Percentage Calculator
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Every need to calculate a percentage? It is something that comes up regularly for teachers, business owners, sports fans and poker players.
You can probably remember learning about percentages in school, but it isn't always easy to remember how to find a percentage. Instead of working it out in your head, use our free online percentage calculator at the top of this page.
Below we'll explain how percentages are calculated and how to figure out percentage differences.
What is percentage?
Percentage expresses a number as a part of 100. If you've ever taken a Latin course you may be able to work out the etymology. It comes from "per centum". "Per" means "through or by", while "centum" means "hundred"
How to calculate percentage?
Percentage expresses the relationship between two numbers in an easy-to-understand and consistent way. At its most basic, it's division.
Here's the formula to figure out a percentage:
Keep in mind
Divide your first number by your second number and then multiply the result by 100.
x/y * 100 = percentage
For example, say you have 5 apples, but you ate 3 of them. Want to find the percentage of the number you just ate? Divide the 3 apples eaten by the 5 you started with. Then multiply it by 100.
Good to know
3/5 = 0.60
0.60 * 100 = 60%
If you move that decimal over two places, you get 60, or the percentage of eaten apples.
How is percentage used?
Percentage is used all the time, but essentially it shows the relationship between two numbers.
Let's assume that you're taking a mathetics class at a Canadian university. You earn 89 points on a test with a maximum of 100 points possible. What percentage is that? That's easy, you got an 89%.
Usually, you won't have a percentage to work out that's already on a 100-point scale. We use percentages to express how numbers relate to one another on a 100-point scale. It makes them easier to think about and compare.
Here's a problem to think about:
Keep in mind
Which is larger? 9/16ths or 5/9ths?
Most of us can't quickly figure this out in our heads. Not so easy, is it? But if we take 9 and divide it by 16 to get 0.5625 and 5 by 9 to get 0.5555 then it's easy. Is 0.5625 or 0.5555 the bigger number? Expressed like that, we can compare and work out through the percentage that 9/16ths is slightly larger.
Percentages are used all of the time. Examples include you wanting to figure out the percentage of your total credit card payment is interest or to compare the potential return on your investments.
How do I calculate a percentage increase?
Has your rent increased recently? Let's say it went up $125 from $1,200 to $1,325. It feels like too much to you, so you want to find out as a percentage how much it increased.
It's easy to find the relationship between your old and new rent using the calculator at the top of the page, but knowing how the calculation is done is important.
Here are two formulas for calculating a percentage increase:
Keep in mind
Percentage Increase = ((New Number ÷ Initial Number) – 1) ×100
-or-
Percentage Increase = (New Number - Original Number) ÷ (Original Number) × 100
Let's look at the math for our rent increase example:
Keep in mind
- First, 1325 new rent / 1200 old rent = 1.104167.
- Next, subtract 1 from that to get 0.104167
- Then multiply it by 100 to calculate a percentage increase of 10.4167%.
- Finally, for simplicity, let's round that up to 10.42%
Armed with this information you might decide to tell your landlord that the increase was unfair! If your apartment is in Ontario, you might argue with them that the provincial rent increase guidelines don't let them raise your rent by more 2.5%. That's a maximum of $1230, far lower than the $1,325 figure.
Math is useful! Calculating percentages just saved you $95 per month.
Good to know
If you use the above formula and get a negative number then you have a percentage decrease rather than a percentage increase.
How do you calculate a percentage decrease?
A percentage decrease works the same way as a percentage increase.
Here's the formula again:
Keep in mind
Percentage Increase = (Original Number - New Number) ÷ (Original Number) × 100
Say you have been eyeing a special anniversary edition of your favourite graphic novel at a bookstore. It usually costs $39 but today it is marked down to $35. You can calculate the discount off like this:
Keep in mind
- $39 - $35 = $4
- $4 ÷ $39 = 0.1026
- 0.1026 × 100 = 10.26% percentage decrease
10.26% off your graphic novel is a nice deal, to be sure. But knowing that percentage you might decide that you're patient and better off waiting for next month's 20% sale.
How do I calculate a reverse percentage?
A reverse percentage, or inverse percentage, lets you to calculate the original number if you only have the new number and the percentage was applied to it.
The most common example of this is when you want to know the original price of something that’s been discounted.
Here is the formula:
Keep in mind
(new number × 100 ) ÷ (100 - x%)
For example:
You buy some clothing that costs $225 after a 10% off sale, but you'd like to know much they would have cost without the sale?
Keep in mind
- First, let's work out the first side of the equation: *(225 ×100) = (22 500)) ÷ (100 - 10%)
- Next up is the second side of the equation: (22 500) ÷ ((100 - 10%)= 90)
- Finally, we take the two answers: 22 500 ÷ 90 = 250
The original price prior to the sale was $250.
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