Percentage Calculator
Five percentage questions in one place, each showing its working so you can check the arithmetic rather than trust it. Includes the distinction most calculators blur: percentage change is measured against where you started, percentage difference against the average of the two.
What is …% of …?Pick a question and fill in both boxes
Change and difference are not the same thing. Going from 80 to 100 is a 25% increase, measured against where you started. But the percentage difference between 80 and 100 is 22.22%, because that one divides by the average of the two. Change has a direction; difference does not. Reports and spreadsheets mix these up constantly, which is why both are here as separate questions.
Margin and markup are the same profit over two different divisors. Something that costs 40 and sells for 100 earns 60 either way, but the margin divides that by the selling price and is 60%, while the markup divides it by the cost and is 150%. Margin can never pass 100%; markup has no ceiling. The profit margin question above reports both, each beside the number it divided by.
Common questions
- What is the difference between percentage change and percentage difference?
- Change is directional and divides by the starting value: going from 80 to 100 is a 25% increase. Difference is symmetric and divides by the average of the two: the percentage difference between 80 and 100 is 22.22%. Change answers "how much did it grow", difference answers "how far apart are these two". Swapping the numbers changes the first and not the second.
- How do I work out a percentage increase?
- Subtract the old value from the new one, divide by the old value, then multiply by 100. From 80 to 100 that is (100 − 80) ÷ 80 × 100 = 25%. The tool shows this line for every calculation, so you can paste the arithmetic into a document rather than just the answer.
- How do I reverse a percentage to get the price before a discount?
- Divide the amount you have by the percentage it represents, then multiply by 100. If £60 is 75% of the original price, the original was 60 ÷ 75 × 100 = £80. Use the "X is P% of what" mode. Note that reversing a 25% discount is not the same as adding 25% back.
- Why can't I calculate a percentage change from zero?
- Because it is mathematically undefined. Any increase from zero is infinitely large as a proportion of zero. Spreadsheets show a divide-by-zero error here for the same reason. If you need to express the gap between zero and something, percentage difference will give you a usable answer.
- What is a percentage point?
- The plain arithmetic gap between two percentages, as opposed to the relative change between them. If a rate rises from 4% to 5%, that is a rise of one percentage point, but a 25% increase. News reports mix these up often, and the difference matters a great deal in interest rates and polling.
- Are the results exact?
- They are computed in double precision and cleaned to twelve significant digits, which removes the floating-point artefacts that make 10% of 0.3 display as 0.030000000000000002. Both the rounded and the exact result are shown.
Exact, computed in double precision and cleaned to twelve significant digits, with the working shown.