What is the difference between a percentage and a percentage point?

A rate moving from four to five per cent has risen by one percentage point and by twenty-five per cent. Both are correct descriptions of the same change, and confusing them is how figures get made to sound larger or smaller than they are.

Why does a forty per cent drop and a forty per cent rise not cancel out?

Because the rise is calculated on the reduced amount. Something that falls forty per cent to 60 and then rises forty per cent reaches 84, not 100. This is why a halved investment needs to double to recover.

Do two discounts add together?

No. Twenty per cent off followed by ten per cent off is twenty-eight per cent off, not thirty, because the second applies to the already-discounted price. The same compounding applies to successive increases.

How do I work out what percentage one number is of another?

Divide the part by the whole and multiply by a hundred. The usual mistake is dividing the wrong way round, which the labelled fields here prevent.

Percentage Calculator

Percent of, percent change, and what percent one number is.

Everything runs inside your browser. Your files never leave your device.

Result

The result appears here as you type.

Ask about Percentage Calculator

Questions about what this tool does, which option to pick, or what it can and cannot handle.

The question you type here is sent to an AI provider to be answered — your files and whatever you put in the tool above are not, and the assistant cannot see them. Answers are generated and can be wrong. The tool itself is not guessing: it runs deterministic code on your device.

About the Percentage Calculator

Percentages are simple arithmetic that people get wrong constantly, usually because the question is ambiguous rather than because the sum is hard. This handles the several distinct calculations that all get called "percentage".

What is fifteen per cent of 240? What percentage is 36 of 240? What is the change from 240 to 276? Those are three different formulas and this does each of them, which removes the step where you work out which one you meant.

The distinction that causes the most trouble is percentage change against percentage points. If an interest rate moves from four per cent to five, that is a rise of one percentage point and an increase of twenty-five per cent. Both statements are true and they describe the same event; reporting that mixes them is either careless or deliberately misleading, and it is worth noticing which.

The second common error is assuming percentage changes reverse. A price that falls forty per cent and then rises forty per cent does not return to where it started — it ends at 84 per cent of the original, because the rise is calculated on the reduced figure. This is why a stock that halves needs to double to recover, and it is the arithmetic behind a great many disappointing investment stories.

The third is compounding two increases. A twenty per cent rise followed by a ten per cent rise is not thirty per cent; it is 32, because the second applies to the already-increased amount. The same is true of successive discounts, which is why stacking "twenty per cent off" and "ten per cent off" gives twenty-eight per cent off rather than thirty.

How to use it

1Choose the calculation that matches your question — a share of a total, a proportion, or a change between two figures.
2Enter the numbers and read the result.
3For a change, check whether you want percentage change or percentage points, since they answer different questions.
4Where two changes stack, apply them in sequence rather than adding them together.

Questions

What is the difference between a percentage and a percentage point?: A rate moving from four to five per cent has risen by one percentage point and by twenty-five per cent. Both are correct descriptions of the same change, and confusing them is how figures get made to sound larger or smaller than they are.
Why does a forty per cent drop and a forty per cent rise not cancel out?: Because the rise is calculated on the reduced amount. Something that falls forty per cent to 60 and then rises forty per cent reaches 84, not 100. This is why a halved investment needs to double to recover.
Do two discounts add together?: No. Twenty per cent off followed by ten per cent off is twenty-eight per cent off, not thirty, because the second applies to the already-discounted price. The same compounding applies to successive increases.
How do I work out what percentage one number is of another?: Divide the part by the whole and multiply by a hundred. The usual mistake is dividing the wrong way round, which the labelled fields here prevent.