Calculate the percent error of a data set. Enter the true value and observed value to determine the percent error of your experiment or calculation.

## Percent Error Formula

The following formulas are used to calculate a percentage of error.

Where abs stands for the absolute value of the difference between the true and measured values. This causes the percent to always be positive, but it does not have to be. In some cases the absolute value is dropped in order to determine which direction the error occurred in, i.e. either too high or too low.

## Percent Error Definition

Percent error is used to determine the accuracy of an experiment or measurement. In simple terms, it’s the difference of the measured value to the known true value. In this case, the true value must be known to determine the real % error. The formula is usually displayed as follows:

## How to calculate percent error?

An example of this being used is in an experiment. Lets say you are performing an experiment on some new rare element that has been tested in a certain way. First, you want to set up your experiment with a control in order to determine it’s accuracy. Because of either science, math, or previous experiments, you know what that controls true value should be. Then you run your test and get an experimental error. Next you calculate the percent error, and then you have a gauge for how accurate your test will be on the unknown material.

Let’s take a look at an example of how you can calculate percent error in a real world experiment. For this example we will say we are in a physics lab and we are trying to calculate the weight of an object.

- First, we must calculate the true theoretical weight of the object. This can be done through exact equations using volume and density. We assume the object is a perfect sphere and uniform density. Using the mass equations we calculate that our sphere is 20kg.
- Next, we need to measure the weight using our scale. This will be our measured value and will show how accurate the scale really is. We find the scale reads 19.95kg.
- Finally, we plug these values into the formula above for our answer of .25% error.
- Last, we can analyze these results and adjust our scale so that it is more accurate.

It’s important to remember and consider that the percent error depends entirely on the accuracy of your “true value”. For example, for the problem above we assume a perfect sphere and uniform density. In the real world, sphere’s are neither perfect nor uniform in density. In reality, the sphere’s weight could have been much different than the theoretical value we calculated. As a result, the percent error we calculated also would have been off.

## FAQ

**What is a percent error?**

In simple terms, it’s the difference of the measured value to the known true value. In this case, the true value must be known to determine the real % error. The formula is usually displayed as follows:

**What is percent error used for?**

Percent error is used to calculate the accuracy of an experiment.

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