Type A and Type B uncertainty: which divisor to use

By Anna Badanina, MSc in Metrology and Information-Measuring Technology · 8 November 2026

Every row of an uncertainty budget must be a standard uncertainty: a value with the meaning of one standard deviation. The GUM (JCGM 100:2008) gives two ways to get it. The names say nothing about importance or quality; they only describe how the number was obtained.

• Type A: by statistical analysis of a series of observations you made.
• Type B: by any other means, such as certificates, specifications, handbooks, resolution or experience.

Both kinds are combined in the same way in the budget. A Type B uncertainty is not "less accurate" than a Type A one.

Type A: from repeated readings

Take n independent readings q₁ … q_n under the same conditions. Then:

Example: five readings of a thermometer, 50.31, 50.28, 50.33, 50.30 and 50.27 °C, give q̄ = 50.298 °C, s = 0.0239 °C and u(q̄) = 0.0239 / √5 = 0.0107 °C, with ν = 4 degrees of freedom.

Two points that are easy to get wrong:

• The divisor √n applies only if you report the mean of the n readings. If the result will be a single reading, use s.
• Small n means few degrees of freedom. With 3 or 4 readings, s itself is very uncertain. This is why the coverage factor must be increased: see Coverage factor k and Welch–Satterthwaite.

Pooled standard deviation

Laboratories often know the repeatability of a method from earlier, larger studies. EA-4/02 uses this in its worked examples: a standard deviation s_p determined once from many measurements, and a routine calibration with only n = 3 readings. The standard uncertainty is then s_p / √n, and the degrees of freedom are those of the study that produced s_p, not n − 1.

Type B: from what you know

For Type B you choose a probability distribution that matches your knowledge of the quantity, then divide by the matching factor.

Calibration certificates

A certificate that says U = 0.10 °C, k = 2 gives u = 0.050 °C. If a certificate states a coverage probability (for example 95 %) and no k, it is usually based on a normal distribution, and you divide by the k that corresponds to that probability. Never put the certificate U straight into the budget.

Specifications and tolerances: rectangular

A manufacturer specification such as "accuracy ±0.2 % of reading", or the maximum permissible error of a class, tells you only the limits. Without other information, the rectangular distribution is the standard, conservative choice: u = a / √3.

Resolution

A digital display with a step of 0.1 °C shows 50.3 for any true value between 50.25 and 50.35. The half-width is a = 0.05 °C, and with a rectangular distribution u = 0.05 / √3 = 0.029 °C. A common mistake is to use the full step (0.1) as a, which doubles the contribution.

Triangular

Use it when you have good reason to think values near the centre are more likely, for example when a quantity is the difference of two rectangular ones, or when experience shows that drift rarely reaches its limit. EA-4/02 uses triangular distributions in some of its worked examples. It gives a smaller u than the rectangular one, so be ready to justify it.

U-shaped

Typical for quantities that swing between two limits, such as a temperature controlled by an on/off regulator, or mismatch effects in RF power measurement. The quantity spends most of its time near the limits, so u is larger: a / √2.

Degrees of freedom for Type B

A Type B estimate is usually treated as having infinite degrees of freedom: you assume the limits are known exactly. If you are unsure of the limits themselves, the GUM gives a way to assign a finite ν from your relative doubt about u. In practice most budgets use ν = ∞ for Type B rows and only Type A rows bring finite degrees of freedom into the Welch–Satterthwaite calculation.

Back to the full method: How to make a measurement uncertainty budget.