How to calculate relative error

Relative error is defined as the ratio of the absolute error of the measurement to the actual measurement. Using this method we can determine the magnitude of the absolute error in terms of the actual size of the measurement. If the true measurement of the object is not known, then the relative error can be found using the measured value. Relative error gives an indication of how good a measurement is relative to the size of the object being measured.

If x is the actual value of a quantity, x₀ is the measured value of the quantity and Δx is the absolute error, then the relative error can be measured using the below formula.

Relative error = (x₀-x)/x = (Δx)/x

An important note that relative errors are dimensionless. When writing relative errors it is usual to multiply the fractional error by 100 and express it as a percentage.