Input quantities

Enter standard uncertainties (1σ). Distribution widths are calculated from u; enter uniform half-width / √3 or triangular half-width / √6. Degrees of freedom are optional and affect independent-input linear coverage only.

Matrix ordering follows the variable table. Correlated Monte Carlo supports normal inputs only; singular positive-semidefinite matrices are accepted.

Type A & Type B helpers

Analysis overview

Imported data worksheet

100-row pages show every imported row. Search affects the preview only. Blank/non-numeric measurement rows are reported or rejected according to the selected method.

Workflow, methods and limitations

1. Import data or load a labeled synthetic example.
2. Review the worksheet, header setting, columns and physical units.
3. Choose method controls and run the analysis.
4. Inspect numerical tables, plots, exclusions and method assumptions.
5. Export the settings with the results for reproducibility.

The measurement equation accepts named variables, + − * / ^, parentheses and exp, ln, log10, sqrt, abs, trigonometric and hyperbolic functions. Use consistent units before evaluating the equation; there is no symbolic dimensional analysis. Up to 12 variables.

First-order combined variance is J C Jᵀ, with covariance built from standard uncertainties and a validated correlation matrix. Sensitivities use finite differences. Welch–Satterthwaite effective degrees of freedom and t coverage are used only for independent inputs; correlated-input coverage uses a normal approximation.

Monte Carlo uses seeded draws from normal, uniform, symmetric triangular or log-normal distributions. Log-normal values represent a positive arithmetic mean and standard deviation. Correlation is supported only for normal Monte Carlo inputs. If more than 1% of draws leave the equation domain, analysis stops. Rare rejected draws are reported and intervals are conditional on retained draws; remove domain failures before relying on the result.

Type A computes the sample mean, sample standard deviation, SEM = s/√n and df = n−1. This assumes independent replicates; drift and autocorrelation require additional assessment. Type B helper converts U/k only when the quoted coverage factor is appropriate. No automatic certification or GUM compliance is claimed.

Reference: NIST uncertainty-propagation guidance.

Uploaded measurements are processed locally. Native proprietary instrument files, PDF/image extraction and calibrated medical analysis are not supported. Excel formulas use stored values. Host over HTTP/HTTPS because computation uses workers. Reloading clears the session.