BioDeviceHub

Percent Error Calculator

Calculate the percent error of an experimental value against a theoretical or accepted value, with the signed relative error and the absolute error.

Formula

percent error=∣experimental−theoretical∣∣theoretical∣×100\text{percent error} = \dfrac{|\text{experimental} - \text{theoretical}|}{|\text{theoretical}|}\times 100
signed relative error=experimental−theoretical∣theoretical∣×100\text{signed relative error} = \dfrac{\text{experimental} - \text{theoretical}}{|\text{theoretical}|}\times 100
experimental\text{experimental}
the measured value
theoretical\text{theoretical}
the accepted or true value

How it works

Percent error expresses how far a measurement is from the accepted value, as a share of that value. The signed form shows the direction, a negative result meaning the measurement was low.

It compares one measurement with a value taken as true and mixes random and systematic error, so it cannot tell them apart. To separate them, repeat the measurement and look at the mean's offset from the true value and the spread of the results, as in the Accuracy and Precision calculator.

Worked example

A measured g of 9.62 m/s² against the accepted 9.81 m/s².

  1. Difference = 9.62 − 9.81 = −0.19.
  2. Percent error = 0.19 / 9.81 × 100 = 1.94%.

The measurement is 1.94% low.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The accepted value is correct and non-zero.

Common mistakes

  • Dividing by the experimental value instead of the accepted one.
  • Using percent error when the accepted value is zero or near it.
  • Taking one measurement's error as the instrument's accuracy.

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