Topic: Metrology

Metrology: II - Fundamental concepts and definitions

Author: B. Černe, Ph.D.

Reading time: 9 min

Test specimen clamped into tensile testing device
Metrology, often described as the science of measurement, goes beyond simply quantifying physical attributes; it strives to establish universal standards and methodologies that guarantee consistency and comparability across various domains, from manufacturing and healthcare to scientific research and trade. In this article, we will explore these foundational concepts in metrology, shedding light on the critical terminology and principles that enable the precise measurements upon which our modern world relies.

Metrology is almost as much about terminology and standardization as it is about actual measurements. The Joint Committee for Guides in Metrology (JCGM) even provides an International Vocabulary of Metrology or the VIM which serves to provide a common language and terminology in the field of metrology. Along with it, the Guide to the Expression of Uncertainty in Measurement or GUM, also curated by JCGM, defines general rules for evaluating and expressing uncertainty in measurements.

Key to these guidelines are the definitions listed in the image below. You probably stumbled into these terms many times in the past. Most of these are also covered in many graduate engineering programs but, going through this list, can you confidently distinguish and describe in exact terms what each of these definitions means in the domain of metrology? Let’s take a look at their specific meaning and implementation.

Fundamental terms in metrology


Definition: 'Closeness of agreement between a measured value and a true quantity value of a measurand.'

Based on this definition, we might think of accuracy as something quite tangible and quantifiable but, as the VIM notes, measurement accuracy is a qualitative term, i.e., it is not actually a numerical quantitative value. A measurement is simply said to be more accurate when it offers a smaller measurement error.

The qualitative nature of the term stems from the fact that the 'true value' in the definition is never actually known since no reference measurement instrument is infinitely precise and there is always as small degree of uncertainty remaining about the actual true value. Nevertheless, ISO 5725-1:2023 ---the official standard defining accuracy, precision, and trueness---accepts that the 'true value' can be replaced with an 'accepted reference value' (see Reference quantity value section below), making accuracy quantifiable.


Definition: Closeness of agreement between the average of an infinite number of replicate measured quantity values and a reference quantity value.

Measurement trueness is inversely related to systematic measurement error (see below), but is not related to random measurement error.

Similar to measurement accuracy, trueness is also a qualitative term since it compares the mean of actual measurements to a 'true value' which is inherently unknown. Again though, ISO 5725-1, allows to replace the 'true value' with an 'accepted reference value'.


Definition: Closeness of agreement between indications or measured quantity values obtained by replicate measurements on the same or similar objects under specified conditions.

Measurement precision is a measure of how closely repeated measurements of the same quantity under the same conditions agree with each other. Precision evaluates the consistency and reliability of a measurement method. A high-precision measurement system produces closely clustered measurements, while a low-precision system results in more scattered or variable measurements.

Precision is often used to define measurement repeatability and is expressed using statistical measures such as standard deviation or variance, which quantify the spread or dispersion of repeated measurements. It doesn't necessarily guarantee that the measured values are accurate; they can be consistently off-target.

Diagram depicting correlation between accuracy, trueness and precision

Repeatability and Reproducibility

Definition: Repeatability and reproducibility are defined as measurement precision under a set of repeatability or reproducibility conditions of measurement respectively.

We’ve seen that the general term for variability between replicate measurements is precision. When we want to talk about how precise a measurement method is, we use two conditions: repeatability and reproducibility. These conditions help us understand how much the measurements can vary in practice.


Under repeatability conditions, we ensure that everything that could change the measurement stays the same, and we measure how much the results still vary. This helps us understand the smallest possible variation in the results. To maximize repeatability of your measurements it is recommendable to ensure that:

  1. The same measurement procedure or test procedure is used
  2. The same operator performs the measurements
  3. The same measuring or test equipment is used under the same conditions
  4. The measurements are done at the same location
  5. Repetition over a short period of time


Under reproducibility conditions, we let some or all of the things that could change the measurement actually vary, and we see how much the results change because of that. This helps us understand the biggest possible variation in the results.

Other intermediate conditions between these two extreme conditions also occur when one or more of the factors that influence the measurement are allowed to vary, and are used in certain specified circumstances


  • 'Non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used.' - VIM
  • 'Parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand' - GUM

Uncertainty of measurement acknowledges that no measurements can be perfect. It is typically expressed as a range of values in which the value is estimated to lie, within a given statistical confidence. It does not attempt to define or rely on one unique true value.

The term measurement uncertainty is so broad and absolutely crucial to the field of metrology that it deserves its own article (or, more likely, a full book) so it will be dealt with in more detail in the next post.

Measurement error

Definition: measured quantity value minus a reference quantity value (used as a basis for comparison with values of quantities of the same kind)

Measurement error refers to the difference between a measured value and the true or accepted value of the quantity being measured. It represents the discrepancy or inaccuracy in a measurement result and can result from various factors, including equipment limitations, environmental conditions, human factors, and inherent uncertainties in the measurement process. We can hence think of measurement error as being inversely related to the measurement accuracy.

Measurement error = Systematic Measurement Error + Random Measurement Error

  1. Systematic Error: This type of error is consistent and reproducible, affecting all measurements in a predictable way. Systematic errors result from flaws or biases in the measurement system or procedure. They can be caused by equipment calibration issues, instrumentation limitations, or incorrect measurement techniques. Systematic errors often lead to inaccuracies in the measured values and can be minimized through proper calibration and correction.
  2. Random Error: Random errors are unpredictable variations in measurement results that occur from one measurement to another, even when using the same equipment and following the same procedures. They are typically caused by inherent fluctuations in the system, environmental conditions, or human factors. Random errors are characterized by their variability and can be reduced by increasing the precision of measurements, such as using more precise instruments or averaging multiple measurements.

Reference quantity value

Definition: quantity value used as a basis for comparison with values of quantities of the same kind

A reference quantity value can be a true quantity value of a measurand, in which case it is unknown, or a conventional quantity value, in which case it is known.

A reference quantity value with associated measurement uncertainty is usually provided with reference to:

  • material, e.g. a certified reference material,
  • a device, e.g. a stabilized laser,
  • a reference measurement procedure,
  • a comparison of measurement standards.

In the upcoming post we'll take a look more in detail into the definition and methods of evaluation of uncertainty.


[1] The International System of Units (SI) as defined by BIPM
[2] National Institute on Standards and Technology (NIST) - Measurement Uncertainty
[3] NIST Uncertainty Machine
[4] NIST/SEMATECH e-Handbook of Statistical Methods
[5] International Vocabulary of Metrology
[6] JCGM 100:2008 GUM 1995 with minor corrections - Evaluation of measurement data — Guide to evaluating and expressing uncertainty in measurement

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