Uncertainty of Measurement

To make measurements comparable, the quality of a measurement must be characterized by the expression of the measurement uncertainty. An internationally standardized procedure is necessary to interpret measurement results in science and technology correctly. Whereas the definition and realisation of the units of measurement are regulated within the scope of the International System of Units (SI), it was only recently that such an established concept was developed for measurement uncertainty.

normal distribution

In 1993 seven international organisations (BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML) together published the („Guide to the expression of uncertainty in measurement” GUM. This guide lays a solid foundation for the determination of measurement uncertainties on the basis of a modern probability theory. GUM and VIM (International vocabulary of basic and general terms in metrology) define measurement uncertainty as follows:


Measurement uncertainty is a parameter

characterizing the dispersion of the quantity

values being attributed to a measurand.


The parameter may be, for example, a standard deviation (or a specified multiple of it), or the half-width of an interval, having a stated coverage probability.

Measurement uncertainty comprises, in general, many components. Some of these may be evaluated from the statistical distribution of the quantity values from series of measurements and can be characterized by empiric standard deviations. The other components, which may also be characterized by standard deviations, can be evaluated from probability distributions based on experience or other information.


It is understood that a measuring result is the best estimated value for a measurand and that all components of uncertainty contribute to the dispersion including those stemming from systematic effects, i.e. corrections and reference standards. National metrology institutes and numerous international organisations declared the GUM as binding. The term uncertainty of measurement as a quantifiable property is relatively new in the history of metrology, although statistics and “error calculation” have long since been metrological practice.

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