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CalculatorPercentage Calculator
Five separate percentage questions, one workspace. Pick the question you actually have, and the calculator shows the arithmetic it used rather than just dropping a number on you.
Result
120
25 ÷ 100 × 480 = 120
Which mode answers your question
Most percentage mistakes are not arithmetic errors — they are picking the wrong question. These five cover almost everything people actually need, and the wording matters more than it looks.
| Mode | Reads as | Result |
|---|---|---|
| P% of X | 60% of 240 | 144 |
| X is what % of Y | 60 is what percent of 240 | 25% |
| Increase X by P% | 240 increased by 60% | 384 |
| Decrease X by P% | 240 decreased by 60% | 96 |
| Change from X to Y | from 60 to 240 | +300% |
Notice the last row. Going from 60 to 240 is a 300% increase, not a 400% one, because the increase is 180 and 180 is three times the starting value. The finished amount is 400% of the start; the change is 300%. That single distinction accounts for a large share of arguments about growth figures.
Why −20% then +20% does not put you back where you started
Take away 20% and add 20% back and you land below your starting number every time, because the two percentages are taken from different bases. The 20% you removed came off the original; the 20% you added went on top of the smaller figure.
| P | After the drop | After the rise | Net |
|---|---|---|---|
| 5% | 950 | 997.50 | −0.25% |
| 10% | 900 | 990.00 | −1.00% |
| 20% | 800 | 960.00 | −4.00% |
| 30% | 700 | 910.00 | −9.00% |
| 50% | 500 | 750.00 | −25.00% |
The net column follows a tidy rule you can do in your head: the shortfall is always P² ÷ 100 percent. A 30% swing leaves you 9% down (30² = 900, ÷ 100 = 9). A 50% swing leaves you 25% down. This is why a stock that halves needs to double — not rise 50% — to recover.
Stacked discounts never add up
"30% off, then an extra 10% at checkout" is not 40% off. The second discount applies to the already-reduced price, so the true saving is smaller. The combined rate is 1 − (1 − a) × (1 − b).
| Advertised | Sounds like | Actually | You pay |
|---|---|---|---|
| 20% then 20% | 40% | 36% | 64% |
| 30% then 10% | 40% | 37% | 63% |
| 25% then 15% | 40% | 36.25% | 63.75% |
| 40% then 10% | 50% | 46% | 54% |
| 50% then 20% | 70% | 60% | 40% |
The order does not matter — 30% then 10% gives exactly the same price as 10% then 30%, because multiplication is commutative. What does matter is whether tax is applied before or after the discount, and that varies by jurisdiction and by shop.
Working backwards to the original price
This is the mistake that costs real money. If a price of 1,150 already includes 15% tax, the pre-tax price is not 1,150 minus 15%.
Wrong: 1,150 − (15% of 1,150) = 1,150 − 172.50 = 977.50
Right: 1,150 ÷ 1.15 = 1,000.00
The gap is 22.50 on a single item. On an invoice with fifty lines it stops being a rounding curiosity.
The rule: to remove a percentage that has already been added, divide by (1 + rate). To remove a discount that has already been taken off, divide by (1 − rate). Subtraction only works when you are going forwards.
Percent versus percentage point
If an interest rate moves from 4% to 6%, it has risen by two percentage points — but by 50 percent. Both statements are true and they describe the same event. Headlines pick whichever sounds more dramatic, so it is worth checking which one is being used before you react to a number.
Quick reference
| Percent | Fraction | Decimal | Shortcut |
|---|---|---|---|
| 5% | 1/20 | 0.05 | Take 10%, then halve it |
| 10% | 1/10 | 0.10 | Move the decimal one place left |
| 12.5% | 1/8 | 0.125 | Halve, halve, halve |
| 20% | 1/5 | 0.20 | Divide by 5 |
| 25% | 1/4 | 0.25 | Halve it twice |
| 33⅓% | 1/3 | 0.333… | Divide by 3 |
| 75% | 3/4 | 0.75 | Take a quarter off |
One more that saves time: x% of y equals y% of x. Working out 16% of 25 is fiddly; 25% of 16 is 4, instantly. They are the same number because both are 0.16 × 25.
Questions people ask
Why does the calculator show negative percentages?
In change mode, a negative result means the value went down. Going from 200 to 150 is −25%. The sign is part of the answer, not an error.
Can I calculate a percentage change from zero?
No, and no calculator honestly can. Percentage change divides by the starting value, and dividing by zero is undefined. If your figure went from 0 to 40, the meaningful statement is "increased by 40", not a percentage. The tool will tell you this rather than printing infinity.
Is the result rounded?
The display rounds to six decimal places so long division does not fill your screen. The underlying calculation uses full double precision. For money, round to two places yourself at the end — never at each step, or the rounding errors compound.
Does anything I type get sent anywhere?
No. The calculation runs in your browser tab. There is no request to a server, so there is nothing to store or log. You can disconnect from the internet and the page keeps working.