FAQ - Math

How to Calculate Percentage Error

How to Calculate Percentage Error

A percentage error provides an easy-to-understand measure of error margins. It lets you know how big an error is. For instance, a 3-percent error value means that your measured figure is very close to the actual value. On the other hand, a 50-percent margin means your measurement is a long way from the real value. If you end up with a 50-percent error, you probably need to change your measuring instrument.

Why Do We Calculate Percentage Error?

There are many reasons for calculating percentage errors. Engineers use it to determine the precision of a measuring instrument. Within the finance sector, statisticians and data analysts rely on it to verify if a data set is progressing in the right direction. Outside the workspace, we use percentage errors for lots of everyday tasks. For instance, if you’re baking a cake and the recipe calls for four and a half teaspoons of sugar, you could simply round it off. You could indulge your sweet tooth by adding five teaspoons or opt for four spoons. Either option would be about a 10% error margin—and still lead to tasty results.

Note: If the measured value is the same as the actual value, then the percentage error is zero.

How to Calculate Percentage Error

Calculating the percentage error is a lot less complicated than calculating standard deviation. You only need to complete several quick steps.

  1. Subtract the actual value from the estimated value

  2. Divide the results from step 1 with the real value

  3. Multiply the results by 100 to find the total percentage

All of this is summed up with the formula:

  • Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100

To see how the calculation works, let’s look at a quick example.

While measuring the layout for a pool, a landscaper accidentally records 8m. What is the percentage error if the actual length is 10m?

To solve for this, we’ll use the formula:

Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100

  • Where the Actual Value = 10m

  • And the estimated value = 8m. 

Step 1. Subtract the actual value from the estimated value. 

8m – 10m = -2m

Step 2. Divide the results with the actual value

-2m/10m = -0.2

Step 3. To find the percentage error, multiply the results by 100 

-0.2 x 100 = -20%

The percentage error in the measurement was -20%

Percentage Error = 8 – 10/10 x 100 = -2/10 x 100 = -20%. 

What are the Differences between Percentage Error, Absolute Error, and Relative Error?

The absolute error is simply the absolute value (written as |x|) between the experimental measure and the actual measure (the difference between the two, ignoring any negative sign). It provides a magnitude of the difference between both figures.** In comparison, the relative error refers to the ratio between the absolute error and the actual value. You can calculate it by dividing the absolute error and the actual value. For instance, if the absolute error is 2 and the actual value is 6, the relative error is 2/6, which is 0.3333... When the relative error is turned into a percentage, it becomes a percentage error. 

In summary

  • Absolute Error = |Experimental Measurement – Actual Measurement| 

  • Relative Error= Absolute Error/Actual Measurement 

  • Percentage Error = Decimal Form of Relative Error x 100

**For instance, the absolute error between 4 and 6 is 2, not -2. Written as a formula: |4 - 6| = 2. Another example: |7-4| = 3.