Percentage calculator
Two numbers. That is the whole question, so that is all this asks for — and rather than making you pick which of five forms you wanted, it answers all of them at once.
This one runs on your own device. It is worked out in your browser, so there is nothing to send and nothing to log. Where a tool on this site does send something out, that page says so and names where it goes.
Why this does not ask which question you meant
A percentage calculator is usually built as a stack of separate forms: one for “what is A% of B”, another for “A is what percent of B”, another for percentage change, another for percent off. Each needs the same two numbers, and you have to know the name of the thing you want before you can find the box to type it in.
But there are only two numbers in this question, and every one of those answers falls out of them. So you type them once and they all appear, labelled in words rather than by formula name, with the arithmetic beside each one. Nothing is hidden behind a choice you have to make first.
Percent and percentage points are not the same thing
This is the mistake that turns up in newspapers. If a rate goes from 5% to 7%, that is a rise of two percentage points and a rise of 40 per cent. Both are true, they are wildly different numbers, and which one gets printed usually depends on which makes the better headline.
When your two numbers are themselves percentages, tick the option above and the reading will give you the percentage-point difference as well, so you can see both and say which you mean.
Why taking 25% off and then adding it back leaves you short
Add 25% to 100 and you get 125. Take 25% off 125 and you get 93.75, not 100. The percentages are the same; the numbers they are percentages of are not, and the second one is bigger.
This is not a rounding error and it is not a trick. It is the single most common way people are caught out by percentages — in sale prices, in pay cuts restored, and in tax rates — so the reading above says so whenever you ask for a percentage to be added or taken off.
Where to go next
Percentages turn up everywhere, and these are where they turn up most:
- loan and mortgage calculator — interest, which is a percentage with a timetable
- salary converter — and rises, cuts and pro rata
- fraction calculator — the same quantities written the other way
What this does not do
Some of these questions have no answer, and where that is so the reading says nothing rather than something plausible. There is no percentage change from zero: going from 0 to 50 is not a rise of any percentage at all, because there is nothing to compare the rise with. Nothing can be expressed as a percentage of zero either.
Where a number is negative, a change is measured against its size, so −10 to −5 reads as an increase of 50%. That is the usual convention and it is worth knowing it is a convention rather than a fact.