Percentage calculator
Four sums, each with its own answer: the percentage, the change, and the tax.
What is a percentage of an amount?
Check the numbers you entered.
What percentage is one amount of another?
45 is 25% of 180.
From one figure to another, how much changed?
From 1,200 to 1,500 is a rise of 25%.
The way back is not the same percentage: from 1,500 to 1,200 is a fall of 20%. Same difference, different percentage, because they are measured against different figures.
Add or remove a percentage from a price
Type the price and the percentage.
- Adding 20%
- 144.00
- Removing 20% (÷ 1.20)
- 100.00
- Subtracting 20% (× 0.80)
- 96.00
Removing is not subtracting: if 120.00 already has 20% inside it, the base comes from dividing by 1.20 (100.00), not from subtracting 20% (96.00). By the same token, adding and then removing the same percentage does not bring you back to the starting price: 120.00 → 144.00 → 115.20.
100% private — the maths happens on your device. Neither the amounts nor the prices you type are sent to any server.
Pure arithmetic: there are no rates here that expire and no tables that go stale. Figures are rounded to two decimals when displayed, never before the calculation. Tax rates differ by country and by what is being sold, so check which one applies to you before putting a number on an invoice.
Reference table
The most-searched percentages, applied to 340, the amount you typed above.
| Percentage | Is | Subtracting it |
|---|---|---|
| 1% | 3.40 | 336.60 |
| 5% | 17 | 323 |
| 10% | 34 | 306 |
| 15% | 51 | 289 |
| 20% | 68 | 272 |
| 25% | 85 | 255 |
| 30% | 102 | 238 |
| 40% | 136 | 204 |
| 50% | 170 | 170 |
| 75% | 255 | 85 |
"Subtracting it" is what is left after taking that percentage off the amount: it is the sales-and-discounts column. It will not give you the pre-tax base of a price that already has tax inside it — for that you divide, and the last block of the calculator handles it.
How to use it
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1. The percentage and the amount
At the top sits the everyday sum: how much a given percentage of a figure comes to. Type the two numbers or drag the slider and the answer appears straight away.
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2. Scroll to the sum you need
Underneath are the other three, each with its own title and its own answer: what percentage one figure is of another, how much a price has moved, and how to add or strip out tax.
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3. Check the table at a glance
The reference table shows the most common percentages of your amount, alongside what is left once they are taken off: the number you actually want in a sale.
Percentages, and the four places they go wrong
A percentage is a part of every hundred, which is why every sum below comes down to multiplying and dividing by 100. Working out 20% of 340 means multiplying 340 by 20 and dividing by 100: it comes to 68. The mental shortcut works just as well: 10% of 340 is 34, so 20% is twice that.
So far, no trouble. The tangles start when the percentage is already inside the figure, when it has to be compared with another percentage, or when two are applied one after the other. These are the four stumbles, in order of how often they happen.
Removing a percentage is not subtracting it
This is the most repeated mistake on the internet, and it is an expensive one because it turns up on every invoice. A price of 120 with 20% VAT included does not have a pre-tax base of 96, it has exactly 100. Subtracting 20% from 120 gives 96, and that figure means nothing at all: the tax was never calculated on the 120, it was calculated on the 100 that existed before it was added.
The key is noticing that, when the percentage is already inside, the figure in front of you is not 100%, it is 120%. Going back means undoing a multiplication, and a multiplication is undone by dividing: 120 ÷ 1.20 = 100. The general rule, for any rate: base = price ÷ (1 + rate ÷ 100). At 20% you divide by 1.20; at 10%, by 1.10; at 5%, by 1.05.
The check takes a second and is always worth doing: if 100 were the base, adding 20% would give 120, which matches the invoice. If the base were the 96 you get from subtracting, adding the tax back would give 115.20, which matches nothing. In the last block of the calculator both figures are shown side by side so the difference is visible without having to take anyone's word for it.
One geographic note, since this page is read in a lot of places: in the United States, sales tax is added at the till and almost never sits inside the shelf price, so this particular trap comes up far less often. Where VAT or GST is included in the displayed price — the UK, the EU, Australia, and most of the world — it comes up constantly.
A rise and a fall of the same percentage do not cancel out
An item at 100 goes up 20% and lands at 120. A few weeks later it comes down 20% and stops at 96, not 100. There is no trick and no rounding error: the rise was 20 calculated on 100, and the fall was 24 calculated on 120. Each percentage applies to whatever figure is in front of it at that moment, and the figures were different.
A useful consequence follows: to undo a 20% rise you have to take off 16.67%, not 20%. And a less pleasant one: when something falls 50%, getting back requires a 100% rise. That is the arithmetic behind why a portfolio that loses half its value has to double to return to where it started.
Percentage points are not percentages
When the figure under discussion is itself a percentage, the change is measured in percentage points. If an interest rate goes from 5% to 6%, it has risen one percentage point and at the same time risen 20%. Both statements are true and they do not say the same thing, which is why it pays to look closely at which one is being used.
It is the slip newspapers make daily, and almost always in whichever direction is more striking: "unemployment jumps 20%" sounds like a catastrophe when what happened is a move from 5% to 6%, and "the tax only goes up a point" sounds like nothing when that rise takes a fifth more of your money. Neither phrasing is a lie; picking one and staying quiet about the other is what misleads.
Two discounts in a row do not add up
20% off followed by "a further 10% at the checkout" is not 30%: it is 28%. On 100, the first discount leaves 80 and the second is worked out on that 80, so it takes off 8 and leaves 72. The second percentage always applies to the already-reduced price, never to the original. The same happens with two rises in a row, except that there the total comes out higher than the sum: two 10% rises make 21%, not 20%.
What this calculator does not do
It does arithmetic, and only arithmetic. It applies no tax rules: it does not know your country's rates, which goods qualify for a reduced rate, what rounding your tax authority requires, or how withholding works. Nor does it do compound interest, which is a percentage applied many times over and has its own tool.
On decimals: figures are rounded to two places when displayed, never before the calculation. That is the difference between seeing 68 and seeing 68.00000000000001, and also the reason 3% of 19.99 shows as 0.60 rather than 0.5997. If you need an exact figure to the cent for an invoice, bear in mind that legal rounding is applied to the total, not line by line.
Frequently asked questions
How do you work out a percentage of an amount?
Multiply the amount by the percentage and divide by 100. 20% of 340 is 340 × 20 ÷ 100 = 68. The mental shortcut is to move the decimal point: 10% of 340 is 34, so 20% is 68.
How do you remove VAT from a price?
By dividing, not subtracting. A price with 20% VAT already inside it is divided by 1.20: 120 comes back to 100. Subtracting 20% would give 96, which is a different and wrong figure, because the tax was never calculated on the 120 — it was calculated on the 100 that existed before it was added. For a 5% rate you divide by 1.05, and so on.
What percentage is one amount of another?
Divide the part by the total and multiply by 100. For example, 45 out of 180 is 45 × 100 ÷ 180 = 25%. If the total is zero the sum does not exist: you cannot divide by zero, and no amount is a percentage of nothing.
How do you calculate the percentage change between two figures?
Subtract the old figure from the new one, multiply by 100 and divide by the old one. From 1,200 to 1,500 is 300 × 100 ÷ 1,200 = a 25% rise. Watch the direction: from 1,500 back to 1,200 is a 20% fall, not 25%, because it is measured against a different starting figure.
Why doesn't a 20% rise followed by a 20% fall leave the price unchanged?
Because each percentage is worked out on a different figure. A price of 100 that rises 20% becomes 120, and that 120 falling 20% lands on 96: the rise was 20 on 100 and the fall was 24 on 120. To undo a 20% rise you have to take off 16.67%.
What is the difference between a percentage point and a percentage?
When the figure being discussed is itself a percentage, the change is measured in points. Going from 5% to 6% is a rise of one percentage point, and at the same time a rise of 20%. Both statements are true and they do not mean the same thing: saying a 5% tax has risen 20% sounds like far more than it is, and saying it has gone up one point hides that it now takes a fifth more of your money.
How do two consecutive discounts work?
One after the other, never added together. 20% off and then a further 10% off is not 30%: on 100, the first leaves 80 and the second leaves 72, so the real discount is 28%. The second percentage always applies to the already-reduced price, not to the original.
Do you store what I type?
No. Every calculation happens inside your own browser. Neither the amounts nor the prices you type leave your device: there is no server to receive them and no database to keep them. You can check by turning on airplane mode and watching the calculator carry on working.