Track physical units and propagate measurement uncertainty in scientific calculations using pint and uncertainties. Use for unit conversion and dimensional checking, GUM uncertainty budgets, Type A and Type B evaluation, coverage factors and expanded uncertainty, Monte Carlo propagation, significant

Uncertainty and units Scope Use this skill whenever a calculation carries physical units or a reported number needs an uncertainty. Concretely: converting between units, including conversions that need a physical context (wavelength to photon energy, mass to amount of substance, energy to temperature); propagating uncertainty through a measurement model, with or without correlated inputs; building a GUM uncertainty budget from calibration certificates, specifications, and repeatability data; choosing a coverage factor and deciding whether k = 2 is defensible; rounding and writing a result so a reader knows what the ± means; extracting parameter uncertainties from a curve fit without discarding correlations; reviewing existing analysis code for silent unit and uncertainty defects; checking that a dimensionally consistent answer is also physically possible — the order of magnitude, the dimensionless group, and the regime it implies. This skill covers the metrology and the two libraries that implement it. It does not cover statistical inference, model selection, or study design — see statistical analysis , statistical power , and experimental design . Current release and installation Verified 2026 07 26: pint 0.25.3 , released 2026 03 19; requires Python 3.11+. uncertainties 3.2.3 , released 2025 04 21; requires Python 3.8+. NumPy 2.5.1 and SciPy 1.18.0 ; both require Python 3.12+. scipy.constants in SciPy 1.18.0 serves CODATA 2022 . SciPy 1.11 and earlier served CODATA 2018, and several recommended values differ between them. pint pandas and pint xarray add unit aware columns and arrays and are separate installs. Non negotiable workflow 1. Attach units at input and strip them only at output. Convert at function boundaries with ureg.wraps or m as("unit") , never mid calculation. 2. Write the measurement model explicitly before computing anything, including corrections whose estimated value is zero. A correction left out of the model leaves its uncertainty out of the budget. 3. Give every input four things : an estimate, a standard uncertainty, the distribution the uncertainty came from, and its degrees of freedom. 4. Convert Type B statements with the right divisor. A certificate's expanded uncertainty divides by its stated k ; rectangular limits divide by sqrt(3) . 5. Identify correlations before combining. Inputs calibrated against the same standard, measured on the same instrument, or drawn from the same fit are correlated. 6. Compute sensitivity coefficients , and read the budget from c i u(x i) rather than from the raw uncertainties. 7. Check the linearization. Run Monte Carlo alongside the GUM framework and apply the JCGM 101 clause 8 comparison. Report the Monte Carlo result when it fails. 8. Choose k from the effective degrees of freedom , not by habit. 9. Round the uncertainty first, then the value to the same decimal place. 10. State what the ± is — standard or expanded, with k , the coverage probability, and the method. 11. Sanity check the magnitude before reporting. A dimensionally consistent result can still be impossible. Compare it against a known scale or a dimensionless group, and confirm every assumption you relied on still holds in that regime. The failures this skill exists to prevent Each of the following runs without error and produces a plausible number. A unit stripped at an unknown scale .magnitude returns whatever the quantity happened to be carrying. Name the unit at the point of extraction, every time. Offset temperature arithmetic Celsius and Fahrenheit are interval scales. An uncertainty on a temperature is always a difference and belongs in a delta unit: converting 20 ± 0.5 degC to Fahrenheit gives 68 degF ± 0.9 delta degF , two different conversions on one line. Logarithmic units that add by multiplying That is 10 mW × 10 mW, not 20 mW and not 13 dBm. Nothing raises. Convert to a linear unit before any arithmetic. A correlation destroyed by a round trip Rebuilding a variable from its nominal value and standard deviation creates an independent variable. So does any serialization that passes through a pair of floats. Use correlated values(values, covariance matrix) to rebuild a correlated set. A covariance matrix silently rescaled The default rescales pcov by the reduced chi square, so the parameter uncertainties absorb the goodness of fit and match what you would get by passing no sigma at all. On one synthetic straight line fit the two give [0.0364, 0.2154] and [0.0477, 0.2820] — a 31% difference. Pass absolute sigma=True whenever sigma holds real standard uncertainties. A linearization that was never checked For y = x² with x = 1.0 ± 0.5 , the GUM framework gives y = 1.0 , u c = 1.0 , and a 95% interval of [ 0.96, 2.96] — mostly negative, for a squared quantity. Monte Carlo gives a mean of 1.25, u c = 1.06 , and a shortest 95% interval of [0, 3.32] . Nothing in a linear propagation library will tell you this happened. Bundled local CLIs All helpers run offline, reject URLs and symlinks, bound their inputs, write output atomically with private permissions, and refuse to overwrite without force . propagate uncertainty.py Runs both propagation methods on the same model and applies the JCGM 101 clause 8 validation test. Each variable is name=value,standard uncertainty[,distribution[,dof]] , where the distribution is normal , rectangular , triangular , arcsine , or exact and controls Monte Carlo sampling only. Correlations go in as correlation "a,b=0.9" . A JSON spec file holds the same model for anything long lived. The expression is parsed into an abstract syntax tree and reduced by an explicit walk over + / and a fixed list of functions. It is never compiled or executed. The report gives the estimate, u c , sensitivity coefficients, the budget in percent, effective degrees of freedom, k , U , both Monte Carlo coverage intervals, and the verdict on whether the linearized result may be reported. uncertainty budget.py Combines components stated the way certificates and data sheets state them. Each component names a distribution that fixes its divisor — expanded divides by its coverage factor , rectangular by sqrt(3) , triangular by sqrt(6) , arcsine by sqrt(2) , normal by 1 — with an optional sensitivity , dof , and relative: true . The tool computes u c , the Welch Satterthwaite effective degrees of freedom, k from the t distribution, and U , and warns when a Type A component has no degrees of freedom, when nu eff is small enough that k = 2 is wrong, when one component dominates, and when a Type B component declared normal is probably an undivided expanded uncertainty. format result.py Returns 12.346 ± 0.023 mm , 12.346(23) mm , the scientific and LaTeX forms, and the sentence that has to accompany the number. Warns when one significant digit is requested for an uncertainty beginning in 1 or 2, and when the uncertainty exceeds the estimate. convert units.py Carries the uncertainty through the conversion's local derivative, which matters because context conversions are reciprocal rather than proportional. Names the context in the error message when a conversion needs one, and flags offset and logarithmic units. list contexts shows what the registry defines. audit units.py Static review of existing analysis code. Parses, never imports or runs. Rule Severity Detects UNIT001 medium a second UnitRegistry in one module — cross registry ValueError UNIT002 medium offset temperature units with no delta unit anywhere UNIT003 high .magnitude without a preceding .to(...) or .m as(...) UNIT004 medium logarithmic units, whose + multiplies UNC001 high curve fit without absolute sigma UNC002 medium np.std / np.var without ddof UNC003 medium math or numpy functions in a module that uses uncertainties UNC004 high a ufloat rebuilt from .nominal value and .std dev CONST001 low a literal within 0.1% of a CODATA constant Exit status is 1 when a finding meets fail on (default high ), which makes it usable as a pre commit or CI check. The rules are heuristics, so a false positive is suppressed with a directive comment — trailing to cover its own line, or alone on a line to cover the next one: audit units: ignore file CONST001 covers a whole module, and naming no rule suppresses all of them. Suppressions are counted in the report rather than hidden, so a file that silences everything still says so. check plausibility.py Dimensional consistency is not physical possibility. A cell 2 m across and a Reynolds number of 4e7 in a capillary both pass every unit check. This tool tests a set of quantities against dimensionless groups, characteristic scales, and curated magnitude bands, and verifies each formula's dimensionality before reporting a number. group evaluates one of 14 dimensionless groups and names the regime it places the system in; scale computes a characteristic scale such as a diffusion time, Debye length, or Stokes settling velocity; band compares a supplied quantity against an observed range. list prints the whole catalogue with the inputs each formula needs. Physical constants ( k B , N A , R gas , g earth , and the rest) are available to every formula without being supplied, and are read from scipy.constants at run time rather than written as literals, so they track the CODATA release SciPy ships. The dimensionality check is the point. Passing a kinematic viscosity where the formula needs a dynamic one — both called "viscosity", both tabulated for water, differing by a factor of ρ — is refused before any number is computed: Exit status is 1 when the verdict meets fail on (default implausible ; a value within one decade of a band is questionable ). The thresholds are conventions with soft edges and assume the geometry their correlation was fitted for — see references/plausibility scales.md for the characteristic length to use in each case. Choosing a propagation method Situation Method Linear or near linear model, normal ish inputs, large dof GUM framework alone Any nonlinearity across ±2u of an input run both, apply the clause 8 test Relative uncertainty above ~20% on any input Monte Carlo Dominant rectangular or otherwise non normal component Monte Carlo Output bounded below (variance, concentration, squared quantity) Monte Carlo Asymmetric output distribution Monte Carlo, shortest coverage interval Correlated inputs either, but supply the covariance matrix, not the standard uncertainties alone A model dominated by rectangular contributions fails the clause 8 test even when it is perfectly linear: the framework's k = 1.96 over covers a nearly trapezoidal output. The estimate and u c are still right; only the interval is too wide. Constants Never type a constant from memory. The 2019 SI redefinition fixed c , h , e , k , and N A exactly, so their relative standard uncertainty is zero; everything else is a measured value that moves between CODATA releases. precision returns a relative standard uncertainty; multiply by the value for the absolute one. Reference files references/gum methodology.md — Type A and Type B evaluation, distribution divisors, the law of propagation, Welch Satterthwaite, when the framework fails, the Monte Carlo procedure, and the clause 8 validation test. references/pint recipes.md — registries, offset and logarithmic units, contexts, boundary enforcement with wraps and check , NumPy interoperability, custom units, formatting.

uncertainty-and-units