How to understand and calculate percentages

This guide is one in a series on different aspects of statistical literacy. The others can be found in the House of Commons Library's Good Information Toolkit.

Percentages express proportion: they show how big one number is compared with another. For example, 62.5% of households in England and Wales were homeowners in 2021 2: this compares the number of homeowning households with the number of households overall.

They can also be used to show how big a change is as a proportion of the starting number.

What are percentages?

Percentages are a way of expressing what one number is as a proportion of another.

Percentages are essentially a way of writing a fraction with 100 on the bottom (the denominator). For example:

• 20% is the same as 20/100
• 30% is the same as 30/100
• 110% is the same as 110/100

The term ‘percent’ comes from the Latin ‘per centum’, meaning ‘by a hundred’.

Why are percentages useful?

Percentages are useful because they allow us to compare groups of different sizes.

For example, if we want to know how smoking varies between countries, we use percentages. We could compare Belgium, where 22.9% of all adults smoke, with Greece, where 29.6% of all adults smoke. This is far more meaningful than a comparison of the total number of people in Belgium and Greece who smoke because this would not account for the size of each country’s population.

How to calculate percentages

In general, to work out what w is as a percentage of y, we use the following equation:

(w ÷ y) x 100 = z%

Sometimes we know w and y and want to work out the percentage z; sometimes we know the percentage z and the number w and want to work out the number y.

The following sections work with different rearrangements of this equation to work out w, y, and z in example calculations.

How to calculate a percentage of a whole number

To calculate what 40% of 50 is, first write 40% as a fraction (40/100) and then multiply this by 50:

(40 ÷ 100) x 50 = 0.4 x 50 = 20

To calculate what 5% of 1,500 is, write 5% as a fraction (5/100) and then multiply this by 1,500:

(5 ÷ 100) x 1,500 = 0.05 x 1,500 = 75

In general, to calculate what a% of b is, first write a% as a fraction (a/100) and then multiply by b:

a% of b = (a ÷ 100) x b

How to change a number by a certain percentage

To calculate what we get if 30 increases by 40%, we first use the method shown above to calculate the size of the increase, which is 40% of 30:

(40 ÷ 100) x 30 = 0.4 x 30 = 12

As we are trying to work out what the final number is after this increase, we then add the size of the increase on the original number to find the answer:

30 + 12 = 42

To calculate what a 20% decrease is from 200, we first calculate 20% of 200:

(20 ÷ 100) x 200 = 0.2 x 200 = 40

As we are trying to work out what the final number is after this decrease, we then subtract the size of the decrease from the original number to find the answer:

200 – 40 = 160

In general, to calculate what a c% increase or decrease is on d is, we first calculate c% of d:

(c ÷ 100) x d

We then add this to our original number for an increase, or subtract for a decrease:

d + (c ÷ 100) x d

d – (c ÷ 100) x d

How to calculate what one number is as a percentage of another number

To calculate what 5 is as a percentage of 20, we divide 5 by 20, and then multiply by 100:

(5 ÷ 20) x 100 = 25%

So, 5 is 25% of 20. We can check our calculation by working out what 25% of 20 is:

25% of 20 = (25 ÷ 100) x 20 = 0.25 x 20 = 5%

To calculate what 3 is as a percentage of 9, we divide 3 by 9, and then multiply by 100:

(3 ÷ 9) x 100 = 33.3%

So, 3 is 33.3% of 9.

In general, to calculate what e is as a percentage of f, we first divide e by f and then multiply by 100 to give (e ÷ f) x 100. So, e is:

e is ((e ÷ f) x 100) % of f

How to calculate percentage change from one number to another

To calculate the percentage increase from 10 to 15, we first work out the difference between the two numbers:

15 – 10 = 5

We then work out what this difference (5) is as a percentage of the number we started with (10):

(5 ÷ 10) x 100 = 0.5 x 100 = 50%

This gives us the answer: there is a 50% increase from 10 to 15.

To calculate the percentage decrease from 50 to 40, we first work out the difference between the two numbers:

50 – 40 = 10

We then work out what this difference (10) is as a percentage of the number we started with (50):

(10 ÷ 50) x 100 = 0.2 x 100 = 20%

This gives us the answer: there is a 20% decrease from 50 to 40.

In general. to work out the percentage change from g to h, we first work out the difference between the two numbers:

h – g

We then work out what this difference (h – g) is as a percentage of the original figure (g):

((h – g) ÷ g) x 100

What are the potential problems with percentages?

If percentages are treated as actual numbers, results can be misleading.

When you work with percentages you multiply. Therefore, you cannot simply add or subtract percentage changes.

For example, the percentage change from 2% to 3% is not 1%; in fact, 3% is 50% greater than 2%. We can see this in an example: 2% of 1,000 is 20, and 3% of 1,000 is 30. The percentage increase from 20 to 30 is 50%. To avoid the confusion, we say 3% is 1 ‘percentage point’ greater than 2%.

Similarly, when two or more percentage changes follow each other, they cannot be added because the original number changes at each stage. A 100% increase followed by another 100% increase is a 300% increase overall. We can see this in another example: a 100% increase on 10 gives 10 + 10 = 20. Another 100% increase gives 20 + 20 = 40. From 10 to 40 is a 300% increase.

A 50% fall followed by a 50% increase is a 25% fall overall. Again, we can see this in an example: a 50% decrease on 8 gives 8 – 4 = 4. A 50% increase then gives 4 + 2 = 6. From 8 to 6 is a 25% decrease.