What this percentage calculator does
This percentage calculator puts the six percentage questions people actually ask on one page, each in its own card: what is X% of Y, X is what percent of Y, the percentage change from one value to another, the percentage difference between two values, adding or subtracting a percentage, and working backwards to an original value. Every card updates as you type and shows three things: the answer, the formula with your own numbers substituted, and a one-line sentence you can paste into a report or message.
Many percentage mistakes come from using the right numbers in the wrong formula: dividing by the new value instead of the old one, or adding 15% back onto a sale price to "undo" a discount. Showing the working lets you check the method as well as the answer. The calculator accepts decimals, negative numbers, currency symbols and thousands separators such as 12,500 or 1,25,000, and it tells you plainly when a calculation has no answer, for example a percentage change that starts from zero.
How to use the calculator
- Pick the card that matches your question. The heading of each card is the question it answers, with an everyday example underneath.
- Type your two numbers. Commas, spaces, a currency sign such as
$or€, a leading+and a trailing%are all accepted. Use a dot for the decimal point: a value written with a decimal comma, such as12,5, is flagged rather than guessed as 125. If a field holds something that is not a number, it turns red and says why. - Read the result. The large number is the answer, rounded to at most four decimal places. The monospace line below it is the formula with your values, and the sentence underneath explains the result in words.
- Choose a direction where needed. In Add or subtract a percentage, switch between Add % (tax, tips, raises) and Subtract % (discounts). In Reverse percentage, say whether the final value came after a decrease or after an increase.
- Swap values in the percentage change card with the ⇄ button to see the change in the other direction.
- Copy a single result with the Copy button on its card, or every result at once with Copy all results. Load examples refills all six cards with sample numbers and Clear all empties them. Your inputs are kept in this browser tab if you refresh.
The formulas, with worked examples
1. What is X% of Y?
result = X ÷ 100 × Y
A 20% tip on a restaurant bill of 86.40 is 20 ÷ 100 × 86.40 = 17.28. Sales tax of 7.25% on a 249.99 laptop is 0.0725 × 249.99 = 18.124275, or 18.12 at the till.
2. X is what percent of Y?
result = X ÷ Y × 100
A student who scores 43 out of 52 has 43 ÷ 52 × 100 = 82.6923%. The same card answers "how far through my target am I": 1,150 words written of a 1,500-word essay is 76.6667%. The word counter gives you the first number.
3. Percentage change (increase or decrease)
change = (new − old) ÷ |old| × 100
A salary that goes from 58,000 to 61,480 has risen by 3,480 ÷ 58,000 × 100 = +6%. A share that falls from 142.50 to 118.30 has changed by −24.20 ÷ 142.50 × 100 = −16.9825%. The calculator adds the direction word (increase or decrease) so the sign cannot be misread. Dividing by the absolute value of the old number keeps the sign right when the start is negative: a loss that shrinks from −200 to −50 shows as a +75% increase.
4. Percentage difference
difference = |a − b| ÷ ((a + b) ÷ 2) × 100
Two contractors quote 1,840 and 2,160 for the same job. They differ by 320, and their average is 2,000, so the percentage difference is 320 ÷ 2,000 × 100 = 16%. The answer is the same whichever quote you enter first.
5. Adding or subtracting a percentage
add: value × (1 + P ÷ 100)
subtract: value × (1 − P ÷ 100)
A 65 jacket at 25% off costs 65 × 0.75 = 48.75. A 250 purchase plus 8.25% tax is 250 × 1.0825 = 270.625, which a till rounds to 270.63.
6. Reverse percentage (finding the original)
original = final ÷ (1 ± P ÷ 100)
A coat on sale for 68 after 15% off was originally 68 ÷ 0.85 = 80. A receipt total of 53.50 that includes 7% tax had a pre-tax price of 53.50 ÷ 1.07 = 50. The tempting shortcut, adding 15% to 68, gives 78.20. It is wrong because 15% of the sale price is smaller than 15% of the original.
Percentage points vs percent: the mistake everyone makes
When a rate moves from 4% to 5%, it has risen by 1 percentage point but by 25 percent (1 ÷ 4 × 100). Both statements are true and they mean very different things. A headline saying "unemployment rose 1%" could mean 5% → 6% (a 20% relative jump) or 5% → 5.05%.
The rule is simple. When you subtract one percentage from another, the answer is in percentage points. When you divide the gap by the starting rate, the answer is in percent. Marketers see this constantly: lifting a conversion rate from 2% to 3% is "+1 point" in a dashboard but 50% more conversions from the same traffic.
Percentage change vs percentage difference: which to use
Use percentage change when one value clearly came first: last month and this month, the price before and after, the old salary and the new one. Order matters. From 1,840 to 2,160 is +17.3913%, while from 2,160 to 1,840 is −14.8148%.
Use percentage difference when neither value is the reference: two lab readings of the same sample, the same product in two stores, two survey results. Because it divides by the average, swapping the inputs gives the same result. The difference card shows both change figures underneath so you can see the asymmetry for yourself.
Percentage change is also asymmetric when a value goes down and back up, which is why losses are harder to recover than they look:
| Fall | Rise needed to get back to the start |
|---|---|
| −10% | +11.1111% |
| −20% | +25% |
| −25% | +33.3333% |
| −50% | +100% |
| −75% | +300% |
A portfolio that drops 50% and then gains 50% ends at 75% of where it started, not 100%.
Reference table: common percentages
| Percent | Fraction | Decimal | Multiply to add it | Multiply to take it off |
|---|---|---|---|---|
| 5% | 1/20 | 0.05 | × 1.05 | × 0.95 |
| 10% | 1/10 | 0.10 | × 1.10 | × 0.90 |
| 12.5% | 1/8 | 0.125 | × 1.125 | × 0.875 |
| 20% | 1/5 | 0.20 | × 1.20 | × 0.80 |
| 25% | 1/4 | 0.25 | × 1.25 | × 0.75 |
| 33⅓% | 1/3 | 0.3333 | × 1.3333 | × 0.6667 |
| 50% | 1/2 | 0.50 | × 1.50 | × 0.50 |
| 75% | 3/4 | 0.75 | × 1.75 | × 0.25 |
Quick mental-math shortcuts
- 10% is a decimal shift. 10% of 386 is 38.6. From there, 5% is half (19.3), 20% is double (77.2) and 15% is 10% + 5% (57.9).
- 1% is two decimal shifts. 1% of 4,250 is 42.5, so 3% is 127.5.
- Swap the numbers. X% of Y equals Y% of X, so 8% of 25 is the same as 25% of 8, which is 2.
- Use fractions for round percentages. 25% is a quarter, 12.5% is an eighth and 33⅓% is a third.
- Stack discounts by multiplying. 20% off and then another 10% off is 0.80 × 0.90 = 0.72, a 28% total discount, not 30%.
- Sense-check the size. A percentage of a positive number is smaller than the number when the percentage is under 100%. If your answer is bigger, the decimal is in the wrong place.
Tips and common mistakes
- Dividing by the wrong base. Percentage change always divides by the old value. 80 → 100 is +25%, but 100 → 80 is −20%.
- Averaging percentages. Scores of 90% on a 10-question quiz and 60% on a 50-question test do not average to 75%. Add the marks (9 + 30 = 39 of 60) to get the true 65%.
- Changes from zero. Growth from 0 has no percentage. The calculator says so instead of printing "Infinity"; report the absolute change instead.
- Rounding too early. Keep full precision until the final step, then round. Here results are rounded only for display, to four decimal places.
- Confusing markup with margin. Buying at 60 and selling at 80 is a 33.3333% markup (20 ÷ 60, the cost is the base) but a 25% margin (20 ÷ 80, the selling price is the base). Use the X is what percent of Y card with the right base for each.
- Tax-inclusive prices. To remove VAT or sales tax from a total, use the reverse card with "after an increase", not the subtract card.
Privacy and limitations
Every calculation runs in your browser with JavaScript. Nothing you type is sent to a server or logged, and inputs are kept only in this tab's session storage so a refresh does not wipe them. Closing the tab clears them.
Numbers are standard double-precision floating point, accurate to about 15 significant digits. That is more than enough for prices, grades and statistics, but figures above one quadrillion may lose their final digits, and the calculator warns you when that happens. Results show at most four decimal places. Very small non-zero results switch to scientific notation so they are never displayed as a misleading 0. Money figures are estimates for informational purposes. Real receipts, payroll and tax bills may round each line separately, so a result can differ by a cent.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 18% of 250, that is 18 ÷ 100 × 250 = 45. You can also move the decimal point: 18% is 0.18, and 0.18 × 250 = 45. The order does not matter, so 18% of 250 equals 250% of 18. Use whichever version is easier to do in your head.
How do you calculate percentage increase or decrease?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Rent that rises from 1,200 to 1,290 is (1,290 − 1,200) ÷ 1,200 × 100 = 7.5%, an increase. A positive result is an increase and a negative result is a decrease. Always divide by the starting value, not the new one, or the answer will be wrong.
What is the difference between percent change and percent difference?
Percent change has a direction: it measures movement from an old value to a new one and divides by the old value. Percent difference has no direction: it compares two values of equal standing and divides by their average. Use change for before-and-after figures such as last year's sales versus this year's. Use difference for side-by-side comparisons such as two lab measurements or two stores' prices.
How do I calculate 20% off a price?
Multiply the price by 0.80, because paying 20% less means paying 80% of the price. A 65 jacket at 20% off costs 65 × 0.80 = 52, a saving of 13. In the calculator, use Add or subtract a percentage, choose Subtract %, enter the price and 20. For stacked discounts, such as 20% off then an extra 10% off, multiply by 0.80 and then by 0.90. The total is 28% off, not 30%.
How do you reverse a percentage to find the original price?
Divide the final value by the multiplier that produced it. If a sale price of 68 is after 15% off, the original is 68 ÷ 0.85 = 80. If a total of 108.25 includes 8.25% tax, the pre-tax price is 108.25 ÷ 1.0825 = 100. Do not add 15% back onto 68: that gives 78.20, because 15% of the smaller sale price is less than 15% of the original.
What is the difference between percent and percentage points?
Percentage points measure the plain gap between two percentages. Percent measures the relative change. If a mortgage rate goes from 4% to 5%, it rose by 1 percentage point, which is a 25% increase in the rate itself. News reports often mix these up. Use percentage points when you subtract one rate from another, and percent when you divide by the starting rate.
How do I calculate a percentage in Excel or Google Sheets?
Both use the same formulas. For X% of a value, enter =A215% or =A20.15. For what percent A2 is of B2, enter =A2/B2 and format the cell as a percentage. For percentage change from A2 to B2, enter =(B2-A2)/A2, or =(B2-A2)/ABS(A2) when the old value can be negative. Percent formatting multiplies by 100 for display, so do not multiply by 100 in the formula as well.
Why can't I calculate a percentage change from zero?
Percentage change divides by the starting value, and dividing by zero is undefined. Going from 0 to 50 is an infinitely large relative increase, so no percentage describes it. Report the absolute change instead (“up 50 from zero”), or pick a non-zero baseline period. The calculator shows a message when this happens instead of a misleading number.