Percentage error is a measurement of the discrepancy between an observed and a true, or accepted value. When measuring data, whether it be the density of some material, standard acceleration due to gravity of a falling object, or something else entirely, the result often varies from the true value. Error can arise due to many different reasons that are often related to human error, but can also be due to estimations and limitations of devices used in measurement. Regardless, in cases such as these, it can be valuable to calculate the percentage error. The computation of percentage error involves the use of the absolute error, which is simply the difference between the observed and the true value. The absolute error is then divided by the true value, resulting in the relative error, which is multiplied by 100 to obtain the percentage error. Refer to the equations below for clarification.

Absolute error = |V_{true} - V_{observed}|

Relative error =

|V_{true} - V_{observed}|

V_{true}

Percentage error =

|V_{true} - V_{observed}|

V_{true}

× 100

The equations above are based on the assumption that true values are known. True values are often unknown, and under these situations, standard deviation is one way to represent the error. Please refer to the Standard Deviation Calculator for further details.