The uncertainty budget behind the number you are about to report — checked, propagated and rounded properly
Paste the inputs with their uncertainties and units, and the formula. The browser checks the dimensions, propagates the uncertainty the GUM way, finds the degrees of freedom and the coverage factor, cross-checks it all by Monte Carlo and rounds the result — free, before you sign in. Then a metrologist reviews the budget, and then writes the uncertainty section for your report.
All three examples ship with a saved model run, so you can see the whole result — the engine's budget, the review, the report — without signing in and without spending a credit.
What this does, and what it does not
The engine is a small metrology toolkit that runs entirely in your browser. It reads the sheet's
grammar — a value, a unit, a ± uncertainty, tags for Type A repeat counts, half-widths, coverage
factors and distributions, corr() lines, CODATA 2018 constants — checks every formula
in the seven SI base dimensions, and evaluates it with forward-mode automatic differentiation, so the
GUM sensitivity coefficients are exact rather than finite differences. It combines the contributions
with their correlation terms, computes Welch–Satterthwaite effective degrees of freedom and the
coverage factor from the Student t distribution, then runs two Monte Carlo propagations: one with
every input normal, whose spread against the GUM value exposes non-linearity, and one with the stated
distributions, whose interval is the one to report when the ± form misleads. It rounds the result
the way GUM 7.2.6 asks, checks your own draft statement, and computes an En number against
a reference. Everything it finds becomes a flag the model must answer, and the reply is checked
against the engine afterwards — if the model changes a digit, this page says so.
The model does what arithmetic cannot: it knows what a competent budget for this kind of measurement usually carries — the resolution nobody wrote down, the reaction time, the temperature, the approximation in the model — and hands each one back as a sheet line you can paste and confirm. It judges whether a stated uncertainty is plausible, ranks the improvements by share of variance, and writes the section a report needs in GUM vocabulary with a thirteen-point reporting checklist. The numbers in its prose are the engine's; it never re-rounds.
Nothing here is sent anywhere until you press the button, and then only the sheet, your hint and the engine's facts go to the model. Plus-Minus holds itself to its own rules: every uncertainty on this page is stated to two significant figures with its coverage factor and coverage probability, and the value is rounded to the same place. Nothing to hand? Load , the , or the . All three replay a saved run for free.