Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities.^[1] Despite the name, it is more analogous to a system of algebra than calculus in the mathemtaical sense of the term. However, units refer to actual quantities, such as the cm, and are not algebraic symbols.

The basic axiom of quantity calculus can, for most purposes, be taken to be Maxwell's description^[2] of a physical quantity as the product of a "numerical value" and a "unit of measurement", although the roots can be traced to Fourier's concept of dimensional analysis (1822)^[3] and a full axiomatization has yet to be completed.^[1]

A careful distinction needs to be made between abstract quantities and measurable quantities. The multiplication and division rules of quantity calculus are applied to SI base units (which are measurable quantities) to define SI derived units, but if the units are algebraically simplified, it has been suggested that they then are no longer units of that quantity. ^[4]

[edit] References

[edit] Further reading

• International Organization for Standardization. ISO 31:1992 Quantities and Units. Part 0 - General Principles. ISO. Geneva
• International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 131–35, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 
• International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 3. Electronic version.