Methodology
How these calculators are built, which standards are verified against original text, which automated checks run on every change, and what we do not claim.
Where the formulas live
The calculation layer is not written inside this website. Every general engineering formula lives in formulab, an open-source TypeScript library with no runtime dependencies, and this site is a thin wrapper around it. That separation is deliberate: the formulas can be read, tested, and challenged independently of the user interface that presents them. formulab currently ships 206 functions and is covered by 3,131 automated tests across 208 test files, all passing at the version this site is pinned to.
What "verified against the standard" means here
We distinguish two things that are often blurred. A citation names the standard a formula comes from. A verification means someone obtained the standard's original text and checked the implemented numbers against it, line by line. Across all tools there are 460 standard citations, and 61 of them are currently backed by a machine-checked provenance annotation in formulab source. The remaining citations are context and further reading, not evidence of verification. We report the ratio rather than implying every citation is verified, because that distinction is the whole point of publishing a methodology.
- ISO 7243:2017 — WBGT heat stress reference values, all five work-intensity classes cross-checked against the original text
- ISO 7870-2:2023 — X-bar/R control chart constants; five table cells were found to disagree by ±0.001 and were corrected
- ISO 7870-3 — acceptance control charts, formula re-derived from the standard's worked examples
- ISO 7870-4:2011 — CUSUM control charts
- ISO 7870-5 — moving average / moving range control charts, golden values recomputed from the standard's raw data table
- ISO 4000-1 — tyre load index and speed symbol tables
Checks that run on every change
Verification that is not automated decays. These checks run in continuous integration and block a release when they fail, so a formula cannot silently drift away from the source it claims.
- Golden tests that reproduce the worked examples printed in the standards themselves
- Constant-table checks that compare hard-coded coefficient tables against their published source
- Arithmetic checks on every worked example shown in the prose, across nine locales
- Consistency checks between the prose on a page and the formula that page actually evaluates
- Threshold checks so a limit value appears in exactly one place and cannot disagree with itself
Solver engines behind the heavier tools
Optimization, scheduling, statistics, and design-of-experiments tools do not reimplement their algorithms here either. They call open-source engines compiled to WebAssembly and executed in your browser.
- u-numflow — mathematical, statistical, and probabilistic primitives
- u-analytics — SPC control charts, process capability, Weibull reliability, hypothesis testing
- u-insight — clustering, anomaly detection, PCA, regression, data profiling
- u-metaheur — genetic algorithms, simulated annealing, ALNS, constraint programming
- u-geometry — polygon operations, collision detection, Minkowski sums, spatial indexing
- u-nesting — 2D polygon nesting and 3D bin packing
- u-routing — vehicle routing (TSP, CVRP, VRPTW)
- u-schedule — job-shop scheduling
- u-doe — factorial, RSM and Taguchi designs, ANOVA, power analysis
What we do not claim
These are screening and estimation tools. They do not replace the governing standard, a qualified engineer, or a measurement. Safety-related results in particular — heat stress, arc flash, fall clearance, load limits — are starting points for a decision, not the decision. If you find a number that disagrees with the standard you hold, tell us and we will check it against the source: [email protected].