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Percentage Calculator.
Four percentage questions, each with its own line, all live. Type and the answers update.
Results are computed in your browser from the numbers you enter; nothing is sent to us. Double-check anything you rely on. Terms.
Guide
How to use the Percentage Calculator
This page is four small calculators, each built for one question. Pick the one that matches what you are asking, type in two numbers, and the answer updates as you type.
- If you want to know what a slice of something is worth, use the first calculator, What is X% of Y? Put the percent in X (percent) and the whole amount in Y. 15 and 240 gives you 36.
- If you have a part and a whole and want the percent, use the second, X is what percent of Y? The part goes in X, the whole in Y. 30 and 120 gives you 25%.
- If you have a before and an after, use the third, Percent change from X to Y. The old number goes in From (X), the new number in To (Y). 80 to 100 shows a 25% increase; a decrease is shown as a decrease.
- If you need to mark a number up or down, use the fourth, Increase or decrease X by Y%. Enter the starting number in X and the percent in Y (percent); the results show both directions. 240 up 15% is 276; 240 down 15% is 204.
- Enter percents as whole numbers (15, not 0.15), and check the direction before you trust a result. In the change calculator, swapping the two numbers changes the answer.
How the math works
A percent is just a fraction with 100 on the bottom. "15 percent" means 15 out of every 100, so every percent problem is a multiplication or division by 100 in disguise.
Finding a percent of a number means multiplying by that fraction. Finding what percent one number is of another means dividing the part by the whole. Percent change is the difference between two numbers measured against where you started. Increasing or decreasing by a percent is one multiplication: by 1 plus the percent for an increase, by 1 minus the percent for a decrease.
The formula
What is X% of Y: Result = Y × X ÷ 100
X is what percent of Y: Percent = X ÷ Y × 100
Percent change from X to Y: Change = (Y − X) ÷ X × 100
Increase X by Y%: Result = X × (1 + Y ÷ 100). Decrease X by Y%: Result = X × (1 − Y ÷ 100)
In each line, X and Y are the two numbers you type in. In the change formula, X is the old value and Y is the new one. A positive change is an increase; a negative change is a decrease, and the calculator labels it that way.
Worked example
Here are the four calculators run on one set of numbers.
| Question | Math | Answer |
|---|---|---|
| What is 15% of 240? | 240 × 15 ÷ 100 = 240 × 0.15 | 36 |
| 30 is what percent of 120? | 30 ÷ 120 = 0.25, × 100 | 25% |
| Percent change from 80 to 100 | (100 − 80) ÷ 80 = 20 ÷ 80 = 0.25 | +25% |
| Percent change from 100 to 80 | (80 − 100) ÷ 100 = −20 ÷ 100 = −0.20 | −20% |
| 240 increased by 15% | 240 × 1.15, or 240 + 36 | 276 |
| 240 decreased by 15% | 240 × 0.85, or 240 − 36 | 204 |
Look at the two change rows. Going from 80 to 100 is a 25% increase, but going from 100 back to 80 is only a 20% decrease. Same 20-unit gap, different percent, because each is measured against a different starting point. Percent change is not symmetric, and that one fact explains most of the traps below.
The last two rows show the markup and discount shortcut: instead of finding 15% of 240 and then adding or subtracting it, multiply once by 1.15 or 0.85.
The classic traps
Percentage points are not percent
If a conversion rate goes from 2% to 3%, it went up 1 percentage point. It also went up 50%, because (3 − 2) ÷ 2 = 0.5. Both are true, and the second sounds a lot more impressive. When somebody quotes a percent increase of something that is already a percent (a rate, a share, a margin), ask which one they mean.
A 50% drop needs a 100% gain to recover
Lose half of something and you need to double what is left to get back to even: 100 falls to 50, and climbing from 50 back to 100 is a 100% gain. Smaller moves are lopsided too: drop 20% from 100 to 80 and you need 25% to get back. Drop 30% and then gain 30% and you end at 91, not 100. Fall and rise by the same percent and you always finish lower than you started.
Reversing a discount
A price tag says $204 after 15% off. The original price is not 204 plus 15%, which gives 234.60, because the discount was 15% of the original, not of the sale price. Divide instead: 204 ÷ 0.85 = 240. Undo a decrease by dividing by (1 − the percent) and an increase by dividing by (1 + the percent); backing 7% sales tax out of a $256.80 receipt works the same way, 256.80 ÷ 1.07 = 240.
Stacked percents do not add
"30% off, plus an extra 20% off at the register" is not 50% off. It is 100 × 0.70 × 0.80 = 56, which is 44% off, because the second discount applies to the already-reduced price. The same thing happens in reverse with compounding returns.
Quick mental math
Anchor on 10%, which is the number with the decimal point moved one place left: 10% of 240 is 24. From there, 5% is half of that (12), 1% is a tenth of it (2.4), and 15% is 10% plus 5% (24 + 12 = 36). Twenty percent is 10% doubled; 25% is a quarter.
One more trick: X% of Y always equals Y% of X. Eight percent of 50 feels awkward, but 50% of 8 is obviously 4, the same answer. Flip the problem whenever one side is a round number.
What this calculator doesn't do
It does not know what your numbers mean. It will tell you a 2-to-3 jump is a 50% increase without warning that it is also just 1 percentage point. Choosing the honest framing is your job.
It also handles one step at a time. For discounts stacked on discounts, run the result through the Increase or decrease X by Y% calculator again. For percents that compound over many periods, such as interest or investment returns, use the Compound Interest Calculator or the ROI Calculator; they are built for that.
Frequently asked questions
How do I calculate the percentage of a number?
Multiply the number by the percent and divide by 100. For 15% of 240, that is 240 × 15 ÷ 100 = 36. You can also move the decimal point two places left and multiply: 240 × 0.15 = 36.
How do I figure out what percent one number is of another?
Divide the part by the whole, then multiply by 100. For example, 30 ÷ 120 = 0.25, so 30 is 25% of 120. Always put the whole, not the part, on the bottom of the division.
How is percent change calculated?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 = 0.25, a 25% increase. A negative result means a decrease.
Why is a 25% increase not undone by a 25% decrease?
Because each percent is measured against a different starting number. Rising from 80 to 100 is a 25% increase, but falling from 100 to 80 is only a 20% decrease, since the drop is measured against the larger number. Percent change is not symmetric.
What is the difference between percent and percentage points?
Percentage points measure the raw gap between two percents; percent measures the relative change. A rate that moves from 2% to 3% is up 1 percentage point but up 50% relative to where it started. Both are correct, so ask which one someone means.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount as a decimal. A $204 price after 15% off was 204 ÷ 0.85 = $240 originally. Adding 15% back to $204 gives the wrong answer, $234.60, because the discount was taken off the original, not the sale price.
How do I increase a number by a percentage?
Multiply the number by 1 plus the percent as a decimal. To increase 240 by 15%, multiply by 1.15 to get 276. To decrease it by 15%, multiply by 0.85 to get 204.
Results are computed in your browser from the numbers you enter; nothing is sent to us. Double-check anything you rely on. See the terms of use.
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