How to calculate a percentage
- Choose which of the four questions you are asking.
- Enter the two numbers. The labels change to match the mode.
- Read the result and the breakdown beneath it.
- Switch modes to check the same figures a different way.
- Press Copy results to take the whole breakdown.
The four modes
- X% of Y: the everyday case: 20% of 250.
- X is what % of Y: turning a part into a percentage of a whole.
- Percentage change: the increase or decrease between two figures.
- Reverse: recovering the original amount before a percentage was applied.
- The working shown for every answer, so you can check it rather than trust it.
- Live updating with no upload and no rounding surprises.
Four questions that all get called "percentage"
Percentage problems feel confusing because one word covers several different calculations, and each divides a different way round. Getting the wrong one produces an answer that looks plausible and is wrong, which is worse than an obvious error.
Naming them separately removes the confusion. "20% of 250" multiplies. "50 is what percent of 250" divides. "From 250 to 300" is a change. "300 after a 20% increase" works backwards. Choosing the mode first is most of the work.
Percentage change, and why the base matters
Change is always measured against the starting figure, and that asymmetry surprises people. A price rising from 100 to 150 is a 50 per cent increase. The same price falling from 150 back to 100 is a 33 per cent decrease, not 50, because the base changed.
This is why a 50 per cent drop followed by a 50 per cent rise does not return you to where you started. Halve 100 to 50, add 50 per cent of 50, and you have 75. The arithmetic is correct and the intuition is wrong, which is exactly the sort of thing worth checking rather than assuming.
Reversing a percentage
This is the mode people most often get wrong by hand. If a price is £120 after a 20 per cent increase, the original is not £120 minus 20 per cent, that gives £96, which is too low. The correct calculation divides by 1.2, giving £100.
The same applies to tax-inclusive prices. To find the amount before 20 per cent VAT, divide by 1.2 rather than subtracting 20 per cent. Subtracting gives an answer roughly 4 per cent too small, and it is a genuinely common bookkeeping error.
Percentage points are not percentages
A rate moving from 5 per cent to 7 per cent has risen by two percentage points, and by 40 per cent. Both statements are true and they mean very different things. Reporting the larger figure without saying which is meant is a well-worn way to make a small change sound dramatic.
When you read a claim about a percentage rise in something that is itself a percentage. An interest rate, an unemployment figure, a conversion rate. It is always worth asking which of the two is being quoted.
Where these calculations turn up
- Working out a sale price, or checking that an advertised discount is real.
- Calculating VAT, sales tax or a commission from a gross figure.
- Comparing this month's numbers against last month's.
- Converting a test score or a survey result into a percentage.
- Checking a tip, a service charge or a percentage-based fee.
For sale prices specifically the discount calculator handles stacked offers, and the ratio calculator is the better tool when you are splitting something into proportions rather than measuring a share.