The International System of Quantities (ISQ) consists of the

quantities Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit ...

used in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This system underlies the

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

(SI) but does not itself determine the units of measurement used for the quantities. It is inherently incomplete because the number of quantities is potentially infinite. The system is formally described in a multi-part

ISO standard The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Ar ...

ISO/IEC 80000, first completed in 2009 but subsequently revised and expanded.

Base quantities

The base quantities of a given system of

physical quantities A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...

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. 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 Roman or Romans most often refers to: *Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *''Epistle to the Romans'', shortened to ''Romans'', a letter ...

(upright)

sans-serif In typography and lettering, a sans-serif, sans serif, gothic, or simply sans letterform is one that does not have extending features called "serifs" at the end of strokes. Sans-serif typefaces tend to have less stroke width variation than seri ...

type.

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. The ISQ defines many derived quantities.

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

\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 symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted

\mathsf^

. The following table lists some quantities defined by the ISQ. A ''quantity of dimension one'' is historically known as a ''

dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

'' (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is

1

. Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.

Logarithmic quantities

Level

The ''level'' of a quantity is defined as the

logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

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. Within the ISQ, all levels are treated as derived quantities of dimension 1. Several units for levels are defined by the SI and classified as "non-SI units accepted for use with the SI units". An example of level is sound pressure level.

Logarithmic frequency ratio

Units of logarithmic frequency ratio are the

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

, corresponding to a factor of 2 in frequency (precisely) and the

decade A decade () is a period of ten years. Decades may describe any ten-year period, such as those of a person's life, or refer to specific groupings of calendar years. Usage Any period of ten years is a "decade". For example, the statement that "du ...

, corresponding to a factor 10.

Information entropy

The ISQ recognizes another logarithmic quantity:

information entropy In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable X, which takes values in the alphabet \ ...

, for which the coherent unit is the natural unit of information (symbol nat).

Documentation

The system is formally described in a multi-part

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, ISO and 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

that are measured with the

SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...

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 The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...

(CGPM) to describe the system of quantities that underlie the

Base quantities

Derived quantities

Dimensional expression of derived quantities

Logarithmic quantities

Level

Logarithmic frequency ratio

Information entropy

Documentation

See also

Notes

References

Further reading