Error propagation

The error propagation describes the effect that inaccurate input values as basis of a function always result in an inaccuracy of the result of the same function. A measured value always represents only an approximation to the expected value of a physical quantity. Even if modern methods deliver highly precise results, a single perfect measurement is simply impossible. In many measurement tasks, moreover, a physical quantity cannot be measured directly, but must be calculated indirectly from other measurable quantities using mathematical formulas. Every measured value has certain measurement deviations, which are then transferred with the formula. The errors are propagated, so to speak. Thus, the calculated measurement result will also have a deviation as a result of the measurement deviations of the input variables. To calculate the size of the deviation of such measurement results, there are mathematical formulas such as the Gaussian error propagation or the general error propagation law. Since a conceptual distinction has been made between measurement deviation and measurement error, the term error propagation is considered obsolete from this point of view, but since no new term has yet been established, it continues to be used.