National Physical Laboratory

Measurement Uncertainties


All measurements are subject to uncertainty, and a measurement result is only complete if it comprises a measured value accompanied by a statement of the associated uncertainty. Understanding and evaluating uncertainty is important to anyone wishing to make good quality measurements and, in particular, where measurement results are used to:

  • Maintain quality control during production processes
  • Show compliance with regulations
  • Support research and development
  • Calibrate instruments
  • Demonstrate traceability to national measurement standards
  • Cevelop, maintain and compare national and international measurement standards

In many cases, quantifying measurement uncertainty and expressing it in a valid form are not straightforward tasks. Extensive knowledge (metrological, mathematical and statistical) may be needed to obtain high quality results on which you, your customers and regulatory organisations can rely.


In order to make a statement concerning the measurement of a quantity of interest, it is required to provide a value of the quantity, through measurement, and an associated uncertainty. The uncertainty is a quantitative measure of the quality of the value as an estimate of the quantity of interest. It can take the form of a standard uncertainty, which is the uncertainty associated with the value expressed as a standard deviation. It can also take the form of a coverage interval, which is the uncertainty expressed as an interval within which the quantity is expected to lie with a stated (coverage) probability.

There are established rules for the evaluation of uncertainty. The 'Guide to the expression of uncertainty in measurement' (GUM), published by the member organisations of the Joint Committee for Guides in Metrology (JCGM), is the primary document regarding uncertainty in measurement. The United Kingdom Accreditation Service (UKAS) publishes the document 'M3003: The expression of uncertainty and confidence in measurement', based on the GUM, for accredited laboratories in the UK.

There are other approaches to measurement uncertainty evaluation, including the use of Monte Carlo and Bayesian methods. These methods are intended to be used for more general measurement problems than those directly covered by the GUM. The approaches are described in Supplements to the GUM and other supporting documents.


We contribute to standards activities undertaken by the following organisations:

  • BSI (British Standards Institution)
  • ISO (International Organization for Standardization)
  • JCGM (Joint Committee for Guides in Metrology)

We chair the BIPM Director's Advisory Group on Uncertainties, and provide input to Consultative Committees of the CIPM.

We aim to bring expertise in mathematics and statistics, particularly good practice in uncertainty evaluation and related mathematical and statistical modelling, to benefit relevant metrology standards development. We also aim to raise awareness throughout the National Measurement System of the activities of these standards committees.


NPL has a highly experienced team of technical experts in the area of uncertainty evaluation. We are part of a world-class physical metrology organisation, with experience and expertise in this field that is unique in the UK. Our team is playing a leading international role in promoting the GUM and extending the application of the GUM through its revision and the preparation of supporting documents. We offer a range of services including advice, consultancy and training in the areas of uncertainty evaluation, statistical analysis and modelling.

The propagation of distributions offers a more general capability than the law of propagation of uncertainty. It is relevant when the conditions for that law to apply do not hold or when there is doubt over whether they hold.
Having confidence in measurement results requires a quantitative statement of the quality of the results, with such a statement taking the form of measurement uncertainties associated with measured values.