SI Units

SI Units are the most widely used system of units. They are the most common system for everyday commerce in the world, and are almost universally used in the realm of science. The name derives from the French phrase, Système International d'Unités, or International System of Units. The system consists of a set of seven base units together with a set of prefixes from which all other units are derived.

In 1960, SI was selected as a specific subset of the existing Metre-Kilogram-Second systems of units (MKS), rather than the older Centimetre-Gram-Second system (CGS). Various new units were added with the introduction of the SI and at later times. SI is sometimes referred to as the metric system, especially in the United States, whose population has not widely adopted it, and in the United Kingdom, where conversion is only partial. SI is a specific canon of measurements derived and extended from the Metric system; however, not all metric units of measurement are accepted as SI units.

History

The metric system was officially adopted in France after the French Revolution. During the history of the metric system a number of variations have evolved and their use spread around the world replacing many traditional measurement systems.

By the end of World War II a number of different systems of measurement were still in use throughout the world. Some of these systems were metric system variations whilst others were based on the Imperial and American systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.

Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units recommended were the metre, kilogram, second, ampere, Kelvin degree (later renamed the kelvin), and the candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name: Le Système International d'Unités. The seventh base unit, the mole, was added in 1970 by the 14th CGPM.

The International System is now either obligatory or permissible throughout the world. It is administered by the standards organisation: the Bureau International des Poids et Mesures (International Bureau of Weights and Measures).

Base units

The following are the fundamental units from which all others are derived, they are dimensionally independent. The definitions stated below are widely accepted.

Name	Symbol	Measure	Definition
kilogram	kg	Mass	The unit of mass is equal to the mass of the international prototype kilogram (a platinum-iridium cylinder) kept at the Bureau International des Poids et Mesures (BIPM), Sèvres, Paris (1st CGPM (1889), CR 34-38). Note that the kilogram is the only base unit with a prefix; the gram is defined as a derived unit, equal to 1/1000 of a kilogram; prefixes such as mega are applied to the gram, not the kg; e.g. Gg, not Mkg. It is also the only unit still defined by a physical prototype instead of a measurable natural phenomenon (see the kilogram article for an alternate definition).
second	s	Time	The unit of time is the duration of exactly 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-133 atom at a temperature of 0 K (13th CGPM (1967-1968) Resolution 1, CR 103).
meter (or metre)	m	Length	The unit of length is equal to the length of the path travelled by light in a vacuum during the time interval of 1/299 792 458 of a second (17th CGPM (1983) Resolution 1, CR 97).
ampere	A	Electrical current	The unit of electrical current is the constant current which, if maintained in two straight parallel conductors, of infinite length and negligible cross-section, placed 1 meter apart in a vacuum, would produce a force between these conductors equal to 2×10 ⁻⁷ newtons per meter of length (9th CGPM (1948) Resolution 7, CR 70).
kelvin	K	Thermodynamic temperature	The unit of thermodynamic temperature (or absolute temperature) is the fraction 1/273.16 (exactly) of the thermodynamic temperature at the triple point of water (13th CGPM (1967) Resolution 4, CR 104).
mole	mol	Quantity of matter (mass/mass)	A mole is the quantity of substance that contains the same number of elementary entities (atoms, molecules, ions, electrons or particles, depending on the substance) as there are atoms in 0.012 kilograms of pure carbon-12 (14th CGPM (1971) Resolution 3, CR 78). This number (N_A) is approximately equal to 6.02214199×10²³.
candela	cd	Luminous intensity	The unit of luminous intensity is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian (16th CGPM (1979) Resolution 3, CR 100).

Length

The most important unit is that of length: one metre was originally defined to be equal to 1/10 000 000^th of the distance from the pole to the equator along the meridian through Paris. (Prior discussions had often suggested the length of a seconds pendulum in some standard gravity, which would have been only slightly shorter, and perhaps easier to determine.) This is approximately 10% longer than one yard. Later on, a platinum rod with a rigid, X-shaped cross section was produced to serve as the easy-to-check standard for one metre's length. Due to the difficulty of actually measuring the length of a meridian quadrant in the 18th century, the first platinum prototype was short by 0.2 millimetres. More recently, the metre was redefined as a certain multiple of a specific radiation wavelength, and currently it is defined as the distance travelled by light in a vacuum in a specific period of time. Attempts to relate an integer multiple of the metre to any meridian have been abandoned.

Mass

The original base unit of mass in the metric system was the gram, chosen to match the mass of one cubic centimetre of water. For practical reasons, the reference standard that was deposited at the Archives de la république on June 22, 1799 was a kilogram (a cylinder of platinum). One kilogram is about 2.2 pounds. In 1889, the first General Conference on Weights and Measures (CGPM) sanctioned a replacement prototype, a cylinder of a 90% platinum, 10% iridium alloy; this has served as the standard ever since, and is stored in a Paris vault. The kilogram became the base unit in 1901.

Also in 1901, a kilogram of distilled pure water at its densest (+3.98 degrees Celsius) under a standard atmosphere of pressure was used to define the litre, a more convenient unit than the very large cubic metre. Because this litre turned out to be different from the cubic decimetre by about 28 millionths, this definition was abandoned in 1964 in favour of the cubic decimetre.

The kilogram is the only base unit not to have been redefined in terms of an unchanging natural phenomenon. Such a definition, said to be in terms of an artefact (the cylinder in Paris), is particularly inconvenient, because, in principle, it can be used only by travelling to Paris and, with permission, comparing one's own candidate standard to the reference one. For this reason, as well as the effort required to protect the standard from absorption or dispersion of gases and vapours, at a meeting of the Royal Society in London on 15 February, 2005, scientists called for the mass of the standard kilogramme in Paris to be replaced by a standard based on "an invariable property of nature"; but no decision on redefinition can be taken before 2007.

Temperature

The unit of temperature became the centigrade or inverted Celsius grade, which means the mercury scale is divided into 100 equal-length parts between the water-ice mixture at 0 °C and the boiling point of pure, distilled water at 100 °C (under a standard atmosphere). This is the metric unit of temperature in everyday use. A hundred years later, the discovery of absolute zero prompted the establishment of a new temperature scale, the Kelvin Scale which relocates the zero point at absolute zero, with the difference between freezing and boiling water close to 100 K.

Time

The metric unit of time became the second, originally defined as 1/86 400^th of a mean solar day. The formal definition of the second has been changed several times as more accurate definitions became possible, based first on astronomic observations, then the tuning fork clock, quartz clock, and today the caesium atomic clock.

Cultural issues

The swift worldwide adoption of the metric system as a tool of economy and everyday commerce was based mainly on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardize the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our decimal numeral system.

Cultural differences can be represented in the local everyday uses of metric units. For example, bread is sold in one-half, one or two kilogram sizes in many countries, but you buy them by multiples of one hundred grams in the former USSR. In some countries, the informal cup measurement has become 250 mL, and prices for items are sometimes given per 100 g rather than per kilogram. A profound cultural difference between physicists and engineers, especially radio engineers, existed prior to the adoption of the MKS system and hence its descendent, SI. Engineers work with volts, amperes, ohms, farads, and coulombs, which are of great practical utility, while the CGS units, which are fine for theoretical physics can be inconvenient for electrical engineering usage and are largely unfamiliar to householders using appliances rated in volts and watts.

Non-scientific people should not be put off by the fine-tuning that has happened to the metric base units over the past 200 years, as experts have tried frequently to refine the metric system to fit the best scientific research (e.g. CGS to MKS to SI system changes or the invention of the Kelvin scale). These changes do not affect the everyday use of metric units. The presence of these adjustments has been one reason advocates of the U.S. customary units had used against metrication; these customary units, however, are nowadays defined in terms of SI units, thus any difference in the definition of the SI units results in a difference of the definition of the customary units.

SI writing style

Symbols are written in lower case, except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa" whereas the unit itself is written "pascal". The one exception is the litre, whose original abbreviation "l" is dangerously similar to "1". The NIST recommends that "L" be used instead, a usage which is common in the U.S., Canada and Australia, and has been accepted as an alternative by the CGPM. The cursive "ℓ" is occasionally seen, especially in Japan, but this is not currently recommended by any standards body. For more information, see Litre.
Symbols are written in singular form: i.e. "25 kg", not "25 kgs". Pluralization would be language dependent; "s" plurals (as in French and English) are particularly undesirable since "s" is the symbol of the second.
Symbols do not have an appended period (.).
It is preferable to write symbols in upright Roman type (m for metres, L for litres), so as to differentiate from the italic type used for mathematical variables (m for mass, l for length).
A space should separate the number and the symbol, e.g. "2.21 kg", "7.3×10² m²", "22 °C" [1]. Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
Spaces should be used to group decimal digits in threes, e.g. 1 000 000 or 342 142 (in contrast to the commas or dots used in other systems, e.g. 1,000,000 or 1.000.000).
The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". In practice, the full stop is used in English, and the comma in most other European languages.
Symbols for derived units formed from multiple units by multiplication are joined with a space or centre dot (·), e.g. N m or N·m.
Symbols formed by division of two units are joined with a solidus (/), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s^-1", "m·s^-1" or ${\frac {\mbox{m}}{\mbox{s}}}$ . A solidus should not be used if the result is ambiguous, i.e. "kg·m^-1·s^-2" is preferable to "kg/m/s²".

With a few exceptions (such as draught beer sales in the United Kingdom) the system is legally being used in every country in the world and many countries do not maintain definitions of other units. Those countries that still give recognition to non-SI units (e.g. the US and UK) have defined many of the modern units in terms of SI units; for example, the common yard is defined to be exactly 0.9144 metres. In the US, survey distances are also defined in terms of metric units, but differently: 1 survey yard = 3600/3937 m. They have, however, not been redefined due to the accumulation of error it would entail and the survey foot and survey mile remain as separate units. (This was not a problem for the United Kingdom, as the Ordnance Survey has been metric since before World War II.) (See weights and measures for a history of the development of units of measurement.)

Units

Dimensionless derived units

The following SI units are actually dimensionless ratios, formed by dividing two identical SI units. They are therefore considered by the BIPM to be derived. Formally, their SI unit is simply the number 1, but they are given these special names, for use whenever the lack of a unit might be confusing.

Name	Symbol	Quantity	Definition
radian	rad	Angle	The unit of angle is the angle subtended at the center of a circle by an arc of the circumference equal in length to the radius of the circle. There are $2\pi$ radians in a circle.
steradian	sr	Solid angle	The unit of solid angle is the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r². There are $4\pi$ steradians on a sphere.

Derived units with special names

Base units can be put together to derive units of measurement for other quantities. Some have been given names.

Name	Symbol	Quantity	Expression in terms of other units	Expression in terms of SI base units
hertz	Hz	Frequency	s⁻¹	s⁻¹
newton	N	Force, Weight	m·kg·s⁻²	m·kg·s⁻²
joule	J	Energy, Work, Heat	N•m	m²·kg·s⁻²
watt	W	Power, Radiant flux	J/s	m²·kg·s⁻³
pascal	Pa	Pressure, Stress	N/m²	m⁻¹·kg·s⁻²
lumen	lm	Luminous flux	cd·sr = m²·m⁻²·cd	cd
lux	lx	Illuminance	lm/m² = m²·m⁻⁴·cd	m⁻²·cd
coulomb	C	Electric charge or flux	s·A	s·A
volt	V	Electrical potential difference, Electromotive force	W/A = J/C	m²·kg·s⁻³·A⁻¹
ohm	Ω	Electric resistance, Impedance, Reactance	V/A	m²·kg·s⁻³·A⁻²
farad	F	Electric capacitance	C/V	m⁻²·kg⁻¹·s⁴·A²
weber	Wb	Magnetic flux	m²·kg·s⁻²·A⁻¹	m²·kg·s⁻²·A⁻¹
tesla	T	Magnetic flux density, Magnetic inductivity	V•s•m⁻² = Wb/m²	kg·s⁻²·A⁻¹
henry	H	Inductance	V•s•A⁻¹ = Wb/A	m²·kg·s⁻²·A⁻²
siemens	S	Electric conductance	Ω⁻¹	m⁻²·kg⁻¹ s³·A²
becquerel	Bq	Radioactivity (decays per unit time)	s⁻¹	s⁻¹
gray	Gy	Absorbed dose (of ionising radiation)	J/kg	m²·s⁻²
sievert	Sv	Equivalent dose (of ionising radiation)	J/kg	m²·s⁻²
katal	kat	Catalytic activity	mol/s	s⁻¹·mol
degree Celsius	°C	Thermodynamic temperature	t_°C = t_K - 273.15
molarity	M	Concentration (moles of substance per liter of solution)	mol/L	10^{3^{•m^{−3^•mol}}}
molality	m	Concentration (moles of substance per kilogram of solution)	mol/kg	kg^{−1^•mol}

Non-SI units accepted for use with SI

The following units are not SI units but are "accepted for use with the International System."

edit Non-SI units accepted for use with SI
Name	Symbol	Quantity	Equivalent SI unit
minute	min	time	1 min = 60 s
hour	h	time	1 h = 60 min = 3600 s
day	d	time	1 d = 24 h = 1440 min = 86400 s
degree of arc	°	angle	1° = (π/180) rad
minute of arc	′	angle	1′ = (1/60)° = (π/10800) rad
second of arc	″	angle	1″ = (1/60)′ = (1/3600)° = (π/648000) rad
liter	l or L	volume	1dm³ = 0.001 m³
tonne	t	mass	1 t = 10³ kg
Non-SI units not formally adopted by the CGPM
neper, field quantity	Np	ratio (dimensionless)	L_F = ln(F/F₀) Np
neper, power quantity	Np	ratio (dimensionless)	L_P = ½ ln(P/P₀) Np
bel, field quantity	B	ratio (dimensionless)	L_F = 2 log₁₀(F/F₀) B
bel, power quantity	B	ratio (dimensionless)	L_P = log₁₀(P/P₀) B
Non-SI units with values obtained only by experiment
electronvolt	eV	energy	1 eV = 1.60217733 (49) × 10⁻¹⁹ J
atomic mass unit	u	mass	1 u = 1.6605402 (10) × 10⁻²⁷ kg
astronomical unit	AU	length	1 AU = 1.49597870691 (30) × 10¹¹ m
Non-SI units whose use is not encouraged
nautical mile		length	1 nautical mile = 1852 m
knot		speed	1 knot = 1 nautical mile per hour = (1852/3600) m/s
are	a	area	1 a = 1 dam² = 100 m²
hectare	ha	area	1 ha = 100 a = 10000 m²
bar	bar	pressure	1 bar = 10⁵ Pa
ångström, angstrom	Å	length	1 Å = 0.1 nm = 10⁻¹⁰ m
barn	b	area	1 b = 10⁻²⁸ m²

SI prefixes

The following SI prefixes can be used to prefix any of the above units to produce a multiple or submultiple of the original unit. This includes the degree Celsius (e.g. "1.2 m°C"); however, to avoid confusion, prefixes are not used with the time-related unit symbols min (minute), h (hour), d (day). They are not recommended for use with the angle-related symbols ° (degree), ' (minute of arc), and " (second of arc) [2], but for astronomical usage, they are sometimes used with seconds of arc.

10ⁿ	Prefix	Symbol	Short scale*	Long scale**	Decimal equivalent
10²⁴	yotta	Y	Septillion	Quadrillion	1 000 000 000 000 000 000 000 000
10²¹	zeta	Z	Sextillion	Trilliard (thousand trillion)	1 000 000 000 000 000 000 000
10¹⁸	exa	E	Quintillion	Trillion	1 000 000 000 000 000 000
10¹⁵	peta	P	Quadrillion	Billiard (thousand billion)	1 000 000 000 000 000
10¹²	tera	T	Trillion	Billion	1 000 000 000 000
10⁹	giga	G	Billion	Milliard (thousand million)	1 000 000 000
10⁶	mega	M		Million	1 000 000
10³	kilo	k (K)		Thousand	1 000
10²	hector	h (H)		Hundred	100
10¹	deca, deka	da (D)		Ten	10
10⁰	none	none		One	1
10⁻¹	deci	d		Tenth	0.1
10⁻²	centi	c		Hundredth	0.01
10⁻³	milli	m		Thousandth	0.001
10⁻⁶	micro	µ (u)		Millionth	0.000 001
10⁻⁹	nano	n	Billionth	Milliardth	0.000 000 001
10⁻¹²	pico	p	Trillionth	Billionth	0.000 000 000 001
10⁻¹⁵	femto	f	Quadrillionth	Billiardth	0.000 000 000 000 001
10⁻¹⁸	atto	a	Quintillionth	Trillionth	0.000 000 000 000 000 001
10⁻²¹	zepto	z	Sextillionth	Trilliardth	0.000 000 000 000 000 000 001
10⁻²⁴	yocto	y	Septillionth	Quadrillionth	0.000 000 000 000 000 000 000 001

* Short scale is the English translation of the French term échelle courte, which designates a system of numeric names in which the word billion means a thousand millions.

** Long scale is the English translation of the French term échelle longue, which designates a system of numeric names in which the word billion means a million millions.

Obsolete metric prefixes

The following metric prefixes are no longer in use: myria-, myrio-, and any double prefixes such as those formerly used in micromicrofarads, hectokilometres, millimicrons.

See: Obsolete metric prefixes

Spelling variations

Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre'. This is in keeping with standard American English spelling (for example, Americans also use 'center' rather than 'centre,' using the latter only rarely for its stylistic implications; see also American and British English differences). In addition, the official US spelling for the SI prefix 'deca' is 'deka'.

The US government has approved these spellings for official use. In scientific contexts only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.

The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and use is declining.

External links

Official

BIPM (SI maintenance agency) (home page)
BIPM brochure (SI reference)
ISO 1000:1992 SI units and recommendations for the use of their multiples and of certain other units, with its price tag of 99 Swiss francs for a 22 page, coverless pamphlet showing why the public is sometimes a little slow to pick up on their recommendations.

Information

US NIST reference on SI
- chart
SI - Its history and use in science and industry
A Dictionary of Units of Measurement
Cyrillic transcription of SI symbols
Judson, Lewis B., Weights and Measures Standards of the United States: A brief history, NBS Special Publication 447, orig. iss. October 1963, updated March 1976 (46 page PDF file)
Metric system and conversion tables (courtesy French property advice)
metre-info - an encyclopaedia of all metric units

Pro-metric pressure groups

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