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Percentage Calculator
Five modes: of, is-what, increase, decrease and difference.
What it does. A percentage calculator handles the five distinct percentage questions: what is X% of Y, X is what percent of Y, percentage increase, percentage decrease, and percentage difference. Each uses a different formula, and this tool shows the arithmetic for whichever one you pick.
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How to use Percentage Calculator
- Pick the calculation that matches your question.
- Enter the two numbers.
- Read the answer along with the formula and the substituted working.
The five percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is 15% of 240? | (P ÷ 100) × N | 0.15 × 240 = 36 |
| 36 is what percent of 240? | (A ÷ B) × 100 | 36 ÷ 240 × 100 = 15% |
| Increase from 240 to 288? | ((New − Old) ÷ Old) × 100 | 48 ÷ 240 × 100 = +20% |
| Decrease from 288 to 240? | ((Old − New) ÷ Old) × 100 | 48 ÷ 288 × 100 = −16.67% |
| Difference between 240 and 288? | (|A − B| ÷ ((A+B)÷2)) × 100 | 48 ÷ 264 × 100 = 18.18% |
The third and fourth rows are the trap. Going from 240 to 288 is a 20% increase, but going back from 288 to 240 is a 16.67% decrease — not 20%. Percentage change is always relative to the starting value, so the same absolute change gives different percentages depending on direction.
Why do percentage increases and decreases not cancel out?
Because each is calculated against a different base, and this is where a lot of money gets lost.
A stock falls 50%, then rises 50%. It is not back to where it started — it is down 25%. £100 becomes £50, then rises by 50% of £50, which is £25, reaching £75.
To recover from a 50% loss you need a 100% gain. From a 20% loss you need 25%. From a 90% loss you need 900%.
The same asymmetry catches retailers. A 25% discount followed by a 25% markup does not return to the original price — it lands 6.25% below it. And stacking discounts multiplies rather than adds: 20% off then a further 10% off is 28% off, not 30%.
What is the difference between percentage points and percent?
A percentage point is an absolute difference between two percentages. A percent is a relative one. Conflating them is the most common numerical error in journalism and in marketing.
If a conversion rate moves from 2% to 3%, that is an increase of 1 percentage point and an increase of 50 percent. Both are correct; they describe different things.
If an interest rate rises from 4% to 5%, your mortgage cost rises by 25%, not by 1%. If a poll moves a party from 30% to 33%, they gained 3 points and grew 10%.
The abbreviation "pp" or "bps" (basis points, one hundredth of a percentage point) exists to remove the ambiguity in finance. A 25 bps rate rise is 0.25 percentage points.
Quick percentage arithmetic
- 10% — move the decimal one place left. 10% of 847 is 84.7.
- 1% — move it two places. 1% of 847 is 8.47.
- 5% — take 10% and halve it.
- 15% — 10% plus half of it. The standard way to work out a US tip in your head.
- 20% — 10% doubled. UK VAT and the common US tip.
- Reversal trick — x% of y equals y% of x. 4% of 75 is hard; 75% of 4 is obviously 3.
- Removing VAT at 20% — divide the gross by 6 to get the tax.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply. 15% of 240 is 0.15 × 240 = 36.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. 36 out of 240 is 36 ÷ 240 × 100 = 15%.
Why is a 50% loss not recovered by a 50% gain?
Because the gain is calculated on the reduced base. £100 falls to £50; a 50% gain on £50 is £25, reaching £75. You need a 100% gain to recover a 50% loss.
What is the difference between percent and percentage points?
Percentage points measure the absolute gap between two percentages. Percent measures the relative change. Moving from 2% to 3% is 1 point and 50 percent.
How do I calculate a discount?
Multiply the price by (100 − discount) ÷ 100. A 30% discount on $80 is 80 × 0.70 = $56.
Do stacked discounts add up?
No, they multiply. 20% off then 10% off is 0.8 × 0.9 = 0.72, so 28% off in total, not 30%.
What is a basis point?
One hundredth of a percentage point. A 25 basis point rate rise is 0.25 percentage points. The term exists to avoid the percent versus percentage point ambiguity.
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