# Can percent error be negative? Simply explained

Percent error is a common metric to use for measuring the accuracy of a prediction or estimation, and as the name suggests, it is provided in the form of a percentage.

Percent error is a common metric to use for measuring the accuracy of a prediction or estimation, and as the name suggests, it is provided in the form of a percentage.

**But, can percent error be negative?**

Yes percent error *can* be negative, but the accepted norm is to calculate percent error as an absolute value where it is *always* positive. For example -10% percent error would be written as the absolute value, 10%.

## Can percent error be negative?

Imagine an example where you have to estimate the height of people in your class, you end up with the following table comparing your estimations and the actual height:

Name | Estimated height (cm) | Actual height (cm) |
---|---|---|

Stephen | 170 | 180 |

Jane | 150 | 140 |

Manny | 140 | 160 |

Nora | 160 | 145 |

### Percent error definition

We can see that we didn’t get any guesses exactly correct, but we want to understand *how* incorrect we were, for this we can calculate the **percent error**.

**The percent error is the absolute difference between the actual and the estimate (the error), divided by the actual.**

### Calculating percent error

Let’s now calculate the percent error for our height example:

Name | Estimated height (cm) | Actual height (cm) | Difference | Absolute difference | Percent error |
---|---|---|---|---|---|

Stephen | 170 | 180 | 10 | 10 | 5.6% |

Jane | 150 | 140 | -10 | 10 | 7.1% |

Manny | 140 | 160 | 20 | 20 | 12.5% |

Nora | 160 | 145 | -15 | 15 | 10.3% |

As you can see, percent error is always positive as we take the absolute difference between the estimate and the actual before we divide by the actual.

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