About the Percentage Calculator
The Percentage Calculator puts the six most common percentage questions side by side. Find a percentage of a number, work out what percent one number is of another, find the whole from a part, measure the percentage change between two values, add or subtract a percentage, and compare two values with the percentage difference.
These come up every day: a 20% tip on a restaurant bill, sales tax on a purchase, a discount in a store, a test score, a raise, a rent increase, or a change in sales from last month. Each card answers as you type and shows the formula it used, so you can check the math or reuse it in a spreadsheet.
Results are shown with up to six decimal places, without rounding to cents, so you decide how to round. Everything is calculated in your browser.
How to use it
- Pick the right cardEach card is one question, written as a sentence: "What is X% of Y?", "X is what percent of Y?" and so on.
- Fill in the two numbersType a number into each box. Decimals and negative numbers are allowed.
- Choose increase or decreaseOn the "Increase or decrease by a percentage" card, pick "increased by" or "decreased by" from the menu.
- Read the result and the formulaThe result appears in large type, with the formula used underneath.
- Copy the resultClick the copy icon next to a result to put the number on your clipboard.
Key features
Six calculators on one page
Percent of a number, percent of a total, the whole from a part, percentage change, increase or decrease, and percentage difference.
Formula under every answer
See exactly how each number was calculated, ready to rebuild in a spreadsheet.
Increase and decrease in one card
Apply a markup, a tax, a raise or a discount, and see both the new value and the size of the change.
Honest about impossible math
Dividing by zero, such as a change from 0, shows "Not defined" instead of a misleading number.
Clean numbers
Results are trimmed of floating-point noise and shown with thousands separators and up to six decimals.
Private by design
No account and nothing sent anywhere. The math runs in your browser.
Examples
Everyday questions
| Question | Card | Result |
|---|---|---|
| 20% tip on an $85.50 bill | What is 20% of 85.5? | 17.1 |
| 45 points out of 60 on a test | 45 is what % of 60? | 75% |
| $30 is a 20% deposit. What is the full price? | 30 is 20% of what? | 150 |
| A $80 jacket at 25% off | 80 decreased by 25% | 60 |
| 8.25% sales tax on $59.99 | 59.99 increased by 8.25% | 64.939175 |
The tip is $17.10 and the jacket costs $60. With the sales tax, round to cents yourself: $64.94, of which the tax is 4.949175, or $4.95. Stores round each item's tax according to local rules, so a receipt can differ by a cent.
Percentage change
| From | To | Change |
|---|---|---|
| 80 | 100 | 25% (an increase) |
| 100 | 80 | -20% (a decrease) |
| 50 | 50 | 0% (no change) |
| 0 | 5 | Not defined |
The formula is (new − old) ÷ |old| × 100. Going from 80 to 100 is +25%, but going back from 100 to 80 is only −20%, because the starting value is different. A change from 0 cannot be expressed as a percentage, because it would mean dividing by zero.
Up 10%, then down 10%
A price of 100 increased by 10% becomes 110 (a change of 10). Decrease 110 by 10% and you get 99, not 100, because the 10% is now taken from the larger number (a change of 11). That is why a 50% loss needs a 100% gain to get back to where you started.
Percentage difference
Percentage difference compares two values without picking one as the starting point. For 40 and 50: |40 − 50| ÷ 45 × 100 = 22.222222%, where 45 is the average of both. Swap them, or try 100 and 80, and you also get 22.222222%. Use it to compare two prices, two measurements or two quotes where neither is "before" or "after".
Tips
- To get a total with tax or a tip in one step, use "increased by" instead of finding the percentage and adding it yourself.
- For a discount, use "decreased by". 25% off $80 gives the sale price right away, and the formula line shows the amount saved.
- If a value went up and you want to know by how much in percent, use Percentage change with the old value first.
- A quick mental check: 10% is the number with the decimal point moved one place left. 20% is double that, 5% is half of it.
- Copy the formula into a spreadsheet by replacing the numbers with cell references, such as =(B2-A2)/ABS(A2)*100.
Common mistakes and limits
- Mixing up percent and percentage pointsAn interest rate going from 4% to 5% rose by 1 percentage point, but by 25 percent. Say which one you mean.
- Reversing a percentage changeUndoing a 20% discount takes a 25% increase, not 20%. Each change is a percentage of a different starting value.
- Adding percentages from different basesTwo raises of 10% add up to 21%, not 20%, because the second one applies to the already raised amount.
- Using percentage change when neither value is the startWhen you just compare two things, use percentage difference. It gives the same answer in either order.
- Forgetting to round moneyResults keep up to six decimals. Round to cents only at the end, the way your store, bank or tax form does.
