Measurement Uncertainty Basics: Type A, Type B, Combined and Expanded Uncertainty (Caliper Example)

Measurement uncertainty basics

1 min readUpdated 2026-10-07

Key answer

Error is the difference from the true value; uncertainty is a parameter describing the spread of values that can reasonably be attributed to the measured quantity (VIM 2.26). A result is written as value ± U (k = 2, about 95 %).

Lab clipDigital caliper on a stepped shaft (readout view)Open in the lab →

Type A and Type B

Type A: from repeated readings — standard deviation s of n readings, u = s/√n for the mean.
Type B: from other information — a specification limit ±a with rectangular distribution gives u = a/√3; a resolution δ gives u = δ/(2√3).
Combined: u_c = √(u₁² + u₂² + …) for independent sources.
Expanded: U = k · u_c, usually k = 2.

Worked example: a caliper reading

Source	Value	Standard uncertainty
Caliper MPE	±0.02 mm	0.02/√3 = 0.0115 mm
Resolution	0.01 mm	0.01/(2√3) = 0.0029 mm
Repeatability (10 readings)	s = 0.008 mm	0.008/√10 = 0.0025 mm

u_c = √(0.0115² + 0.0029² + 0.0025²) ≈ 0.0122 mm, U = 2 × 0.0122 = 0.0243, rounded up to 0.025 mm. Mean reading 25.03 mm → 25.030 mm ± 0.025 mm (k = 2). Temperature, force and zero setting add further terms in a full budget.

Why it matters for pass/fail

If the tolerance band is 0.05 mm and U is 0.025 mm, most of the band is uncertainty — the instrument is unsuitable (see the 10:1 rule). By default (when the supplier proves conformity) ISO 14253-1 accepts conformity only when the result lies inside the limits reduced by U; other decision rules can be agreed.

References

JCGM 100:2008 — Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM) · JCGM / BIPM
JCGM 200:2012 — International vocabulary of metrology — Basic and general concepts and associated terms (VIM, 3rd edition) · JCGM / BIPM
JJF 1059.1-2012《测量不确定度评定与表示》 (cited by number; no public page) · 国家质量监督检验检疫总局
ISO 14253-1:2017 — GPS — Inspection by measurement of workpieces and measuring equipment — Part 1: Decision rules for verifying conformity or nonconformity with specifications · ISO

Watch it done

Watch in the lab → Follow step by step →

Played back in the lab from domain commands; the reading and verdict come from the measurement model.

Questions

What is the difference between error and uncertainty?

Error is a single difference from the true value (often unknown); uncertainty quantifies the doubt about the result and is stated with a coverage factor.

Why divide by √3?

A limit ±a with every value equally likely (rectangular distribution) has a standard deviation of a/√3.

Try it yourself

Open the same setup in the 3D lab and take the reading yourself.

Open in the lab →