ToolJovia
Math

Structured Dimensional Equation Auditor

Check every term of a structured SI equation for dimensional homogeneity without executing an expression.

✓ Browser-local processing

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How to use Structured Dimensional Equation Auditor

Map each whitelisted unit to seven base exponents, multiply by the entered integer powers and add within each product term. Compare all term vectors across both sides and retain every mismatch.

  1. Use the example as the schema; replace its labels and entered model assumptions.
  2. Map each whitelisted unit to seven base exponents, multiply by the entered integer powers and add within each product term. Compare all term vectors across both sides and retain every mismatch.
  3. Calculate, inspect the complete witnesses and limitations, then copy or download the JSON report.

Good to know

  • 1–50 terms per side, 0–20 factors per term and whole powers from −12 through 12. Unit symbols are case sensitive; the report lists the supported base and derived symbols.
  • No numeric conversion, arbitrary expression, affine Celsius/Fahrenheit, unknown custom unit, scalar/vector inference or physical equation certification. Equal dimensions do not establish equal physical kind.
  • Local calculation with no upload, input persistence or outside lookup. Model JSON is limited to 30,000 characters and 10,000 values. Decimal quantities are strings with up to six places; count fields use plain JSON integers. Exact fractions are capped at 8,192 bits. The complete JSON output is limited to 1,000,000 characters; approximate numbers preserve their stored values. Unsupported states fail explicitly.

Common questions

If all dimensions match, is the equation physically correct?

Not necessarily. A missing dimensionless constant, a sign, a vector relation or two different kinds of quantity can still make the equation wrong. The report checks this necessary dimensional condition only.

Are my model inputs saved or sent to a server?

No. This model runs in the current browser tab and creates a local JSON download. It does not save your input or call an external data service.

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