Skip to content
Let’s plan the right software for your processes. Call us for a demo or a quote: +90 546 737 48 29

TR EN DE

What is measurement uncertainty?

No measurement is perfect. Measurement uncertainty puts a number on the reasonable doubt about the range in which the true value of the measured quantity lies. A result such as "25.012 mm ± 0.009 mm (k=2)" says that the true value lies between 25.003 and 25.021 mm with a probability of approximately 95%. Uncertainty is not an error; it shows how far you can trust the measurement.

In brief

  • Uncertainty is not an error; it is a numerical statement of how far a measurement can be trusted.
  • Type A comes from repeated measurements, Type B from information such as certificates and resolution.
  • The sources are combined and then expanded with a coverage factor (usually k=2).
  • Uncertainty must be taken into account in a conformity decision.
On this page

The basic concepts

  1. Type A and Type B uncertainty

    The international reference for measurement uncertainty calculations is the GUM (Guide to the Expression of Uncertainty in Measurement, JCGM 100). The GUM divides uncertainty sources into two groups according to the method used to evaluate them:

    • Type A: Calculated statistically from repeated measurements. For example, if the standard deviation of n measurements is s, the standard uncertainty of the mean is s / √n.
    • Type B: Comes from information other than statistics: the calibration certificate of the reference instrument, the resolution of the instrument, the manufacturer's specification, the effect of temperature and so on. For example, if the resolution of a digital display is d, the standard uncertainty arising from it is usually taken as (d / 2) / √3 (rectangular distribution).
    Diagram: Type A uncertainty from repeated measurements, Type B uncertainty from the certificate, resolution and specification : Enlarge

  2. Combined and expanded uncertainty

    If they are independent of one another, the standard uncertainties from each source are combined by taking the square root of the sum of their squares: uc = √(u1² + u2² + …). (If the sources influence the result to different degrees, each is multiplied by its sensitivity coefficient.) When the result is reported, the combined uncertainty is multiplied by a coverage factor k: U = k · uc. The common choice is k = 2, which corresponds to a level of confidence of approximately 95%.

    Uncertainty budget table: repeatability, resolution, reference; combined and expanded uncertainty : Enlarge

  3. A simple example

    The length of a part is measured 10 times with a digital calliper. The mean is 25.012 mm and the standard deviation is 0.004 mm. The resolution of the calliper is 0.01 mm. The uncertainty on the calliper's calibration certificate is 0.006 mm (k=2).

    • Repeatability (Type A): 0.004 / √10 ≈ 0.0013 mm
    • Resolution (Type B): (0.01 / 2) / √3 ≈ 0.0029 mm
    • Reference certificate (Type B): 0.006 / 2 = 0.0030 mm
    • Combined: √(0.0013² + 0.0029² + 0.0030²) ≈ 0.0044 mm
    • Expanded (k=2): 2 × 0.0044 ≈ 0.009 mm

    Result: 25.012 mm ± 0.009 mm (k=2). A real calculation would also evaluate other sources such as temperature difference and measuring force; this example has been simplified to show the method.

    Diagram: the measurement result 25.012 mm and the ± 0.009 mm expanded uncertainty interval : Enlarge

Why does uncertainty matter?

  • Conformity decisions: Uncertainty must be taken into account when deciding whether a measurement result meets a tolerance; if the result is close to the limit, the decision may change.
  • Comparability: It is impossible to say whether two results really differ if their uncertainties are not stated.
  • Accreditation: Laboratories working to ISO/IEC 17025 are expected to evaluate their measurement uncertainty.

Common mistakes

  • Confusing uncertainty with "error" or "deviation".
  • Adding the expanded uncertainty from a certificate (k=2) directly, as if it were a standard uncertainty; it must first be divided by k.
  • Leaving resolution out altogether, or counting it twice in the budget.
  • Combining correlated sources as if they were independent.

Frequently asked questions

Are uncertainty and error the same thing?

No. Error is the difference between the measured value and the reference value; uncertainty expresses the width of the interval in which the true value may lie.

Why is k=2 used?

Assuming a normal distribution, k=2 corresponds to a level of confidence of approximately 95%, and it is widely used in international practice. With a small number of measurements a different value of k may be chosen.

What can be done to reduce the uncertainty?

Using instruments with a finer resolution and references calibrated with a lower uncertainty, increasing the number of measurements and controlling the environmental conditions all reduce the uncertainty.

BYK Yazılım Support Team
This guide is written and regularly reviewed by the BYK Yazılım support team. Last updated: 4 October 2026.

Related guides

Manage your calibration processes in one system

BYK Yazılım's calibration software brings laboratory work together in one system, from quotation to certificate to invoice.

Contact us Calibration laboratory software