A free, GUM-aligned calculator for testing and calibration laboratories. Enter Type A repeated readings and Type B components (rectangular, triangular or normal), with sensitivity coefficients. The tool computes the combined standard uncertainty and the expanded uncertainty at k = 2. Calculations follow JCGM 100:2008; EURACHEM/CITAC CG 4 is cited for the same approach in analytical work. Results stay on this device.
Type A (JCGM 100:2008 4.2): from n repeated readings, the experimental standard deviation s uses n−1 degrees of freedom, and the standard uncertainty of the mean is s/√n (at least two readings are required). Type B rectangular, half-width a: u = a/√3 (4.3.7). Type B triangular, half-width a: u = a/√6 (4.3.9). Type B normal: if an expanded uncertainty U is quoted with coverage factor k, u = U/k (4.3.3, 6.2.1). Uncorrelated combination (5.1.2–5.1.3): u_c(y) = √Σ (c_i · u_i)², where c_i is the sensitivity coefficient (∂f/∂x_i). Expanded uncertainty (6.2.1): U = k · u_c, with k = 2 in this tool (approximately 95 % coverage for a normal distribution). Enter all components in consistent units. This tool does not propagate correlations, degrees of freedom (Welch–Satterthwaite) or coverage factors other than the k you set for a normal Type B input; the reported expansion uses k = 2.
Sources (free publications, not reproduced here)
JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM), BIPM / JCGM.
EURACHEM/CITAC Guide CG 4, Quantifying Uncertainty in Analytical Measurement, 3rd edition (2012).
ISO/IEC 17025 Laboratory Kit — $129 — This tool is free and runs in your browser. Records stay on this device (localStorage) and are not sent to a server. For the full paid ISO/IEC 17025 Laboratory Kit ($129), open the product page. Related training: ISO/IEC 17025:2017 — competence of testing and calibration laboratories on AMAADOR Academy.
Open the Laboratory Kit ($129)AMAADOR Academy — ISO/IEC 17025 trainingThis calculator implements selected formulas from JCGM 100:2008. It is a computational aid, not a substitute for a documented uncertainty budget, and it does not assess whether a laboratory’s model is complete. Clause 7.6 of ISO/IEC 17025:2017 still requires the laboratory to identify significant contributions, including from sampling where relevant, and to evaluate uncertainty for calibrations and for testing (or to estimate it when a rigorous evaluation is not possible). Work from the GUM and, for analytical chemistry, from EURACHEM/CITAC CG 4.