Percentage Calculator
Fill in the blanks and press Calculate. Answers stay exact: 7 out of 8 is 87.5%, not 90%.
This percentage calculator answers the three questions that between them cover almost every percentage anyone actually needs: what is 20% of 80, what percent of 80 is 20, and 20 is 25% of what number. Pick the question, fill in the two blanks, and the answer arrives with its working.
It also does something surprisingly few percentage calculators bother with. Seven out of eight is 87.5%, exactly, and this page says 87.5% rather than rounding it to 90% or handing you 87.50000000000001. More on why that matters further down, because it is the reason this tool exists rather than the hundredth copy of the same form.
Per Cent Means Per Hundred, and That Is the Whole Idea
The word comes from the Latin per centum. Split anything into a hundred equal pieces, count how many of them you are talking about, and you have a percentage. Twenty-five per cent is twenty-five of those hundred pieces, which is why 25% and the fraction 25⁄100 and the decimal 0.25 are three ways of writing the same number.
Fractions with different denominators are a nuisance to compare. Is 7⁄16 bigger than 3⁄7? You have to stop and think. Rewrite them as 43.75% and 42.86% and the answer is immediate. That is the entire reason percentages were invented, and it is worth holding onto: a percentage is not a special kind of number, it is a fraction that has agreed to use 100 as its denominator so that comparisons become easy.
Which means every percentage question in existence is the same fraction wearing different clothes.
One Equation, Three Questions
Three quantities appear in every percentage problem, and they are locked together by a single relationship:
part = (percent ÷ 100) × whole
Know any two of the three and the third follows. That is all this calculator does, and it is why it has three modes rather than three separate tools:
| You know | You want | The question, in words |
|---|---|---|
| percent, whole | the part | What is 20% of 80? |
| part, whole | the percent | 20 is what percent of 80? |
| part, percent | the whole | 20 is 25% of what? |
Students who learn the three as three separate recipes end up memorising three formulas and picking the wrong one under pressure. Students who learn them as one equation rearranged three ways never have that problem. The calculator above is deliberately laid out to encourage the second habit: the question appears as a sentence with two blanks in it, so you read what you are asking rather than filling boxes labelled with letters.
How to Calculate a Percentage of a Number
The most common of the three, and the one people reach for at a restaurant table.
Divide the percentage by 100, then multiply. For 20% of 80: 20 ÷ 100 = 0.2, and 0.2 × 80 = 16.
The first step is the one worth doing carefully, because once the percentage has become a plain multiplier the rest is a single multiplication that nobody gets wrong. A percentage is never used in the form it is written; it always becomes a decimal first, whether you notice yourself doing it or not.
There is a trick here that deserves to be better known. a% of b is always equal to b% of a. Both come out as (a × b) ÷ 100, so the order cannot matter. That sounds like a curiosity until you meet 4% of 75, which is awkward, and realise it is the same as 75% of 4, which is 3 and takes no thought at all. Or 8% of 50, which is 50% of 8, which is 4. Once you have seen it you will use it for the rest of your life.
How to Work Out What Percent One Number Is of Another
Divide the part by the whole, then multiply by 100.
For 20 out of 80: 20 ÷ 80 = 0.25, and 0.25 × 100 = 25%. The division gives a bare ratio — a fraction of one — and multiplying by 100 restates that same fraction out of a hundred instead.
Getting the two the right way up is where the marks disappear. The part goes on top. A useful sanity check costs a second: if the part is smaller than the whole, the answer must be under 100%, and if it is bigger, the answer must be over. A test score of 45 out of 60 cannot possibly be 133%.
How to Find the Whole When You Know a Part
This is the first calculation run backwards, and it is the one people find hardest.
If 20 is 25% of some number, then dividing 20 by 0.25 gives that number: 80. The instinct is to multiply, because percentages feel like they should shrink things, and multiplying is what shrank it in the first place. Undoing a multiplication means dividing.
The check is easy and I would do it every time. If the percentage is under 100, the answer must be bigger than the part you started with. Twenty is a quarter of eighty; eighty is comfortably bigger than twenty; the arithmetic behaved. If your answer comes out smaller, you multiplied when you should have divided.
Working Backwards From a Discounted Price
A jacket is $255 in a sale marked "15% off". What did it cost before?
Almost everybody's first move is to add 15% to 2,550, and almost everybody is wrong — the discount was 15% of the original price, not of the sale price. Set it up as a third-mode question instead and it falls out at once: the sale price is 85% of the original, so ask 2,550 is 85% of what? The answer is $300.
That works, and the calculator above will do it. But it makes you find the 85 yourself, and that is exactly the step people get wrong. The reverse percentage calculator takes the discount you were actually told — 15 — and does the subtraction for you, in the working, with the same treatment for sales tax. If you are working back from a price rather than forward from one, start there.
Why This Calculator Does Not Round Your Answer
Here is the part I care about most.
Type 7 and 8 into most percentage calculators and you get one of two disappointments: 87.50000000000001, which is a floating-point artefact leaking onto the screen, or a value rounded to some fixed number of decimal places on the assumption that you could not possibly need more.
Neither is right, because 7 out of 8 is exactly 87.5%. Nothing was measured. Nothing is uncertain. There are eight of something and seven of them count, and the answer terminates.
This calculator therefore treats whole numbers as what they nearly always are — counts — and leaves their answers exact.
Seven out of 1,600 comes back as 0.4375%, not 0.438%. Nine out of 1,024 comes back as 0.87890625%. Only a value that genuinely never terminates, like one third, gets shortened, and then it is shortened once rather than twice.
There is one exception, and it is deliberate. If you type a value with a decimal point in it — 12.5, or 9.81 — you are almost certainly reporting a measurement, and a measurement carries only so many significant figures. In that case the calculator offers a sensibly rounded figure alongside the full one and tells you how many figures your input justified. A count is exact; a measurement is not; the tool distinguishes between them, which is more than the arithmetic in most textbooks does.
Percentages Worth Knowing by Heart
Some percentages are tidy fractions in disguise, and recognising them turns a calculator job into a mental one. The tool points these out when it spots one.
| Percentage | Fraction | So, in your head |
|---|---|---|
| 50% | 1⁄2 | halve it |
| 25% | 1⁄4 | halve it twice |
| 20% | 1⁄5 | divide by 5 |
| 12.5% | 1⁄8 | halve it three times |
| 33⅓% | 1⁄3 | divide by 3 |
| 75% | 3⁄4 | quarter it, then take three |
Ten per cent is the one to build everything else on. Move the decimal point one place left and you have it — 10% of 847 is 84.7, no working required. From there, 5% is half of that, 20% is double it, and 15% is 10% plus 5%, which is how anyone who tips quickly is actually doing it.
Percentages Above 100, and Why They Are Fine
A percentage can exceed 100 and nothing is broken when it does. It simply means the part is larger than the thing it is being compared against.
If a shop sold 80 units last month and 100 this month, then this month's figure is 125% of last month's. If a recipe needs 40 g of butter and you use 60 g, you have used 150% of what was called for. Both statements are ordinary and correct.
Where it goes wrong is when 125% gets read as "a 125% increase". It is not. This month is 125% of last month, which is a 25% increase — the growth and the proportion are two different numbers, and the words "of" and "increase" are what separate them. Growth between two figures is a question this page deliberately does not answer, because it belongs to the percent change calculator, which handles the sign and the direction properly.
Per Cent and Percentage Points Are Not the Same Thing
This one causes real trouble in newspapers, and it is worth thirty seconds.
Suppose an interest rate goes from 4% to 5%. It has risen by one percentage point. It has also risen by 25 per cent, because one is a quarter of four. Both statements are true and they describe the same event with wildly different-sounding numbers, which is exactly why a headline writer picks whichever suits the story.
The rule is simple. Subtracting one percentage from another gives percentage points. Comparing one percentage to another as a ratio gives a percent change. When you see a bare "up 25%" attached to a rate, ask which was meant.
Where the Other Percentage Tools Come In
This page finds a percentage. Three related questions look similar and are not, and each has its own page because each divides by something different.
If your two numbers are the same quantity at two moments in time — a price last year and this year, a salary before and after a rise — you want growth, and the percent change calculator divides by the earlier value and keeps the direction. If your two numbers are equals, neither one a baseline — two lab trials, two supplier quotes — the percent difference calculator divides by their average, so the answer does not change when you swap them. And if one of your numbers is a known, accepted value and the other is your own measurement, the percent error calculator divides by the truth.
Four tools, four denominators. Choosing correctly is nearly always a matter of asking what the answer is supposed to be a percentage of.
How to Use This Percentage Calculator
Choose your question from the three at the top of the form. The sentence underneath changes to match, so you can read what you are asking before you type anything — the per cent sign moves to whichever box is actually the percentage.
Fill both blanks and press Calculate. Numbers can carry commas, a currency symbol or a unit — $1,500 and 80 kg both read cleanly — and decimals, fractions such as 1/3, and scientific notation all parse. The answer appears with a plain sentence stating the whole relationship, and the working below shows the formula, your own numbers substituted into it, and a check that runs the calculation back the other way.
Percentage Calculator FAQ
How do you calculate a percentage of a number?
How do you find what percent one number is of another?
What is the percentage formula?
How do I find the price before a discount?
Why does this calculator say 87.5% instead of 90%?
Can a percentage be more than 100?
Is 8% of 25 the same as 25% of 8?
What is the difference between per cent and percentage points?
How do I work out a percentage in my head?
Is this percentage calculator free?
Percentages reward a small amount of understanding out of all proportion to the effort. Learn the one equation, know which quantity you are missing, keep the part on top when you divide, and remember that a discount came off the original rather than off the price you can see. The calculator at the top will do the arithmetic in a blink and show you every step of it — but the sanity checks in this article are the part that will still be useful when there is no calculator to hand.
