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Dimensional Consistency Check

Check that quantities, units, and scale relationships are compatible before trusting equations, comparisons, or transfers.

The Diagnostic Story

Symptom: A calculation produces a plausible number but nobody can say what units the output has. Raw totals are compared across differently sized entities, percentages and percentage-point changes are used interchangeably, and one-time costs are compared with recurring costs without conversion. A model works in a pilot but fails after rollout, and a dashboard ranking changes dramatically after normalization with no explanation of why.

Pivot: Expose the quantity structure of the proposed expression, test compatibility across units, dimensions, denominators, time bases, and scale meanings, then correct or reject operations that are structurally invalid before they shape decisions.

Resolution: Invalid comparisons are caught before they become evidence. Metrics become more interpretable and auditable, model transfers become safer, and decision confidence is grounded in valid structure rather than the false precision that formal notation can project.

Reach for this when you hear…

[biomedical research] “You cannot add absolute risk reduction to relative risk reduction in the same summary table — they look like the same kind of number and they are not.”

[financial modeling] “The model divides an annual revenue figure by a monthly cost figure and calls it a ratio — nobody caught it because the output looked reasonable.”

[urban planning] “We compared transit ridership across cities by total boardings, which made the tiny city look terrible and the huge city look great — you have to normalize by population before the numbers mean anything.”

Mechanisms / Implementations

  • Unit Check: The first-line check that every input, output, and intermediate expression carries a compatible unit label before a calculation is trusted.
  • Dimensional Analysis Table: A worksheet that lists every quantity with its units and base dimensions and tracks how they cancel through a formula, so no scale-dependent term is ever combined blindly.
  • Unit Conversion Workflow: Converts every quantity into one shared unit convention before combining them, keeping the conversion factors and assumptions attached to the result.
  • Normalized Metric Design: Designs a metric on a comparable basis — indexed, standardized, or denominator-adjusted — so entities of different size or context can be set side by side honestly.
  • Per-Capita or Per-Unit Conversion: Divides a total by a clearly chosen denominator — people, units, transactions — turning raw counts into rates so differently sized things can be compared.
  • Dimensionless Ratio Construction: Combines quantities into a ratio whose units cancel — a pure number that carries meaning across scales, but only when its parts are chosen to mean something.
  • Stock / Flow Separation Check: Separates accumulated stocks from the flows that fill or drain them — balances from rates, prevalence from incidence — so a level is never compared directly with a speed.
  • Spreadsheet Unit Audit: Walks an actual spreadsheet cell by cell — columns, hidden intermediate cells, and formula chains — to surface the unlabeled unit and denominator slips that spreadsheets breed.
  • Model Input / Output Contract: A written specification pinning the unit, dimension, scale basis, and valid range of every model input and output, so an upstream change cannot silently corrupt a downstream result.
  • Cross-Scale Transfer Review: Rechecks whether a metric, rule, or equation that held at one scale still holds after it moves to another — and draws the boundary where its validity ends.

Abstractions this archetype builds on — directly (a source ingredient) or as a related pattern. Links follow the typed catalog namespace.

Built directly on (3)

Also references 6 related abstractions

Variants

Narrower or domain-specific specializations that share this archetype's core structure. Recognized variants are established; candidate variants are provisional.

Unit Consistency Check · mechanism family variant · recognized

A narrower variant focused on compatible unit labels and conversions across inputs, formulas, and outputs.

Scale Normalization Check · scale variant · recognized

A variant that verifies totals, rates, percentages, indexed values, and normalized metrics are being compared on a compatible basis.

Dimensionless Ratio Design · mechanism family variant · recognized

A variant focused on constructing ratios, coefficients, or indices that remove units or expose scale-invariant structure.

Semantic Quantity Alignment · other · candidate

A candidate variant that checks whether quantities with compatible units actually represent the same construct or decision-relevant meaning.

Cross-Scale Transfer Check · scale variant · recognized

A variant that verifies whether an equation, rule, metric, or comparison remains valid when moved across scale, population, scope, or context.

Stock / Flow Separation · subtype · recognized

A variant that prevents accumulated quantities from being confused with rates or flows over time.