 is
2.5 × 40 = 100. A percentage above 100 just means more than the whole: 100% of something is all of it, 200% is twice it. - Under 1%. 0.5% of 3,000 is
0.005 × 3,000 = 15. Small percentages are where a misplaced decimal point causes the biggest errors, so check that 0.5% became 0.005 and not 0.05. - A part bigger than the whole. In “X is what % of Y” mode, a part larger than the whole gives a result over 100%. 30 is 150% of 20. That is a correct answer, not an error.
- A whole of zero. “5 is what percent of 0” has no answer, because it would mean dividing by zero. The same applies to “X is 0% of what.”
When a different percentage tool fits better
The three modes above cover plain percentages. Several common questions look similar but use a different base or a different formula, and each has a dedicated calculator on this site.
| Your question | What makes it different | Tool |
|---|---|---|
| Price went from $80 to $100. By what percent? | Measures change relative to the old value | Percentage change calculator |
| Two quotes are $40 and $50. How far apart in %? | Neither number is the base; uses their average | Percentage difference calculator |
| Paid $96 after a 20% discount. What was the original? | Works back from a changed amount | Reverse percentage calculator |
| 30% off $85 — what do I pay? | Subtracts the percentage from the price | Percent off calculator |
| 18% tip on a $64.50 bill split two ways | Adds a percentage, then divides | Tip calculator |
The “paid $96 after 20% off” case catches people out with the X is Y% of what mode. $96 is not 20% of the original; it is the 80% that was left. Entering 96 is 80% of what gives the right original price of $120, while 96 is 20% of what gives a nonsense 480.
Common mistakes
- Multiplying by the percent instead of its decimal. 15 × 80 = 1,200, not 12. Divide the percent by 100 first.
- Swapping the part and the whole. “What percent of 60 is 15” is 25%. “What percent of 15 is 60” is 400%. The number after of goes on the bottom.
- Adding percentages of different wholes. 10% of your salary plus 10% of your partner’s is not 20% of either salary. Percentages only add directly when they refer to the same whole.
- Treating a discount as a reverse percentage. If something is 20% off, the price you paid is 80% of the original, as the table above shows.
- Stacking percentages by adding them. 20% off and then a further 10% off is 28% off in total, not 30%, because the second discount applies to an already reduced price. The guide on taking a percentage of a percentage explains why.
- Rounding too early. Keep the full decimal until the last step and round once at the end. Rounding 1/3 to 33% and then multiplying by 900 gives 297 instead of 300.
For scores written as “15 out of 20,” the X out of Y as a percentage guide has a conversion table covering the most common test totals.
Frequently asked questions
What is 15% of 80?
15% of 80 is 12. Convert 15% to a decimal by dividing by 100, which gives 0.15, then multiply: 0.15 × 80 = 12. As a mental check, 10% of 80 is 8 and 5% is half of that, 4, so 15% is 8 + 4 = 12. This is the default example the calculator opens with.
How do you calculate a percentage of a number?
Divide the percentage by 100 to turn it into a decimal, then multiply that decimal by the number. For 35% of 240, that is 0.35 × 240 = 84. The same method works for any percent, including values above 100 or below 1. Use the X% of Y mode of the calculator to see the steps written out with your own numbers.
What is 20% of 150?
20% of 150 is 30. Written as a decimal, 20% is 0.2, and 0.2 × 150 = 30. A quick way to see it: 10% of 150 is 15, and 20% is double that. The same doubling trick works for any number, since 20% is always twice 10%.
How do I find what percent one number is of another?
Divide the first number (the part) by the second (the whole) and multiply by 100. For 18 out of 24, 18 ÷ 24 = 0.75, and 0.75 × 100 = 75%. The number that follows the word “of” in your question is the whole and belongs on the bottom of the division. The calculator’s X is what % of Y mode does this for you.
How do I find the whole when I know the part and the percent?
Divide the part by the percent written as a decimal. If 12 is 15% of a number, the number is 12 ÷ 0.15 = 80. Check by going forwards: 15% of 80 is 12. This is the X is Y% of what mode. It is also how you find an original price when you know what a certain percentage of it was.
Is X% of Y the same as Y% of X?
Yes, always. Both equal X × Y ÷ 100, and multiplication gives the same result in either order. That makes some problems much easier: 4% of 75 is the same as 75% of 4, which is 3. When one version of the question looks awkward, try swapping the two numbers and see whether the other version is simpler to do in your head.
What is 25% of 200?
25% of 200 is 50. Since 25% is one quarter, you can divide 200 by 4 instead of multiplying by 0.25. Common percentages have simple fraction equivalents: 50% is a half, 25% a quarter, 20% a fifth, 10% a tenth. Using the fraction is often the fastest way to work one out without a calculator.
Can a percentage be more than 100%?
Yes. A percentage over 100 means more than the whole. 150% of 40 is 60, and 250% of 40 is 100. In the X is what % of Y mode, any part larger than the whole gives a result above 100%, such as 30 being 150% of 20. The only limit is a whole of zero, which has no percentage because you cannot divide by zero.
Related calculators
Guides that use this calculator
Longer explanations of the method behind it, with worked examples.
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