# How to work out percentages

Many people have difficulty with working out percentages or believe they know how to work out percentages but use an incorrect formula.

Below are two ways of working out percentages, both of which can be computed in Excel:

We will use a very basic example to illustrate the formulae and we will demonstrate how to work out a percentage increase.

Method 1  – [(new figure minus old figure) divided by old figure] x 100

Say, for example, you took your car for a service and it cost £150 in 2009, but the price went up to £200 in 2012, to work out the percentage change, you would need to take the difference between the new price (£200) and the old price (£150) ie 200 – 150 = 50; and then divide that number by the old price ie £50 divided by 150 = 0.3333. (to 4 decimal places).
The percentage will always have a percent sign at the end, so in this case, the increase would be (200-150)/150 = 33.3%

Always remember – the percentage difference is (new price minus old price) divided by old price

Or (new figure minus old figure) divided by old figure

Method  2 – alternative method which you may come across in the workplace – [(new figure divided by old figure)  – minus 1] x 100

Using the same example as above, you’d take the new figure divide it by the old figure; minus 1 from that number and then multiply the figure you get by 100

ie (200 divided by 150) minus 1 then multiplied by 100
200 divided by 150 is 1.33.

Minus 1 from that figure and you get 1.33 – 1 = 0.33.

Multiply that figure by 100 and you get 33.33, which is the 33% increase we are working out.

To work out a percentage decrease, you would do the following:

Say, that the car service cost went down from £150 in 2009, to £90 in 2012. Using method 1, the new figure is 90, and the old figure is £150.

So [(new figure minus old figure) divided by old figure]x100 would give us (£90 – £150)/£150 which is   -£60/£150  = -40. So the decrease in percentage would be 40%.

We have also attached an Excel file with the different methods – you can download it here
There are TWO tabs in the Excel file demonstrating how a “percentage increase” is worked out in the first tab and another tab showing how a “percentage decrease” is worked out.