Percentage calculator
Every percentage question, including the two that are always confused with each other.
Percentage change and percentage difference are not the same thing
They get used interchangeably constantly, including in published figures, and they give different answers. Going from 200 to 150 is a 25% change — a decrease of a quarter of the starting value. The difference between 200 and 150 is 28.6%, because that compares the gap to the average of the two rather than to one of them.
Which one you want depends on whether direction is meaningful. Change has a direction and a starting point: revenue fell 25% from last year. Difference is symmetric — swap the two numbers and you get the same answer — which is what you want when neither is the baseline, like comparing two measurements of the same thing. Both are on this page as separate options, labelled, with their formulas, precisely because picking the wrong one is so easy.
The other operations
Most percentage questions are one of five shapes, and they are all here. What is A% of B — the discount case. A is what percent of B — the score case. A is B% of what number — the working-backwards case, which is the one people find hardest to set up. And increasing or decreasing a number by a percentage, which is the price case.
A trap worth knowing
Taking 20% off and then adding 20% back does not return you to where you started. Eighty per cent of 100 is 80, and 120% of 80 is 96. The second percentage is applied to a smaller number, so it is worth less. This is the arithmetic behind a "20% off" sale followed by a "20% price rise", and behind a stock that falls 50% needing to double just to recover.
Where it refuses to answer
Some percentage questions genuinely have no answer, and this says so rather than printing a number. A change from zero cannot be expressed as a percentage, because there is nothing for the change to be a percentage of — going from 0 to 5 is not "infinite growth", it is a question you have to ask a different way. Neither can "A is what percent of zero". A calculator that returns Infinity or NaN there has not answered you.
Decimal places
Percentages get rounded aggressively, and rounding a percentage before you use it in further arithmetic is how small errors become visible ones. The decimal-places control goes up to ten so you can keep the precision when you need it and lose it when you are quoting the figure to somebody.
Common questions
What is the difference between percentage change and percentage difference?
Change is measured against the starting value and has a direction: 200 to 150 is −25%. Difference is measured against the average of the two and is symmetric: between 200 and 150 it is 28.6% either way.
How do I work out what number A is a given percentage of?
Divide A by the percentage expressed as a decimal. If 50 is 25% of something, that something is 50 ÷ 0.25 = 200. It is the third option on this page.
Why does taking 20% off and adding it back not return the original?
Because the second 20% is calculated on the reduced number, so it is a smaller amount. 100 → 80 → 96.
Why will it not calculate a change from zero?
Because there is no meaningful answer. A percentage change compares the change to the starting value, and if that value is zero there is nothing to compare to. The honest response is to say so.
Can I use this for a discount?
Yes — "decrease A by B%" gives the sale price and shows how much came off. For tax, the GST and VAT calculator handles the inclusive-price case properly.
Does it round the intermediate steps?
No. Everything is computed at full precision and rounded only for display, at however many decimal places you choose.