# What is Percentage Error? – Definition & Example

In this lesson, we’ll define what percentage error is, why it is useful, and how to calculate it. We’ll also look at some examples of when you could use percentage error.

What Is Percentage Error?

Look closely at the image of the gumball machine and make your best estimated guess at how many gumballs you think there are.

gumball

Have you ever played this game at school or at a carnival? The person who guesses closest to the actual number of gumballs wins a prize. We’re going to explore how to calculate the winner by learning about percentage error.

Percentage error is the difference between the estimated number and the actual number when compared to the actual number expressed in percent format. The formula looks like this:

formula

In other words, you take the difference between the real answer and the guessed answer, divide it by the real answer, and then turn it into a percent.

For example, let’s say you guessed that there were 230 gumballs in the image, but there were actually 311 gumballs. The difference between your guess (230) and the actual number (311) in comparison to the actual number (311) expressed as a percent is the percentage error.

Did you notice the straight lines that were part of our formula? They indicate that you take the absolute value of that number, or the distance of a number from zero, without regard for negative signs. This simply means that if you get a negative number inside the absolute value signs, you treat it as if it were positive.

To calculate percentage error, you subtract the actual number from the estimated number to find the error. Then, you divide the error in absolute value by the actual number in absolute value. This gives you the error in a decimal format. From there, you can multiply by 100% to find the percentage error.

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