Free tool · Instant
Percentage calculator
Five questions people actually ask, each written as a sentence rather than a grid of unlabelled boxes — and every one shows its working, because most people here are checking a number somebody else gave them.
The four sums behind it
A percentage of a number
Divide by 100, multiply by the number. 18% of 50,000 is 18 ÷ 100 × 50,000 = 9,000. This is the one people reach for when adding sales tax or working out a deposit.
What percent one number is of another
Divide, then multiply by 100. 45 out of 180 is 45 ÷ 180 × 100 = 25%. Marks, conversion rates, and "how much of the budget has gone" are all this question.
Percentage increase and decrease
Take the difference, divide by the old value, multiply by 100. From 120,000 to 150,000 is (150,000 − 120,000) ÷ 120,000 × 100 =25%. Dividing by the new value instead is the most common mistake here, and it always gives a smaller, flattering number.
Reverse percentage — the one that catches people
If a total of 59,000 includes 18% tax, the amount before tax is not 59,000 minus 18%. It is 59,000 ÷ 1.18 = 50,000. Taking 18% off 59,000 gives 48,380 — nearly 1,700 out. The calculator's "Add / take off" mode shows this line every time, because it is the sum people get wrong most often on invoices.
Percentage difference, which is not percentage change
These get used interchangeably and they are different sums. Percentagechange has a direction: something went from an old value to a new one, and you divide by the old one. Percentagedifference compares two values where neither is the starting point — two quotes, two branches, two months that are not in sequence — so there is no "old" to divide by, and you divide by their average instead.
For 40 and 50: the change from 40 to 50 is 10 ÷ 40 = 25%, while the difference between them is 10 ÷ 45 = 22.2%. Note that the change from 50 to 40 is 20%, not 25% — change is not symmetrical and difference is. If someone quotes a percentage between two things without saying which came first, this is the sum they should be using.
Two discounts never add up
"30% off, plus an extra 20% at checkout" is not 50% off. The second discount comes off what is left after the first, so you keep 70% of the price and then 80% of that: 0.7 × 0.8 = 0.56. You pay 56% of the original and the real discount is 44%.
On a 10,000 item that is a 600 difference between what the sign implies and what you pay. The order does not matter — 20% then 30% lands on the same 0.56 — which is worth knowing when a shop offers to apply them "in the best order for you". There is no best order.
The same arithmetic runs the other way and catches more people: a price cut by 50% and then raised by 50% does not return to where it started. It ends at 0.5 × 1.5 = 75% of the original. To undo a 50% cut you need a 100% rise.
Doing it in your head
Most everyday percentages need nothing but 10%, which is the number with the decimal point moved one place left. 10% of 2,480 is 248. From there:
- 5% is half of 10% — 124.
- 20% is double it — 496.
- 15% is 10% plus 5% — 372. This is the tip sum.
- 1% is two places instead of one — 24.8 — and everything awkward is built from 1% and 10% together.
One more that is genuinely useful and almost nobody is taught:x% of y is always y% of x. Both are xy ÷ 100, so the order is free. 4% of 75 takes a moment; 75% of 4 is three, instantly. 18% of 50 is awkward; 50% of 18 is nine.
Percent and percentage points are not the same thing
A rate that goes from 5% to 7% has risen by two percentage points — and by 40 percent. Both are true, and they sound very different in a sentence. When someone quotes a percentage change of a percentage, it is worth asking which one they mean.
Questions
Is 20% off then 30% off the same as 50% off?
No — it is 44%, and it is always less than the two added together. The second discount applies to what is left after the first: 0.8 × 0.7 = 0.56, so you pay 56% of the price. The order makes no difference.
What is percentage difference?
The comparison between two values where neither is the starting point, divided by their average rather than by one of them. For 40 and 50 it is 22.2%, where the change from 40 to 50 is 25%.
Does it round?
The display shows up to twelve significant figures and drops the floating-point noise that would otherwise turn 0.1 + 0.2 into 0.30000000000000004. Nothing meaningful is hidden.
Is anything sent anywhere?
No. It runs in your browser and nothing is uploaded or stored.
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