Percentage calculator

The sums behind it

A percentage of a number

Divide by 100, multiply by the number. 18% of 59,000 is 18 ÷ 100 × 59,000 = 10,620. 1% of 59,000 is 590, and 15% of 59,000 is 8,850. 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 of marks

Divide the marks you got by the total marks, then multiply by 100. 124 out of 180 is 124 ÷ 180 × 100 = 68.9%, and 248 out of 600 is 41.3%. In the calculator, pick "X is what %" and put your marks in the first box and the total in the second.

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. To remove sales tax from a total at any rate, including a total made of several lines, use the sales tax calculator.

Percentage difference, which is not percentage change

These get used interchangeably and they are different sums. Percentage change has a direction: something went from an old value to a new one, and you divide by the old one. Percentage difference 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

What is 18% of 59000?

10,620. What is X percent of Y is X divided by 100, times Y. 18 ÷ 100 × 59,000 = 10,620. 1% of 59,000 is 590. 15% of 59,000 is 8,850.

How do I calculate percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100. From 120,000 to 150,000 is (150,000 − 120,000) ÷ 120,000 × 100 = 25%.

How do I find the original price before a percentage was added?

Divide by one plus the percentage as a decimal — not by subtracting the percentage, which is the common mistake. If 59,000 includes 18% tax, the amount before tax is 59,000 ÷ 1.18 = 50,000, not 59,000 − 18%.

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. Percentage change has a direction — it compares a new value against an old one and divides by the old. For 40 and 50, the change from 40 to 50 is 25%, but the difference between them is 10 ÷ 45 × 100 = 22.2%.

How do I work out a percentage in my head?

Find 10% by moving the decimal point one place left, then build from it: 5% is half of that, 20% is double, 15% is 10% plus 5%. It also helps to know that x% of y always equals y% of x — 4% of 75 is hard, 75% of 4 is three.

What is the difference between percent and percentage points?

A rate going from 5% to 7% has risen by two percentage points, but by 40 percent. Both are correct and they mean very different things, which is why the two phrases are not interchangeable.

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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