Ever find yourself baffled by the innocent percentage? Going mad trying to figure out whether you should divide or multiply? Read on for the ultimate guide to understanding, using and calculating percentages.
Percentages are used very, very frequently in almost all areas of life. If you don't understand them, or how to work with them, it can make life quite frustrating. By the end of this article you'll know exactly how to use them and, hopefully, understand them too.
Long story short: to calculate what percentage a number (the first number) is of another (the second number), simply divide the first number by the second number and multiply by 100. Or in other words (first number / second number) * 100.
What this guide aims to show you
This guide has 3 sections that progress in a logical order to give you an overall understanding and familiarity with percentages.
What is a percentage?
A percentage is just a way of representing fractions or proportions. What makes them special and different from fractions is that they are specifically out of 100.
For example 10% is just another way of writing 0.1, which is just the decimal way of writing the fraction 1/10.
So if you asked someone what is 10% of 50, you’re just saying what is one tenth of 50. Simple right? (The answer is 5 by the way).
Why are they important?
Percentages are used almost everywhere you can think of. Finance, business, marketing, baking, politics…the list goes on.
Basically, anywhere there are numbers, you’ll find percentages. The reason? They are a convenient way to compare things.
Take a scenario where you have to reward one of two children based on who did better on a test. Let's also assume the tests are set to the same standard of difficulty. The first student, Alice, got 21 out 30 on her Mathematics test. The second student, Bryan, got 41 out of 60 on their test. Who did better on their Maths test?
You can't just say "the student who got the higher mark", because that's not comparing apples with apples. Alice and Bryan wrote tests with different numbers of available marks. Bryan, because his test was out of 60, had more available marks to earn, and so it was easier to get more marks than Alice. How do you make an apples to apples comparison?
Percentages are useful here, as you can just work out what percentage Alice and Bryan got on their tests and compare the two numbers easily to see who did better.
In this case Alice (70%) narrowly beat out Bryan (68.33%) and so gets the reward!
How do I calculate a percentage?
Calculating a percentage is easy - just take the first number, divide it by the second number, and multiply the result by 100.
(first number / second number) * 100 = percentage
The difficulty is in knowing which number in your scenario is the first or second number!
If you just want the answer, then feel free to use our ultimate percentage calculator, otherwise, read on.
To work out what number goes where for your scenario, try phrasing it as something like:
What percentage is x of y?
Or
What is x as a percentage of y?
If you can do this, then per the formula above, x will be the first number, and y will be the second number! It's that easy.
In the Alice and Bryan case, we wanted to calculate what percentage they got on the test. So the marks that Alice got right were 21, out of a possible 30. The question is "what percentage is 21 of 30"? So in this case, the first number is 21, and the second number is 30. Follow the formula above and voilà! You get 70%.
In Bryan's case, the question is "what percentage is 41 of 60?". The first number is 41, and the second number is 60. The percentage is 68.33%.
Percentage changes and how to calculate them
Another common use case of percentages is in working out what a percentage change was from one number to another.
Imagine you are trying to work out how much more expensive an apple has gotten.
The last time you went to the grocery store, it was $0.75. This time, it's $0.90! What is the percentage increase in the price of that apple? Or, in other words, what is the increase in the price of the apple, as a percentage of the original price?
This should be very familiar to you, as it's the same formula from above when calculating a percentage! In other words:
"What is [amount that it changed in $] as a percentage of [the original price]?"
Given that calculating the price change of the apple in $ is to just subtract the old price from the new price, the formula for the percentage change is:
([new number - old number] / old number) * 100
So for the apple, the percentage change in price was:
([0.90 - 0.75] / 0.75) * 100 = 20%
(Yikes, that's a much more expensive apple!)
And this works for percentage increases as well as percentage decreases. Just follow the formula.
For example imagine bananas have actually dropped in price from $1.10 to $0.95. The percentage decrease is:
([0.95 - 1.10] / 1.10) * 100 = -13.64%
Or in other words, it dropped by 13.64%.
I hope that guide was helpful! For any other percentage questions, or just feedback on the guide, get in touch.
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