Coverfactor: free online measurement uncertainty calculator

Coverfactor turns a measurement function and what you know about each input into an uncertainty budget. Enter repeated indications, certificate values, limits or standard uncertainties, and it computes the sensitivity coefficients, the combined standard uncertainty with correlations, the effective degrees of freedom, the coverage factor and the expanded uncertainty, following the GUM.

The same budget is propagated by the Monte Carlo method of GUM Supplement 1 with a recorded seed, and the two coverage intervals are compared to show whether the first-order GUM result is good enough. Everything runs in your browser; projects save as JSON, budgets and Monte Carlo summaries export as CSV, and the Verify page re-runs the reference cases. Results support, but do not replace, a laboratory’s own evaluation.

What Coverfactor can do

Explicit measurement functions with up to six outputs and exact symbolic sensitivity coefficients
Type A indications, certificates, normal, t, rectangular, triangular, U-shaped and inexact-limit inputs
Correlated inputs, higher-order terms, Welch-Satterthwaite degrees of freedom and coverage factors
Seeded Monte Carlo propagation with fixed or adaptive trials and symmetric or shortest intervals
Automatic comparison of the GUM and Monte Carlo intervals with the validation verdict
Budget table, contribution chart, histogram, step-by-step report and CSV, SVG and PNG exports

How we verify Coverfactor

Reference cases reproduce worked examples published in JCGM 100 and JCGM 101 and add closed-form and independent-code checks; Monte Carlo checks use fixed seeds and stated statistical tolerances. Pending sources do not count as passes. Where a reference answer exists you can run every check yourself on the Verify page, and the Coverfactor user guide documents every feature and limitation.

The Verify page re-runs 36 reference cases (189 individual checks) in your browser, the same list the automated tests run. 21 compare with numbers published in the worked examples of JCGM 100 (end-gauge calibration, resistance and reactance, the Welch-Satterthwaite example, Table G.2) and JCGM 101 (additive model, mass calibration, comparison loss, gauge block); 15 compare with closed-form results, hand derivations and an independent implementation. Monte Carlo checks use fixed seeds; each tolerance states its basis (half a unit of the published digit plus four standard errors of the Monte Carlo estimate). The badge appears only after every case passes.

Coverfactor is part of Open Tools, the free engineering tools that run in your browser.

Professional use. Results are for education and preliminary design. They must be checked by a qualified professional, and they are not a substitute for code-compliant design or licensed engineering judgement.