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Words and concepts in Metrology

Measurement uncertainty, traceability and measurement results are just some of the words and concepts found in metrology.

Common and quality-assured time is important for communication systems and for financial transactions worldwide.


Metrology is the science of measurement and its application. Metrology concerns:

There are several subfields within metrology. Scientific/fundamental metrology concerns the definition and the realisation of measurement units and metrological traceability at the very highest level. Applied/technical metrology concerns methods and techniques for measuring maintaining traceability in society through chains of calibrations. Legal metrology deals with legal demands and requirements with the aim of protecting health, the environment, and consumers. In Sweden, Swedac is responsible for legal metrology.

Calibrating a pyrometer, a non-contact thermometer.


Calibration is a comparison between a reference (measurement standard) and the measuring device to be calibrated. During a calibration, we determine how much the device’s indication differs from the reference’s quantity value. This gives us the device's measurement error.

For a calibration to be reliable and to ensure traceability, we must use a measurement standard that has been calibrated by a National Laboratory or by an accredited calibration laboratory.

The calibration protocol tells you how to handle your measuring device and how to correct the device’s indication to compensate for the measurement error. The protocol also shows the measurement errors and the measurement uncertainties.

Calibration does not mean that the instrument is adjusted, although many instruments can also be adjusted to display the correct value.

Primary realisations of units have the lowest measurement uncertainty. Here is the laser used to realise the meter at the National Laboratory for Length and Dimensional Metrology.

Measurement uncertainty

Measurement uncertainty is the interval around the measured value within which the true value is likely to be found.

Many factors affect measurements: the person measuring, temperature, humidity, what we measure, which measuring device we use etc. Regardless of how good the measuring devices we use are or how ideal the conditions are, it is not possible to know that the measured quantity value is the true value. The measurement uncertainty indicates how much the indication of the measuring device can differ from the true value with a certain probability (usually 95 percent). 

A measurement result consists of a measurement value, the measurement uncertainty, and a unit (for example meters or kilograms). The measurement result 5.00 m +- 0.05 m means that the true measurement value, with a certain probability, is found between 4.95 m and 5.05 m.

With very good conditions, methods and measuring devices, we can reach a very low measurement uncertainty. The measurement uncertainty at the National Laboratories is in many cases on the order of parts per million or billion. For most applications, this level of measurement uncertainty is not necessary. The needs of the application should always determine the level of measurement uncertainty required. It is important to plan for the desired level of measurement uncertainty when planning for calibration, as the measurement uncertainty increases with each calibration step.

Measurement result

In quality-assured measurements, it is important not only to look at the indicated value from the measurement device, but also to take the measurement uncertainty into account. This is called a measurement result.

A measurement result consists of a measured value, the measurement uncertainty, and a unit, such as meter or kilogram. The measurement result 5.00 m +- 0.05 m means that the true value, with a certain probability (usually 95 percent), is found between 4.95 m and 5.05 m.

A measurement without traceability is not reliable.

Traceability, traceable measurements, traceability chain

Traceability means that a measurement result can be traced back to the definition of the unit through an unbroken chain of comparisons against suitable standards with specified measurement uncertainties. A measurement without traceability is not reliable.

The traceability chain usually goes via a National Laboratory, either in Sweden or in another country, and is maintained via calibrations: The tape measure at the building site is calibrated against a standard, which in turn is calibrated against a standard at an accredited laboratory, which in turn is calibrated against a working standard at a national measurement site, which in turn is calibrated against a primary standard, which is calibrated against the realisation of the unit. The realisation is then quality assured via international comparisons. Each calibration step down from the realisation of the unit increases the measurement uncertainty.

As a result of the traceability chain, we can expect that a meter is a meter throughout the world, which is a prerequisite for international trade, research, and manufacturing.

As the National Metrology Institute of Sweden RISE is responsible for maintaining and providing traceability in Sweden.

The Swedish national kilogram that is stored at RISE in Borås. Nowadays, the kilogram definition is based on constants of nature and its realisation is no longer tied to a physical object.

Realise, realisation of a unit

In metrology realising a unit means to bring the measurement unit from its definition into the real world, either by a physical object or based on a physical phenomenon such as a frequency-stabilised laser for the meter. The realisation of the measurement unit can then be used as the basis for the traceability chain. The realisations of the units are quality assured through international comparison measurements.

Until 2019, the International Prototype Kilogram, IPK, was both the definition and the realisation of the kilogram. The traceability chain for the kilogram went via the Swedish national kilogram, which was flown down to Paris at regular intervals to be calibrated. One of the problems with using a physical object such as the IPK as the definition for the measurement unit is that the object can change due of external effects such as air pollution, but still weigh exactly 1 kg by definition.

Since 2019, the entire international measurement system, SI, is based on defining constants of nature. This means that the definitions of the measurement units are independent of the realisations. For each unit, there are so-called mises en pratique, approved methods, for how the units can be realised. Since the definitions are no longer linked to the realisations, new and better mises en pratique can be developed as technology advances.

By comparing directly with the realisation of the unit, we can produce primary standards with the lowest measurement uncertainty. Although it would be possible to do all calibrations directly against the realisations of the units in theory, it would hardly be possible in practice. Most areas of use do not need the level of measurement uncertainty that a direct comparison with the realisation can provide. Therefore, secondary standards or working standards that are calibrated against the primary standards are used in daily work at the National Laboratories.

Weight standards used at the National Laboratory for Mass.

Standard, measurement standard

A measurement standard is a reference used in the calibration of measurement devices. Standards are fundamental for maintaining traceability and must always have a lower measurement uncertainty than the measurement device to be calibrated. The standard must in turn be calibrated against another standard with even lower measurement uncertainty. In this way, the traceability chain is maintained all the way up to the realisation of the unit. The measurement standard can be physical objects such as a weight or an object with a certain length.

Several different terms are used concerning measurement standards, sometimes with different or overlapping meanings depending on the context:

  • Primary standard/national standard. A measurement standard that is calibrated directly against the realisation of the unit. In Sweden, RISE as the National Metrology Institute maintains the national standards at its National Laboratories. 
  • Secondary standard. A measurement standard that is calibrated against a primary standard.
  • Working standard/calibration standard. A measuring standard that is used in the daily work of calibration. At the National Laboratories, this means either a secondary standard or a measurement standard that is calibrated against a secondary standard.

Measurement device

A device or equipment used to measure one or more physical quantities, such as a tape measure to measure length or a scale to measure mass. All measuring devices are subject to measurement uncertainty. For the measurement device to be reliable, it should be calibrated regularly (considering its area of use).

Measurement error

Measurement error is the measured value minus the "true" value. If the scale shows 80 kg but the true value is 78 kg, the measurement error is 80-78=2 kg. If the scale shows 78 kg but the true value is 80 kg, the measurement error is 78-80=-2 kg. Since we can never know for sure what the true value is due to measurement uncertainty, we cannot know the exact measurement error.


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