Quick answer: a percentage is a number out of 100. To find X% of Y, multiply Y by X and divide by 100. To find what percent A is of B, divide A by B and multiply by 100. For a change, divide the difference by the original value and multiply by 100.
This free tool does that and more with fifteen calculators, and it shows the working for every answer.
How to use this percentage calculator
This percentage calculator has fifteen tools on one page. Choose the one that matches your question, type your numbers, and the answer updates as you type, with the working shown underneath. Everything runs in your browser, so your numbers are never sent anywhere.
- Pick a tool. Use the buttons at the top of the page to jump to it.
- Enter your numbers. Negative numbers work too. Leave a field empty and the result hides until you fill it in.
- Read the result and the steps. The line under the answer shows the exact sum, so you can check it or copy it into homework or a report.
- Use the extras. Set the decimal places and currency symbol once at the top. Use Copy result to copy the answer and Copy link to share your exact numbers, and Reset to go back to the example values.
The fifteen tools
- X% of Y: find 20% of 150, a commission or a tax amount.
- What % is X of Y: turn a score, share or part into a percentage.
- % change: see how much a price, salary or number went up or down.
- % difference: compare two numbers when neither is the starting point.
- Add / subtract %: add sales tax or take a percentage off a number.
- Find the whole: work back from a part and its percentage to the total.
- Discount and original price: get the sale price, or the price before the discount.
- % of a %: take a percentage of another percentage.
- Successive changes: apply up to three percentage changes in a row, such as +50% then −50%.
- Percentage points: compare two percentages as points and as a relative change.
- Tip, tax and split: total a restaurant bill with tax and tip, then split it between people. The tip is calculated on the bill before tax.
- Markup and margin: turn a cost and a selling price into profit, markup % and margin %. They are not the same number.
- VAT and GST: add tax to a price, or take it out of a tax-inclusive price, for any rate you enter.
- Percent error: compare a measured value with the true value, as used in science labs.
New to percentages? Read our step-by-step guide, how to calculate percentages with formulas and examples.
Common percentage mistakes
- Mixing up the base. A 25% increase from 80 to 100 is not undone by a 25% decrease. Going from 100 back to 80 is a 20% decrease, because the base is now 100.
- Adding discounts. 20% off followed by another 10% off is not 30% off. 100 becomes 80, then 72, which is 28% off in total.
- Confusing percent with percentage points. Moving from 4% to 6% is 2 percentage points, but a 50% increase in the rate.
- Reversing a discount by adding it back. If 15% off gives 68, the original was 80, not 78.2. Use the original price calculator above.
Markup vs margin: why the two percentages differ
Markup is profit as a percentage of cost. Margin is profit as a percentage of the selling price. Because the price is larger than the cost, the margin is always the smaller number. A product that costs 80 and sells for 100 earns 20 profit: that is a 25% markup but only a 20% margin.
| Markup on cost | Margin on price | Example: cost 100 sells for |
|---|
| 10% | 9.09% | 110 |
| 25% | 20% | 125 |
| 50% | 33.33% | 150 |
| 100% | 50% | 200 |
To price for a target margin, divide the cost by (1 − margin ÷ 100). For a 30% margin on a cost of 70, the price is 70 ÷ 0.70 = 100. To price for a target markup, multiply the cost by (1 + markup ÷ 100).
Adding and removing VAT or GST
Adding tax is a multiplication, but removing it is a division. A tax-inclusive price of 120 at a 20% rate holds 20 of tax, not 24, because the 20% applies to the 100 before tax. Dividing 120 by 1.20 gives 100. Subtracting 20% of 120 gives the wrong answer of 96. Enter the rate used where you live, since rates differ by country and by product.
Percent error in science and school labs
Percent error shows how far a measurement is from the accepted value, as a percentage of the accepted value. If you measure gravity as 9.6 m/s² and the accepted value is 9.8 m/s², the error is 0.2 ÷ 9.8 × 100 = 2.0408%. The sign is ignored, so a measurement above or below the true value gives the same percent error.
Frequently Asked Questions
What is the formula for a percentage?
To find a percentage of a number, multiply the number by the percentage and divide by 100: (Percentage × Number) ÷ 100. To find what percent one number is of another, divide the part by the whole and multiply by 100.
How do I find what percent one number is of another?
Divide the part by the whole, then multiply by 100. For example, 45 is what percent of 180? 45 ÷ 180 = 0.25, and 0.25 × 100 = 25%.
How do I calculate percentage increase or decrease?
Subtract the original value from the new value, divide by the original value, and multiply by 100. A positive answer is an increase and a negative answer is a decrease. Going from 80 to 100 is a 25% increase, and going from 100 to 80 is a 20% decrease.
What is the difference between percentage change and percentage difference?
Percentage change measures movement from an original value to a new one, so the order matters. Percentage difference compares two numbers without treating either as the starting point, by dividing their gap by their average, so the order does not matter. For 50 and 70, the change from 50 to 70 is 40%, while the percentage difference is 33.33%.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount as a decimal. If an item costs 68 after 15% off, the original price is 68 ÷ 0.85 = 80. Do not just add 15% back to 68, because the discount was taken from the larger original price.
How do I add a percentage, like sales tax, to a number?
Multiply the number by 1 plus the percentage as a decimal. Adding 8% tax to 85 gives 85 × 1.08 = 91.80. To subtract a percentage, multiply by 1 minus the decimal instead, so 250 less 15% is 250 × 0.85 = 212.50.
Why does a 50% increase followed by a 50% decrease not return to the start?
Because the second percentage is taken from a different, larger base. Starting at 100, a 50% increase gives 150, and a 50% decrease of 150 is 75, not 100. To undo a 50% increase you need a decrease of about 33.3%.
How do successive percentage changes work?
Multiply the starting value by one plus each change as a decimal, in order. Starting at 100, a 50% increase and then a 50% decrease gives 100 × 1.5 × 0.5 = 75, a net loss of 25%. Successive changes cannot simply be added together.
How do I calculate a tip and split the bill?
Work out the tax and tip on the bill before tax, add both to the bill, then divide by the number of people. An 80 bill with 8% tax and an 18% tip is 80 + 6.40 + 14.40 = 100.80, which is 50.40 each for two people.
What is the difference between a percentage and a percentage point?
A percentage point is the plain arithmetic gap between two percentages. If an interest rate moves from 4% to 6%, it rose by 2 percentage points, which is a 50% increase in the rate.
What is the difference between markup and margin?
Markup is profit divided by cost, and margin is profit divided by the selling price. With a cost of 80 and a price of 100, the profit is 20, which is a 25% markup and a 20% margin.
How do I remove VAT or GST from a price?
Divide the tax-inclusive price by 1 plus the rate as a decimal. At 20%, a price of 120 divided by 1.20 is 100 before tax, so the tax is 20.
How do I calculate percent error?
Subtract the true value from the measured value, ignore the sign, divide by the true value and multiply by 100. For a measurement of 9.6 against a true value of 9.8, the percent error is 2.0408%.