Unitform

Unitform is a conceptual representation used in measurements and computation to encode both the magnitude of a quantity and the composition of its units within a single, canonical form.

In a unitform, a quantity is typically stored as a scalar coefficient and a unit form, which is a mapping from base units to integer exponents. For example, 3.5 m s^-2 would have a coefficient of 3.5 and a unit form {m: 1, s: -2}.

Arithmetic follows consistent rules: multiplication combines unit forms by adding exponents, while division subtracts exponents. Addition and subtraction require identical unit forms. Conversions between unit systems are handled by adjusting the coefficient with a scale factor while preserving the unit form structure.

Unitform is used in unit-safe programming, scientific data models, and interoperability layers where explicit unit handling reduces errors and enables automatic dimension checks and serialization.

Limitations include handling of non-base or derived units that involve complex relationships, fractional exponents, or context-specific units. Some systems also need support for dimensionless quantities with attached annotations.

See also: dimensional analysis; quantity; unit of measurement; unit conversion.