# Absolute Error, Relative Errors and Percentage Errors

Absolute Error
The magnitude of the difference of true value and the measured value is called absolute error.

Thus, absolute error = true value â€“ measured value

If we regard arithmetic mean as the true value, than absolute error in the i th measurements is given by
Î” ai =

It is expressed in the units of measured value. The final absolute error is taken as the arithmetic mean of the absolute errors in various measurements. Thus,
Î” =
or Î” =

If we take a single measurement, then the result of measurement will lie between
and .

Relative and Percentage Errors
The knowledge of relative error is more important than the absolute error in a measurement.
1. The relative error is defined as the ratio of the absolute error to the true value.
Thus, the relative error is given by
Î´a = ,
Where (arithmetical mean) has been taken as the true value.
The percentage error is given by
2. Percentage error =
Ã— 100 â€‹