[1][a] Its roots can be traced to Fourier's concept of dimensional analysis (1822).
De Boer summarized the multiplication, division, addition, association and commutation rules of quantity calculus and proposed that a full axiomatization has yet to be completed.
[1] Measurements are expressed as products of a numeric value with a unit symbol, e.g. "12.7 m".
Unlike algebra, the unit symbol represents a measurable quantity such as a metre, not an algebraic variable i.e. the unit symbol does not satisfy the axioms of arithmetic.
The multiplication and division rules of quantity calculus are applied to SI base units (which are measurable quantities) to define SI derived units, including dimensionless derived units, such as the radian (rad) and steradian (sr) which are useful for clarity, although they are both algebraically equal to 1.