# Percent Error Calculator

Created by Bogna Szyk
Reviewed by Jack Bowater
Last updated: Jun 29, 2022

This percent error calculator finds the relative error between the true value and the observed value found in a measurement. Thanks to this tool, you will be able to quickly assess whether your measurement was accurate. Read on to learn how to calculate percent error and discover the percent error formula. You could also take a look at the percentage calculator to get a better grasp of the concept of percents.

Prefer watching rather than reading? Learn all you need in 90 seconds with this video we made for you:

## What is the percent error?

Sometimes, we try to estimate the value of a particular quantity by making repeated measurements. For example, we can try to find out what is the gravitational acceleration by measuring the time of free fall from a specific height.

The measured acceleration will probably deviate a bit from the actual acceleration of 9.80665 m/s². To check what is the relative - or percent - error, you need to know two values: the real value and observed (measured) one.

## Percent error formula

Our percent error calculator is based on the following equation:

percent error = (TV - OV) / TV * 100%

where:

• TV is the true value, and
• OV is the observed value.

## How to calculate percent error: an example

To make it easier for you to understand what percent error is, we'll analyze a simple example. Let's assume that we want to find out what is the relative error between the measured and true values of the speed of sound.

1. Check what the real value of the speed of sound is. In the air at 20°C, it is 343 m/s

2. Take your measurement. You found it was equal to 329 m/s.

3. Subtract the observed value from the true value:

343 - 329 = 14 m/s

1. 14 m/s is the absolute error. To calculate the percent error, you need to divide it by the true value:

percent error = 14 / 343 *100% = 4.082%

1. The percent error, otherwise known as the relative error, is equal to 4.082%.

## Percent error, margin of error, and standard error

There are a lot of terms similar to percent error. To ensure you don't get confused and mix them up, we provide a short explanation of each of them here.

Percent error, or relative error, is precisely what we described above - the relative difference between the observed and true value. You can apply the aforementioned percent error formula to calculate it.

Standard error is a value that can be calculated for a set of data. It is a statistical term that describes the accuracy with which a sample represents the whole population.

Margin of error, on the other hand, is closely related to the confidence interval. It can be calculated by multiplying the standard error with the z-score corresponding to a certain confidence level.

Bogna Szyk
True value
Observed value
Percent error
%
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