National Physical Laboratory

Is there a difference between 'accuracy' and 'uncertainty'? (FAQ - Length)

Yes there is a difference.

The words accuracy and uncertainty are sometimes interchanged but the difference between them is significant and, in many applications it is vital.

Accuracy of measurement is the older phrase and its internationally agreed definition is '… the closeness of the agreement between the result of a measurement and a true value of the measurand' (e.g. length). The definition also notes that '... accuracy is a qualitative concept' - it can be high or low for example but strictly is should not be used quantitatively.

In practice, though, it is often used quantitatively by bending the definition to something like '... the difference between a measured value and the true value' - and this leads to phrases like '... accurate to ± X'. Unfortunately this unofficial definition breaks down because it inherently assumes that a true value can be defined, known and realised perfectly. Even in the finest national measurement laboratories, however, perfect values cannot be realised; it is simply impossible to define or make perfect measurements - nature, and hence the laws of physics, don't allow it.

Uncertainty of measurement acknowledges that no measurements can be perfect and is defined as a '… parameter, associated with the result of a measurement, that characterises the dispersion of values that could reasonably be attributed to the measurand'. It is typically expressed as a range of values in which the value is estimated to lie, within a given statistical confidence, but it does not attempt to define or rely on a unique true value.

In summary, common usage of the word accuracy for quantitatively describing the characteristics of measuring instruments, is incompatible with its official meaning but, even ignoring this point, its common usage definition is significantly cruder than the proper metrological term uncertainty.

Does the difference really matter?

In many situations the difference really doesn't matter at all and it remains much easier to say 'This instrument is accurate to…' rather than 'This instrument is uncertain by…' (Swapping convention might have been easier if the term was certainty and not uncertainty; but it isn't.) And an accurate device sounds more impressive than an uncertain one too, which is probably why much equipment sales literature tends to stick with the word accuracy.

In recent years, however, great strides have been made in developing methods for better quantifying the performance of measuring instrumentation - a task that can be relatively complex for even a simple instrument. If you are attempting to make a serious estimate of such performance - and persuade others that the result is valid - you will have to use the modern tools available and they are fundamentally structured around the philosophy of uncertainty, and its adoption from the outset is thoroughly recommended.

Last Updated: 17 Feb 2012
Created: 1 Dec 2010

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