Absolute Error or Absolute Uncertainty Definition

Absolute error or absolute uncertainty is the uncertainty in a measurement, which is expressed using the relevant units. Also, absolute error may be used to express the inaccuracy in a measurement. Absolute error may be called approximation error.

Absolute error is the difference between a measurement and a true value:

E = |x₀ - x|

Where E is absolute error, x₀ is the measured value and x is the true or actual value

Why Is There Error?

Error is not a "mistake." It simply reflects the limitations of measurement instruments. For example, if you use a ruler to measure a length, each tic on the ruler has a width. If a distance falls between marks on the ruler, you need to estimate whether the distance is closer to one mark than the other and by how much. This is error. The same measurement may be taken multiple times to gauge the range of the error.

Absolute Error Example

If a measurement is recorded to be 1.12 and the true value is known to be 1.00 then the absolute error is 1.12 - 1.00 = 0.12. If the mass of an object is measured three times with values recorded to be 1.00 g, 0.95 g, and 1.05 g, then the absolute error could be expressed as +/- 0.05 g.