International System of Quantities

Derived quantities

A derived quantity is a quantity in a system of quantities that is defined in terms of only the base quantities of that system. There are many ISQ derived quantities and corresponding derived units.

Dimensional expression of derived quantities

The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity is denoted by ⁠${\displaystyle {\mathsf{L}}^a{\mathsf{M}}^b{\mathsf{T}}^c{\mathsf{I}}^d{\mathsf{\Theta }}^e{\mathsf{N}}^f{\mathsf{J}}^g}$⁠, where the dimensional exponents are positive, negative, or zero. The dimension symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted ⁠${\displaystyle {\mathsf{L}\mathsf{T}}^{-1}}$⁠. The following table lists some quantities defined by the ISQ. For more, see List of physical quantities.

Dimensionless quantities

A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is ${\displaystyle 1}$. Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension. The named dimensionless units "radian" (rad) and "steradian" (sr) are acceptable for distinguishing dimensionless quantities of different kind, respectively plane angle and solid angle.

Logarithmic quantities

Level

The level of a quantity is defined as the logarithm of the ratio of the quantity with a stated reference value of that quantity. Within the ISQ it is differently defined for a root-power quantity (also known by the deprecated term field quantity) and for a power quantity. It is not defined for ratios of quantities of other kinds. Some units for levels are listed in the SI Brochure as "non-SI units". An example of level is sound pressure level, with the unit of decibel.

Other logarithmic quantities

Units of logarithmic frequency ratio include the octave, corresponding to a factor of 2 in frequency (precisely) and the decade, corresponding to a factor 10.

The ISQ recognizes another logarithmic quantity, information entropy, for which the coherent unit is the natural unit of information (symbol nat).

Documentation

The system is formally described in the multi-part standard ISO/IEC 80000, first completed in 2009 but subsequently revised and expanded, which replaced standards published in 1992, ISO 31 and ISO 1000. Working jointly, International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) have formalized parts of the ISQ by giving information and definitions concerning quantities, systems of quantities, units, quantity and unit symbols, and coherent unit systems, with particular reference to the ISQ. ISO/IEC 80000 defines physical quantities that are expressed in terms SI units and also includes many other quantities in modern science and technology. The name "International System of Quantities" is used by the General Conference on Weights and Measures (CGPM) to describe the system of quantities that underlie the International System of Units.