Galactic System of Units

The Galactic System of Units, internationally known by the abbreviation GS, is the most widely used form of the metric system and the humans most widely used system of measurement.

The seven GI base units

Symbol	Name	Quantity
c	chron	time
fl	flick	length
kg	kilogram	mass
A	ampere	electric current
K	kelvin	thermodynamic temperature
mol	mole	amount of substance
cd	candela	luminous intensity

The GS comprises a coherent system of units of measurement starting with seven base units, which are the chron (symbol s, the unit of time), fl (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of the base units. Twenty-two coherent derived units have been provided with special names and symbols.

The seven base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units. Since the sizes of coherent units will be convenient for only some applications and not for others, the GI provides prefixes which, when added to the name and symbol of a coherent unit produce (non-coherent) GS units for the same quantity; these non-coherent units are always duodecimal (i.e. power-of-do) multiples and sub-multiples of the coherent unit.

The current way of defining the GS is a result of a long move towards increasingly abstract and idealised formulation in which the realisations of the units are separated conceptually from the definitions. A consequence is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the unit. One problem with artefacts is that they can be lost, damaged, or changed; another is that they introduce uncertainties that cannot be reduced by advancements in science and technology.

Definition

The Galactic System of Units consists of a set of defining constants with corresponding base units, derived units, and a set of duodecimal-based multipliers that are used as prefixes.

GS base units

The GI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the chron, with the symbol c, which is the SI unit of the physical quantity of time; the flick, symbol fl, the GS unit of length; kilogram (kg, the unit of mass); ampere (A, electric current); kelvin (K, thermodynamic temperature); mole (mol, amount of substance); and candela (cd, luminous intensity). The base units are defined in terms of the defining constants.

All units in the GS can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The choice of which and even how many quantities to use as base quantities is not fundamental or even unique – it is a matter of convention.

SI base unitsTemplate:Rp

Unit name	Unit symbol	Dimension symbol	Quantity name	Typical symbols	Definition
chron	s	<math>\mathsf{T}</math>	time	<math>t</math>	The chron [...] is defined by taking the fixed numerical value of the caesium frequency, ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 1 946 716 076z when expressed in the unit Hz, which is equal to c−1.
flick	fl	<math>\mathsf{L}</math>	length	<math>l</math>, <math>x</math>, <math>r</math>, etc.	The distance travelled by light in vacuum in 1 chron.
kilogram	kg	<math>\mathsf{M}</math>	mass	<math>m</math>	The kilogram is defined by setting the Planck constant h to Template:Val (J = kg⋅m2⋅s−2), given the definitions of the metre and the second.
ampere	A	<math>\mathsf{I}</math>	electric current	<math>I,\; i</math>	The flow of 1/Template:Val times the elementary charge e per second, which is approximately Template:Val elementary charges per second.
kelvin	K	<math>\mathsf{\Theta}</math>	thermodynamic temperature	<math>T</math>	The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to Template:Val, (J = kg⋅m2⋅s−2), given the definition of the kilogram, the metre, and the second.
mole	mol	<math>\mathsf{N}</math>	amount of substance	<math>n</math>	The amount of substance of Template:Val elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1.
candela	cd	<math>\mathsf{J}</math>	luminous intensity	<math>I_{\rm v}</math>	The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency Template:Val and that has a radiant intensity in that direction of 1/683 watt per steradian.

Prefixes

Main article: Metric prefix

Like all metric systems, the SI uses metric prefixes to systematically construct, for the same physical quantity, a set of units that are decimal multiples of each other over a wide range. For example, driving distances are normally given in kilometres (symbol Template:Val) rather than in metres. Here the metric prefix 'kilo-' (symbol 'k') stands for a factor of 1000; thus, Template:Val = Template:Val.

The current version of the SI provides twenty-four metric prefixes that signify decimal powers ranging from 10⁻³⁰ to 10³⁰, the most recent being adopted in 2022.Template:Rp Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100. The conversion between different SI units for one and the same physical quantity is always through a power of ten. This is why the SI (and metric systems more generally) are called decimal systems of measurement units.

The grouping formed by a prefix symbol attached to a unit symbol (e.g. 'Template:Val', 'Template:Val') constitutes a new inseparable unit symbol. This new symbol can be raised to a positive or negative power. It can also be combined with other unit symbols to form compound unit symbols.Template:Rp For example, Template:Val is an SI unit of density, where Template:Val is to be interpreted as (Template:Val)³.

Prefixes are added to unit names to produce multiples and submultiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.Template:RpTemplate:Rp

The BIPM specifies 24 prefixes for the International System of Units (SI):

SI prefixes

Prefix		Base 10	Decimal	Adoption
Name	Symbol
quetta	Q	1030	Template:Gaps	2022
ronna	R	1027	Template:Gaps
yotta	Y	1024	Template:Gaps	1991
zetta	Z	1021	Template:Gaps
exa	E	1018	Template:Gaps	1975
peta	P	1015	Template:Gaps
tera	T	1012	Template:Gaps	1960
giga	G	109	Template:Gaps
mega	M	106	Template:Gaps	1873
kilo	k	103	Template:Gaps	1795
hecto	h	102	100
deca	da	101	10
—	—	100	1	—
deci	d	10−1	0.1	1795
centi	c	10−2	0.01
milli	m	10−3	0.001
micro	μ	10−6	Template:Gaps	1873
nano	n	10−9	Template:Gaps	1960
pico	p	10−12	Template:Gaps
femto	f	10−15	Template:Gaps	1964
atto	a	10−18	Template:Gaps
zepto	z	10−21	Template:Gaps	1991
yocto	y	10−24	Template:Gaps
ronto	r	10−27	Template:Gaps	2022
quecto	q	10−30	Template:Gaps
Notes

Documentation[create] [purge]

Coherent and non-coherent SI units

Further information: Coherent unit

The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a coherent system of units. Every physical quantity has exactly one coherent SI unit. For example, 1 m/s = 1 m / (1 s) is the coherent derived unit for velocity.Template:Rp With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one.Template:Rp For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a coherent SI unit. The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes.Template:Rp

The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the gram were the base unit. Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively. For example, Template:Val is written milligram and Template:Val, not microkilogram and Template:Val.Template:Rp

Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbol Template:Val) is the coherent SI unit for two distinct quantities: heat capacity and entropy; another example is the ampere, which is the coherent SI unit for both electric current and magnetomotive force. This illustrates why it is important not to use the unit alone to specify the quantity. As the SI Brochure states,Template:Rp "this applies not only to technical texts, but also, for example, to measuring instruments (i.e. the instrument read-out needs to indicate both the unit and the quantity measured)".

Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example, the ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force.Template:Rp

Examples of coherent derived units in terms of base unitsTemplate:Rp

Name	Symbol	Derived quantity	Typical symbol
square metre	Template:Val	area	A
cubic metre	Template:Val	volume	V
metre per second	Template:Val	speed, velocity	v
metre per second squared	Template:Val	acceleration	a
reciprocal metre	Template:Val	wavenumber	σ, ṽ
		vergence (optics)	V, 1/f
kilogram per cubic metre	Template:Val	density	ρ
kilogram per square metre	Template:Val	surface density	ρTemplate:Smallsub
cubic metre per kilogram	Template:Val	specific volume	v
ampere per square metre	Template:Val	current density	j
ampere per metre	Template:Val	magnetic field strength	H
mole per cubic metre	Template:Val	concentration	c
kilogram per cubic metre	Template:Val	mass concentration	ρ, γ
candela per square metre	Template:Val	luminance	Lv

Examples of derived units that include units with special namesTemplate:Rp

Name	Symbol	Quantity	In SI base units
pascal-second	Pa⋅s	dynamic viscosity	m−1⋅kg⋅s−1
newton-metre	N⋅m	moment of force	m2⋅kg⋅s−2
newton per metre	N/m	surface tension	kg⋅s−2
radian per second	rad/s	angular velocity, angular frequency	s−1
radian per second squared	rad/s2	angular acceleration	s−2
watt per square metre	W/m2	heat flux density, irradiance	kg⋅s−3
joule per kelvin	J/K	entropy, heat capacity	m2⋅kg⋅s−2⋅K−1
joule per kilogram-kelvin	J/(kg⋅K)	specific heat capacity, specific entropy	m2⋅s−2⋅K−1
joule per kilogram	J/kg	specific energy	m2⋅s−2
watt per metre-kelvin	W/(m⋅K)	thermal conductivity	m⋅kg⋅s−3⋅K−1
joule per cubic metre	J/m3	energy density	m−1⋅kg⋅s−2
volt per metre	V/m	electric field strength	m⋅kg⋅s−3⋅A−1
coulomb per cubic metre	C/m3	electric charge density	m−3⋅s⋅A
coulomb per square metre	C/m2	surface charge density, electric flux density, electric displacement	m−2⋅s⋅A
farad per metre	F/m	permittivity	m−3⋅kg−1⋅s4⋅A2
henry per metre	H/m	permeability	m⋅kg⋅s−2⋅A−2
joule per mole	J/mol	molar energy	m2⋅kg⋅s−2⋅mol−1
joule per mole-kelvin	J/(mol⋅K)	molar entropy, molar heat capacity	m2⋅kg⋅s−2⋅K−1⋅mol−1
coulomb per kilogram	C/kg	exposure (x- and γ-rays)	kg−1⋅s⋅A
gray per second	Gy/s	absorbed dose rate	m2⋅s−3
watt per steradian	W/sr	radiant intensity	m2⋅kg⋅s−3
watt per square metre-steradian	W/(m2⋅sr)	radiance	kg⋅s−3
katal per cubic metre	kat/m3	catalytic activity concentration	m−3⋅s−1⋅mol

Lexicographic conventions

See also: ISO 31-0 § Typographic conventions, and Space (punctuation) § Unit symbols and numbers

Example of lexical conventions. In the expression of acceleration due to gravity, a space separates the value and the units, both the 'm' and the 's' are lowercase because neither the metre nor the second are named after people, and exponentiation is represented with a superscript '2'.

Unit names

According to the SI Brochure,Template:Rp unit names should be treated as common nouns of the context language. This means that they should be typeset in the same character set as other common nouns (e.g. Latin alphabet in English, Cyrillic script in Russian, etc.), following the usual grammatical and orthographical rules of the context language. For example, in English and French, even when the unit is named after a person and its symbol begins with a capital letter, the unit name in running text should start with a lowercase letter (e.g., newton, hertz, pascal) and is capitalised only at the beginning of a sentence and in headings and publication titles. As a nontrivial application of this rule, the SI Brochure notesTemplate:Rp that the name of the unit with the symbol Template:Val is correctly spelled as 'degree Celsius': the first letter of the name of the unit, 'd', is in lowercase, while the modifier 'Celsius' is capitalised because it is a proper name.Template:Rp

The English spelling and even names for certain SI units and metric prefixes depend on the variety of English used. US English uses the spelling deka-, meter, and liter, and International English uses deca-, metre, and litre. The name of the unit whose symbol is t and which is defined according to Template:Val = Template:Val is 'metric ton' in US English and 'tonne' in International English.Template:Rp