What this calculator does
Get quick answers to everyday percent questions, with every step shown. You can find a percent of a number, like 15% of 80. You can find what percent one number is of another. You can find the whole when you know a part and its percent. And you can find how much a number went up or down, as a percent.
It also shows the number with the percent added and taken away. So "add 15%" and "take 15% off" are answered at the same time. A percent is a way of saying "out of 100": 15% means 15 for every 100. Pick your question, enter the two numbers you know, and the answer appears as you type.
Where it's used
Why this math matters outside the classroom:
- Sale prices. Shoppers take 25% off a $60 jacket by finding 25% of 60 and subtracting it, which leaves $45.
- Restaurant tips. Diners work out an 18% tip on a $42 bill as 0.18 × 42, which is $7.56.
- Test scores. Teachers turn 43 correct answers out of 50 into a score of 86%.
- Price changes. News reports describe a rent rise from $1,200 to $1,290 as a 7.5% increase.
- Sales tax. Buyers estimate the total for a $250 purchase with 8% sales tax as $270.
Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.RP.A.3.c, 7.RP.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose what you want to find. Your options are a percent of a number, what percent a part is of a whole, the whole from a part, or the percent change between two numbers.
- Enter the two numbers you already know. Decimals and negative numbers are fine.
- Read the answer and the steps underneath it. Use the precision control to show more or fewer decimal places.
What the inputs mean
- Percentage (P)
- How many out of 100. Percents above 100% work too: 150% of 40 is 60.
- Part
- The piece you're measuring, such as a test score or a sale amount.
- Whole
- The full amount you're comparing the part with. It can't be zero.
- From (original value)
- The starting value, before the change. It can't be zero, because a change from nothing has no percent.
- To (new value)
- The new value. If it's bigger than the starting value, you get an increase. If it's smaller, you get a decrease.
Formula and method
part = (percent ÷ 100) × whole percent = (part ÷ whole) × 100 whole = part ÷ (percent ÷ 100) increased = number + part; decreased = number − part percent change = (new − original) ÷ |original| × 100
In the formulas, "part" is the piece, "whole" is the full amount and "percent" is how many out of 100. The bars in |original| mean "the size of the original, ignoring any minus sign". The first three formulas are really one idea, rearranged to find whichever number is missing.
Dividing a percent by 100 turns it into a decimal you can multiply by: 15% becomes 0.15. In two of the formulas, you divide by the whole or by the percent. You can't divide by zero, so neither one can be zero there.
A percent change compares the difference with the starting value. So the same gap is a bigger percent when the starting value is small. Dividing by the size of the starting value keeps the direction right, even when that value is negative.
Worked example
A jacket costs $80 and you want to know what 15% of the price is.
- Turn 15% into a decimal: 15 ÷ 100 = 0.15.
- Multiply by the price: 0.15 × 80 = 12.
- Increased by 15%: 80 + 12 = 92. Decreased by 15%: 80 − 12 = 68.
- Percent change from 80 to 92: (92 − 80) ÷ 80 × 100 = 15%.
Result: 15% of $80 is $12. So the price with 15% added is $92, and with 15% off it's $68. Turning it around, 12 is 15% of 80, and 80 is the whole that 12 is 15% of.
Understanding the result
A result over 100% means the part is bigger than the whole you compared it with. That's common when you compare growth with a starting value.
Percents tell you how big something is compared with something else, not how big it is on its own. 10% of a large number can be far more than 50% of a small one.
Assumptions and limitations
- Numbers are worked out exactly. The answer is only rounded when it's shown on screen.
- Negative numbers follow the usual rules of arithmetic: −20% of 50 is −10.
- The percent change option gives the basic change only. For percent difference (compared with the average of the two numbers), use the percentage change calculator. It can also work back to an original value.
- Percentage points and percents are different. A rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase.
Frequently asked questions
How do I work out a percentage of a number in my head?
Find 10% first by moving the decimal point one place to the left. Then build from there. For 15% of 80: 10% is 8, and 5% is half of that, 4. So 15% is 8 + 4 = 12.
Is X% of Y the same as Y% of X?
Yes. Both equal X × Y ÷ 100, so 8% of 50 and 50% of 8 are both 4. Swapping them can make mental math much easier.
Why can't the whole be zero?
To find what percent a part is of a whole, you divide by the whole. Dividing by zero has no answer, so there's no percent to find.
How do I add a percentage to a number?
Multiply the number by 1 plus the percent as a decimal. Adding 15% to 80 is 80 × 1.15 = 92. The calculator shows this as "increased by P%" under the main answer.
How do I work out a percentage increase?
Subtract the old value from the new one. Divide by the old value, then multiply by 100. Going from 80 to 92 is 12 ÷ 80 × 100 = 15%. Choose the percent increase or decrease option to do it in one go.
If a price rises 20% and then falls 20%, is it back where it started?
No, and this one surprises a lot of people. A $100 item that rises 20% costs $120. Then 20% off $120 is $24, which leaves $96. The second percent is taken from a bigger number, so the drop is bigger in dollars.
Can a percentage be more than 100?
Yes. 100% is the whole itself, so 200% is double the whole. You'll see this often when something has grown past where it started.
How this calculator is checked
Method: Definition of percent (per hundred); algebraic rearrangement; relative change (new − old) ÷ |old|. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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