# Percentage Calculator

Percentage calculator is a tool that lets you do a simple calculation: how many percent of X is Y? The tool is pretty straightforward. All you need to do is fill in two fields and the third one will be calculated for you in the real time.

Other than being helpful with learning percentages and fractions, this tool is handy in many different situations. For example, you may use percentage calculator to find an amount of income tax. Keep reading if you would like to see how to find percentages and what's the percentage formula.

There are a few calculators that solve very related problems: percentage decrease and percentage increase calculators show how much things change in plus or in minus, percentage change doesn't care whether it's negative or positive and finally percentage difference takes care of a very similar concept, used when we don't know the direction of the calculation (from number A to B or B to A).

## What is percentage?

One percent is a hundredth. We use a % sign or pct to denote it. So `5 percent`

is the same as `5%`

, `5 pct`

, `0.05`

, `5/100`

or `five hundredths`

. It is as simple as that and percentage calculator is a tool to do it :).

It is all nice, but we usually do not use percents just by themselves. Mostly we want to say how big is one number in relation to another number. For example, what is `40% of 20`

? It is `40 hundredths of 20`

, so if we divided 20 cookies into 100 even parts (good luck with that!), 40 of those parts would be our 40% of 20 cookies. Let's do the math: 40/100 * 20 = 8. A little tip is in order: to divide by 100, simply move the dot two spaces to the left. In our calculation, 40/100 * 20 could be done as (40 * 20) / 100 (same thing). 40 * 20 is 800. Move the dot in 800 by 2 digits to the left and you get 8.00. 8! In our calculator, enter 40 and 20 (so it reads "40% of 20" is...).

Percentage is a way to express a relation between two numbers as a fraction of `100`

. In other words, the percentage tells us how one number relates to another. If we know that number A is `25%`

of number `B`

, we know that `A`

to `B`

is like `25`

is to `100`

(one more transformation: `A`

is four times smaller than `B`

). This is Percentage Calculator's lesson on what is percentage.

It's easiest to explain what is percentage on cookies. It is surprising how often cookies save the day, right? Say we have a big drawer with 100 compartments (a 10x10 grid). Every compartment is `1 hundredth`

, or `1%`

of the whole drawer. We then fill this drawer with cookies in a way that gives us exactly the same number of cookies in each compartment.

At first, let's start with `100 cookies`

. It's easy: every compartment gets exactly `1 cookie`

. So one percent of one hundred is one.

Let's go with something a bit harder and four times more delicious: `400 cookies`

! We're dividing them evenly and every compartment gets `4 cookies`

. Cookies look smaller, but in our imagination they are the the same, just the drawer is much bigger! `One percent`

of `400`

is `4`

. How about `15 percent`

? It's `15 compartments`

times `4 cookies`

- `60 cookies`

. My tummy starts to ache a little, but it has never stopped me from eating more cookies!

Now something even harder - `250 cookies`

. Oh-oh... we divided up the first `200 cookies`

, placing `2`

in every compartment. Now we are left with `50 cookies`

that need to be spread evenly... hmmm... it's half a cookie in every box. You are right - this time `1 percent`

of the total number of cookies is two and a half. How many do we have in `15 boxes`

? `2.5 * 15 is 37.5`

.

So what is percentage good for? As I wrote earlier, percentage is a way to express a ratio. Say you are taking a graded exam. If I told you that you got `123 points`

, it really would not tell you anything. `123`

out of what? Now, if I told you that you got `82%`

, it's a solid information. Even if I told you you got `123 out of 150`

, it's harder to feel how well you did. A week earlier there was another exam and you scored `195 of 250`

, or `78%`

. While it's hard to compare `128`

of `150`

to `195`

of `250`

, it's easy to tell that `82%`

score is better than `78%`

. After all, it's the percentage that counts!

Percentages can easily be converted to decimals. Just divide the percentage by `100`

and you are set. `15%`

is the same as `0.15`

. `0.15`

of `250`

cookies is `thirty seven and a half`

.

## How to find percentage?

While it's certainly quick and painless just to use our percentage calculator, you don't always have an access to a computer or a smartphone. Also, it's just plain cool to be able to perform calculations in your head. Maybe not as cool juggling flaming torches, but close.

The percentage tells you how number A relates to number B. A real world example could be: there are 2 girls in a group of 5 children. What's the percentage of girls? In other words, we want to know what's the ratio of girls to all children. It's `2 out of 5`

, or `2/5`

. We'll call the first number a numerator and the second number a denominator, because this is how we call these two parts of a fraction. To calculate percentage, multiply this fraction by `100`

and add a percentage sign. `100 * numerator / denominator = percentage`

. In our example it's `100 * 2/5 = 100 * 0.4 = 40`

. Forty percent of the group are girls.

Let's go the other way around. Say we know that `70 percent`

of fruits in the basket are apples and there are `30`

fruits altogether. It could be worse, they could be lemons. So how many apples do we have? Let's get our percentage formula: `100 * numerator / denominator = percentage`

. We want to find out the numerator... let's move all the other parts of the equation to the other side. Both divide both sides by `100`

(to get rid of `100`

on the left) and then multiply both sides by the denominator. This is what we get: `numerator = percentage * denominator / 100`

.

Let's substitute percentage and denominator with our values: `numerator = 70 * 30 / 100`

. Now it's easy: `numerator = 1800 / 100 = 18`

We have `18 apples`

. Should be enough for a lunch. Or a rather violent food fight.

Now let's solve a problem with an unknown denominator. I spent `30 percent`

of my pocket money on a bubble gum (I never said I'm a great investor). I bought `12 sticks`

for `$1`

each. So we know that `$12`

was `30`

percent of my total budget. How much money did I have before I almost literally blew it away? Let's start with our formula: `100 * numerator / denominator = percentage`

or `100 * 12 / denominator = 30`

. This time we want to find out denominator... let's multiply both sides by denominator and then divide by percentage... this way we'll get `100 * 12 / 30 = denominator`

.
And the other way around... `denominator = 100 * 12 / 30 = 1200 / 30 = 40`

. We had `40 dollars`

. We spent `30 percent`

, or `$12`

on bubble gum. Totally worth it.

## What's the percentage formula?

Staying with our cookie examples, let's name the three parts in our equation: the percentage (40%), the whole (20) and the part (8).

The formula for percentage is this: `percentage = 100 * part / whole`

and it answers the question "what percentage of 20 is 8".

The formula for a part is: `part = whole * percentage / 100`

and it gives an answer to "what is 40% of 20?".

## History of percentage

The term percent is often attributed to Latin per centum ("per hundred"). Actually it is wrong. We got the term from French pour cent. However, the whole idea of thinking in the terms of hundredths comes from ancient Greece. Please note that it is based on Wikipedia and there is a [citation needed] right where we would like to see a source.

## Spelling

Percent or per cent? It depends on your diet, really. If you eat hamburgers for majority of your meals, it is percent. If you prefer fish and chips, it is per cent. If you spray your fish-smelling chips with vinegar, then it is per cent, mate (as opposed to burger eaters' percent, dude). When it comes to percentage, both sides of the pond are in agreement: it should be a single word. Still confused? Americans say percent, British use per cent. Something tells me American English is more popular nowadays, so this website uses a single-word form.

## Per mille

**Per mille**, **per mil**, **per mill** or simply **‰** is similar to percent, only it is one thousandth (`1/1000`

or `0.001`

). If our household's budget is `$2400`

and we allocated `1 per mille`

of that to buying chewing gum, we would spend `2.4 dollars`

(2 dollars 40 cents) on annoying our teachers (well, 20 years ago it was not allowed in Polish schools... do not know the rules nowadays :-) ). It's almost the same to how you find percentages. If you wanted to use percentage calculator to count per mille, simply use numbers `10x`

lower (`0.2`

instead of `2`

, `4`

instead of `40`

).

## Percentage point

Percentage point is a rather tricky beast. We use it all the time even if we don't know it - and in these situations we often incorrectly say percent instead of percentage point. Once you read this page, you will know how to do it properly and will be annoyed for the rest of your life (because other people will keep making the mistake).

Senator Homer Simpson was polling at `10%`

last month. He had a few successful debates since then and now `12%`

of the population wants to vote for him. What's the change? You want to say `2%`

, am I right? It's wrong! Let's examine this. Imagine the whole population is `1000`

people. `10%`

of them is `100`

. `12%`

is `120`

. What's the percentage increase? It's `100`

* `20`

/ `100`

= `20%`

!

This is when percentage points come in handy. We use percentage points when we want to talk about a change from one percentage to another. A change from `10%`

to `12%`

is `2 percentage points`

(or `20 percent`

).

Another way to think about a difference between a percentage change:

percentage points change is that percentage change is in relation to the previous value (`10%`

in our example... and one percent of that is one hundredth of `10% = 0.1%`

)
change in percentage points is in relation to the whole part (whole being the whole population, or `1000`

in our example. `1%`

of that is `10`

).
To calculate percentage points, simply subtract one percentage from another. `30%`

is `20`

percentage points higher than `10%`

.

Percentage point can be abbreviated as pp.

Now that you know everything about percentage points I guarantee you that you will read or hear other people incorrectly saying percent when they should be using percentage points. If you're anything like me, you will scream at the newspaper, insulting it in some made up language. This helps freeing up space around you when you're using public transportation :).