Percentage Calculator
Four calculations, kept separate.
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Why doesn't a 50% fall followed by a 50% rise get me back to where I started?
Because the rise applies to a smaller number. $100 falling 50% is $50; rising 50% from there is $75, not $100. To recover from a 50% fall you need a 100% gain. The pattern gets steeper: a 25% fall needs a 33% gain, an 80% fall needs 400%. This is the most common percentage error there is.
What is the difference between a percent and a percentage point?
If an interest rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase. Both statements are correct and they mean very different things, which is exactly why the distinction gets exploited in advertising and political claims. When a figure sounds surprising, check which one is meant.
Do stacked discounts add up?
No. '30% off, then an extra 20% off' is not 50% off — it is 0.7 × 0.8 = 0.56, so 44% off. Sequential discounts always come to less than their sum, because each one applies to a smaller amount than the last. The same logic applies to sequential price increases.
What is the difference between margin and markup?
Markup is calculated on cost, margin on selling price. A product costing $100 sold at a 25% markup is $125; sold at a 25% margin it is $133.33. Confusing the two is a common and expensive pricing error for small businesses, because it systematically underprices.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100 — 30 out of 200 is 30 ÷ 200 × 100 = 15%. Use the 'X is what % of Y' tab above. The order matters and getting it backwards is easy: 200 out of 30 would be 667%.
How it works, and more about percentage calculator
Four different questions
“Percentage” covers several distinct calculations that people routinely mix up, which is why this tool separates them rather than offering one box.
- X% of Y — a share of a known amount. 15% of $200 is $30.
- X is what % of Y — expressing one number as a share of another. 30 out of 200 is 15%.
- Percentage change — how much something moved. From 200 to 250 is a 25% increase.
- Add or subtract a percentage — applying a discount or a markup. 200 less 10% is 180.
A rise and a fall of the same percentage do not cancel
This is the most common percentage error there is. A stock that falls 50% and then rises 50% is not back where it started — it is down 25%, because the 50% rise applies to the smaller number. To recover from a 50% fall you need a 100% gain.
| Fall | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 25% | 33.3% |
| 50% | 100% |
| 80% | 400% |
Percent versus percentage point
If an interest rate moves from 4% to 5%, that is a rise of one percentage pointbut a 25% increase. Both are correct and they mean very different things, which is exactly why the distinction gets exploited in advertising and political claims. When a figure sounds surprising, check which one is meant.
Discounts do not stack the way they look
“30% off, then an extra 20% off” is not 50% off. It is 0.7 × 0.8 = 0.56, so 44% off. Sequential discounts always come to less than their sum, because each applies to a smaller amount than the last.
The same applies to markups: a 25% margin and a 25% markup are different numbers. A product costing $100 sold at a 25% markup is $125; sold at a 25% margin it is $133.33.
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