The International System of Quantities (ISQ) is a system based on seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Other quantities such as area, pressure, and electrical resistance are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units and also includes many other quantities in modern science and technology. The ISQ is defined in the international standard ISO/IEC 80000, and was finalised in 2009 with the publication of ISO 80000-1.
The 14 parts of ISO/IEC 80000 define quantities used in scientific disciplines such as mechanics (e.g., pressure), light, acoustics (e.g., sound pressure), electromagnetism, information technology (e.g., storage capacity), chemistry, mathematics (e.g., Fourier transform), and physiology.
A base quantity is a physical quantity in a subset of a given system of quantities that is chosen by convention, where no quantity in the set can be expressed in terms of the others. The ISQ defines seven base quantities. The symbols for them, as for other quantities, are written in italics.
The dimension of a physical quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in roman (upright) sans-serif type.
|Base quantity||Symbol for quantity||Symbol for dimension||SI unit||SI unit symbol|
|amount of substance||mole||mol|
A derived quantity is a quantity in a system of quantities that is a defined in terms of the base quantities of that system. The ISQ defines many 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 , where the dimensional exponents are positive, negative, or zero. The symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted . The following table lists some quantities defined by the ISQ.
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 . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.
|Derived quantity||Symbol for dimension|
In the ISQ, the level of a quantity is a logarithmic quantification of the ratio of the quantity with a stated reference value of that quantity. 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.
The level of a root-power quantity with reference to a reference value of the quantity is defined as
where is the natural logarithm. The level of a power quantity quantity with reference to a reference value of the quantity is defined as
When the natural logarithm is used, as it is here, use of the neper (symbol Np) is recommended, a unit of dimension 1 with Np = 1. The neper is coherent with SI. Use of the logarithm base 10 in association with a scaled unit, the bel (symbol B), where .
An example of level is sound pressure level. All levels of the ISQ are treated as derived quantities of dimension 1.