Percent error (% error), also referred to as percentage error, is a measure of how much a value differs from expected value. It can be to used to determine how far off just about any expected value is from another value, but is often used in the context of scientific experiments.
Percent error formula
Use the following steps along with the percent error formula to determine the percent error between values:
- Determine which value is the value you expect; call this the exact/expected/theoretical value
- Determine which value you actually got; call this the approximate/experimental value
- Plug the values into the following formula:
Note: The term "actual" is used to mean the result obtained from a given experiment or comparison, not necessarily what the value should actually be. Also, when calculating percent error, we use the absolute value because typically we are only concerned with the difference between the two numbers being compared.
If you buy a bag of candy that is supposed to have 20 pieces of candy, but open it to find only 17 pieces of candy, what is the percent error?
In this case, the expected, or theoretical value is 20 pieces of candy and the experimental value, or how many pieces of candy you actually have, is 17. So, to calculate percent error, we plug these into the formula:
So, there is a 15% error between the amount of candy you have, and the amount of candy that is supposed to be in the bag.
Usually we use the absolute absolute value because in many cases, it is the difference that is important rather than whether the difference is positive or negative. In this case though, we could've said that there is a -15% difference, meaning that we have 15% less candy.
Percent error, absolute error, and relative error
These three types of errors are very closely related, but are different, so the terms should not be used interchangeably. Using the percent error formula above,
- Percent error =
- Abolute error =
- Relative error =
So, absolute error is part of the calculation of relative error, and percent error is just relative error multiplied by 100 to convert it from a decimal to a percent.