TheInternational System of Quantities (ISQ) is a standard system ofquantities used inphysics and in modern science in general. It includes seven ISQbase quantities —length,mass,time,electric current,thermodynamic temperature,amount of substance, andluminous intensity — and the relationships between those quantities inderived quantities.^[a] This system underlies theInternational System of Units (SI)^[b] but does not itself determine the units of measurement used for the quantities.The system is formally described in a multi-part standardISO/IEC 80000, which also defines many other derived quantities used in science and technology, first completed in 2009 and subsequently revised and expanded.

Thebase quantities of a given system ofphysical quantities is a subset of those quantities, where no base quantity can be expressed in terms of the others, but where every quantity in the system can be expressed in terms of the base quantities. Within this constraint, the set of base quantities is chosen by convention. There are sevenISQ base quantities. The symbols for them, as for other quantities, are written in italics.^[1]

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 inroman (upright)sans-serif^[c] type.

Base quantity	Symbol for dimension	Symbol for quantity[d]	SI base unit[d]	SI unit symbol[d]
length	${\displaystyle \mathsf{L}}$	${\displaystyle l}$	metre	m
mass	${\displaystyle \mathsf{M}}$	${\displaystyle m}$	kilogram	kg
time	${\displaystyle \mathsf{T}}$	${\displaystyle t}$	second	s
electric current	${\displaystyle \mathsf{I}}$	${\displaystyle I}$	ampere	A
thermodynamic temperature	${\displaystyle \mathsf{\Theta }}$	${\displaystyle T}$	kelvin	K
amount of substance	${\displaystyle \mathsf{N}}$	${\displaystyle n}$	mole	mol
luminous intensity	${\displaystyle \mathsf{J}}$	${\displaystyle I_{\text{v}}}$	candela	cd

Aderived quantity is a quantity in a system of quantities that is defined in terms of only the base quantities of that system. The ISQ defines many derived quantities and correspondingderived units.

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. Thedimension 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.

Derived quantity	Expression in SI base dimensions
frequency	${\displaystyle {\mathsf{T}}^{-1}}$
force	${\displaystyle {\mathsf{L}\mathsf{M}\mathsf{T}}^{-2}}$
pressure	${\displaystyle {\mathsf{L}}^{-1}{\mathsf{M}\mathsf{T}}^{-2}}$
velocity	${\displaystyle {\mathsf{L}\mathsf{T}}^{-1}}$
area	${\displaystyle {\mathsf{L}}^2}$
volume	${\displaystyle {\mathsf{L}}^3}$
acceleration	${\displaystyle {\mathsf{L}\mathsf{T}}^{-2}}$

Aquantity ofdimension one is historically known as adimensionless 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, respectivelyplane angle andsolid angle.^[3]

Thelevel of a quantity is defined as thelogarithm 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 termfield quantity) and for a power quantity. It is not defined for ratios of quantities of other kinds. Within the ISQ, all levels are treated as derived quantities of dimension 1.^{[citation needed]} Several units for levels are defined by the SI and classified as "non-SI units accepted for use with the SI units".^[4]An example of level issound pressure level, with the unit ofdecibel.

Units oflogarithmic frequency ratio include theoctave, corresponding to a factor of 2 in frequency (precisely) and thedecade, corresponding to a factor 10.

The ISQ recognizes another logarithmic quantity,information entropy, for which the coherent unit is thenatural unit of information (symbol nat).^{[citation needed]}

The system is formally described in the multi-part standardISO/IEC 80000, first completed in 2009 but subsequently revised and expanded, which replaced standards published in 1992,ISO 31 andISO 1000. Working jointly,International Organization for Standardization (ISO) and theInternational 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 physicalquantities that are expressed in termsSI units^[5] and also includes many other quantities in modern science and technology.^[1] The name "International System of Quantities" is used by theGeneral Conference on Weights and Measures (CGPM) to describe the system of quantities that underlie theInternational System of Units.

• Dimensional analysis
• List of physical quantities
• International System of Units
• SI base unit

• B. N. Taylor, Ambler Thompson,International System of Units (SI),National Institute of Standards and Technology 2008 edition,ISBN 1-4379-1558-2.

• Physical quantities
• Measurement
• International standards

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