Percentage Calculation

Percentage calculation is often used to compare things or changes. It is important to know how to do this correctly as it is much easier to compare something in percentage than using absolute numbers.

Below is shown how to calculate percentage increase or decrease, difference and percentage of the entire value.

Percentage Change (increase/decrease)

Percentage change is used when we want to know how much better or worse this is compared to some baseline or existing value.

\begin{align} \text{Percentage Change} = 100\% \cdot \frac{\text{New value}-\text{Old value}}{\text{Old value}} \end{align}

Example of calculating the change

This is an example demonstrate how to calculate the change (increase or decrease) between something existing and something new. In this example the fuel consumption of an old car is compared to a new one. The old car runs 12km/l and the the new one 20km/l.

\begin{align} \text{Percentage Change} = 100\% \cdot \frac{\text{20km/l}-\text{12km/l}}{\text{12km/l}}=66.7\% \end{align}

It can be concluded that the mileage of the new car is 66.7% better than the old car.

Percentage Difference

This is at least to my knowledge not used as much as the Percentage Change and to be honest I can not remember to have ever used it. The difference between two values are calculated using:

\begin{align} \text{Percentage Difference}= 100\% \cdot \frac{|Value_1-Value_2|}{0.5(Value_1+Value_2)} \end{align}

The vertical lines i.e. | | indicates that the value inside the two lines shall be taken as absolute value e.g. |-2|=2 and |2|=2.

Example of calculating the difference between two values

Using the same example as before with the two cars. This time we want to find the difference between the two cars. Car 1 has a mileage of 12km/l and car 2 20km/l. The difference between the two is calculated as

\begin{align} \text{Percentage Difference}= 100\% \cdot \frac{|12km/l-20km/l|}{0.5(12km/l+20km/l)}=50\% \end{align}

Percentage part of something

Calculate how large a percentage something is of the entire amount.

\begin{align} \text{Percentage} = 100\% \cdot \frac{\text{Part value}}{\text{Entire Value}} \end{align}

Example of calculating the percentage of something

15844 cars where sold in Denmark in August 2021 and 3050 of those where electric cars. How large a percentage is that?

\begin{align} \text{Percentage} = 100\% \cdot \frac{3050}{15844}=19.3\% \end{align}

19.3% of the cars sold in August 2021 in Denmark were electric cars.