⚡ The short version
15% of 240 is 36. Increase 240 by 15% and you get 276; decrease it and you get 204. Going from 80 to 100 is a 25% increase.
The calculator
How to use it
- Pick the mode first — the seven modes answer genuinely different questions, and the most common percentage mistake is answering the wrong one confidently.
- Basic percentage — X% of Y, the everyday case such as a tip, a discount or a tax rate.
- Increase or decrease — apply a percentage change to a value, forwards.
- What percentage is X of Y — turn a score or a share into a percentage.
- Percentage change — compare old and new values, for prices, metrics and results.
- Reverse percentage — when you know the number after the change and need the number before it, such as removing VAT from a total.
Worked example
15% of 240 is 240 × 0.15 = 36. Once a percentage is a decimal, every other mode is the same arithmetic pointed in a different direction.
Increase: 240 × 1.15 = 276. Decrease: 240 × 0.85 = 204. The multiplier is the whole trick — add or subtract the percentage from 1, then multiply once.
Change between two values: going from 80 to 100 is (100 − 80) ÷ 80 = 0.25, a 25% increase. Going back down from 100 to 80 is not a 25% fall — it is 20%, because the second calculation divides by a larger base. That asymmetry is the single most common percentage error in print.
Reverse: if a total includes 20% VAT and comes to £240, the price before VAT is not £240 − 20%. It is 240 ÷ 1.2 = £200 — dividing out the multiplier rather than subtracting the tax.
Where percentages trip people up
- Stacked percentages do not add. 10% off then another 10% off is 19% off, not 20% — the second discount applies to the reduced price.
- Percentage change is asymmetric. A 50% fall needs a 100% rise to get back, because the two changes use different bases.
- Percentage points are not percent. A rate moving from 4% to 5% has risen by one percentage point, or 25% — both statements are true and they sound very different.
- Averaging percentages. The average of 50% and 100% is not 75% unless both cases have the same base size.
🛠️ Related maths tools
❓ Frequently asked questions
How do I work out a percentage of a number?
Turn the percentage into a decimal and multiply. 15% of 240 is 240 × 0.15 = 36. For a quick mental estimate, 10% means moving the decimal point one place left, then scale from there.
How do I reverse a percentage?
Divide by the multiplier instead of subtracting the percentage. If £240 includes 20% VAT, the pre-VAT price is 240 ÷ 1.2 = £200 — not £240 minus 20%, which would give £192 and understate the tax.
What is the difference between percent and percentage points?
A move from 4% to 5% is one percentage point, and also a 25% increase. Percentages describe relative change; percentage points describe an absolute difference between two percentages. Mixing them is one of the most common errors in reporting.
Why does a 50% fall need a 100% rise to recover?
Because each change is measured against a different base. Falling from 100 to 80 divides by 100; rising back divides by 80. The base set by the changed value is smaller, so the same absolute move is a larger percentage.
Does this calculator handle repeated percentage change?
Yes, use the compound mode: applying the same percentage several times means raising the multiplier to a power. Two consecutive 10% increases are 1.1 × 1.1 = 1.21, a 21% rise, not 20%.