The concept of percentages dates back to the Roman era, during which taxes were often levied as 1/100. In fact, the word itself has Latin origins and is derived from “per centum“, which translates to “by the hundred”. The percentage sign (%) gradually evolved from per 100, to per cent, to p cento, to p/c, and then finally, the modern %. How to calculate percentage
A percentage is a fraction that always has 100 as the denominator. So 30/100 is 30%, for example. Other ratios can be converted into percentages by converting the value of the whole – that is the denominator – to 100 and then converting the value of the part – that is the numerator – by the same metric.
So how do you calculate the percentage? And what other formulas are there for finding solutions to other questions regarding percentages?
We are going to take you through how to calculate various percentages by using a number of different formulas.
How to calculate percentage
There are different ways of calculating the percentage of a number and the method can vary depending on the type of answer you are looking for. The simplest method is to do: Percentage = (Value / Total Value) x 100.
In all cases of finding the percentage value of a number, you must convert the value of the whole to 100. This may sound tricky at first, but we will take you through all the simple steps to get you there.
So let’s jump in and take a look at…
What are the main formulas for calculating percentage?
As we have just seen, the simplest formula for calculating percentage is Percentage = (Value/Total Value) x 100. This is known as the unitary method.
For example, if you wanted to find out what percent 5 is of 25, you would do:
- 5 / 25 = 0.2
- 0.2 x 100 = 20
- 5 = 20% of 25.
And you can also work this out the other way round by converting 25 to 100. Whenever you convert your total value or denominator, you must convert your numerator by the same amount. So you would do:
- 25 x 4 = 100
- 5 x 4 = 20
- 5 = 20% of 100.
However, there are many numbers that are not a factor of 100, so this method would not work. In such an instance, use the first method.
If you want to find out what 20% of 25 is, then you can do so by finding 1% of 25 by dividing 25 by 100 and then multiplying your answer by 20. For example:
- 25 / 100 = 0.25
- 0.25 x 20 = 5
- 20% of 25 = 5
Another good tip to remember with percentages is that they are always reversible. So 25% of 40 (10) is the same as 40% of 25 (also, 10). Sometimes maths just works!
How to calculate the percentage difference between two numbers
The percentage difference, or the percentage change, is the change in the value of a number in terms of the initial value being converted to 100. For example, someone may have a salary raise which can be denoted as a percentage increase.
In any scenario for calculating a percentage difference, you can either calculate a percentage increase or a percentage decrease.
Calculating percentage difference is simple once you know the percentage formula.
To calculate percentage increase you do:
- Percentage Increase = (Increased Value – Original Value) / Original Value × 100
So, if you originally had 20 apples and now you have 25 you would do:
- 25 – 20 = 5
- 5 / 20 = 0.25
- 0.25 x 100 = 25
- There has been a 25% increase.
To calculate percentage decrease you do:
- Percentage Decrease = (Original Value – Decreased Value) / Original Value × 100.
So, if you originally had 20 apples and now you have 15 you would do:
- 20 – 15 = 5
- 5 / 20 = 0.25
- 0.25 x 100 = 25
- There has been a 25% decrease.
How to calculate percentages of more than 100%
Calculating percentages greater than 100% is simple. You may need to do this in scenarios in which there has been a huge increase. For example, you may be told that applications to a school have gone up by 250%.
To calculate a percentage greater than 100%, you simply insert a decimal point between the tens and hundreds unit of the percentage increase and use that number to multiply by the original value.
For example, a 250% rise from 80 would be:
- 2.5 x 80 = 200
- So, a 250% rise from 80 is 200.
Basic percentages for mental maths
If you can work out some basic percentages, then you may find that you are able to perform many percentage calculations in your head.
So remember that:
- 50% is always half. So to calculate 50% of a number, you simply divide it by 2.
- 25% is always a quarter. So to calculate 25% of a number, simply divide it by 4.
- 10% is always one-tenth. So to calculate 10% of a number, simply divide it by 10.
- 5% is half of 10%. So to calculate 5% of a number, simply find 10% of the number and divide the answer by 2.
Online mathematical resources
There are some great resources online that can help you work out percentages along with many other mathematical problems. Here we have included a list of some of our favourites:
- Percentage Calculator allows you to work out a range of different questions relating to percentages.
- Good Calculators has all manner of calculators free to use, including percentage calculators too.
- Calculator-1 is a simple to use online calculator that can perform all the functions of a regular calculator and explain how to use it.
- GCF-LCM is a great calculator for finding greatest common factors and lowest common multiples.
- Desmos is an advanced online scientific calculator that can perform complex equations and offer guidance to users.