The International System of Quantities (ISQ) is a standard system of

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 u ...

used in

physics Physics is the scientific study of matter, its Elementary particle, 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 whi ...

and in modern science in general. It includes 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, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

(SI) but does not itself determine the units of measurement used for the quantities. The system is formally described in a multi-part

ISO standard The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries. Me ...

ISO/IEC 80000 (which also defines many other quantities used in science and technology), first completed in 2009 and subsequently revised and expanded. Unit_relations_in_the_new_SI_planar

Base quantities

The base quantities of a given system of

physical quantities A physical quantity (or simply quantity) is a 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 '' ...

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 seven ISQ 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 Roman civilization *Epistle to the Romans, shortened to Romans, a letter w ...

(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 ...

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 and corresponding

derived unit A base unit of measurement (also referred to as a base unit or fundamental unit) is a unit of measurement adopted for a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the ...

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 dimension 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.

Dimensionless quantities

A ''quantity of dimension one'' is historically known as a ''

dimensionless quantity Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...

'' (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. The named dimensionless units "

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...

" (rad) and "

steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in the fo ...

" (sr) are acceptable for distinguishing dimensionless quantities of different kind, respectively

plane angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...

and

solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poin ...

Logarithmic quantities

Level

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

logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...

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 Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone ...

, with the unit of

decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...

Other logarithmic quantities

Units of logarithmic frequency ratio include the

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

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

decade A decade (from , , ) is a period of 10 years. Decades may describe any 10-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 ...

, corresponding to a factor 10. The ISQ recognizes another logarithmic quantity,

information entropy In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed ...

, 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 ISO 31 (Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrelationships and their presentation. It was revised and re ...

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, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

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 (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre C ...

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

Base quantities

Derived quantities

Dimensional expression of derived quantities

Dimensionless quantities

Logarithmic quantities

Level

Other logarithmic quantities

Documentation

See also

Notes

References

Further reading