SI

For other uses, see SI (disambiguation).

The International System of Units, (symbol: SI) (for the French phrase Syst�me International d'Unit�s), is the most widely used system of units. It is used for everyday commerce in virtually every country of the world except the United States, and it is universally used in scientific work. SI was selected from the existing Metre-Kilogram-Second system of units (MKS), with the addition of extra units, rather than the older Centimetre-Gram-Second system of units (CGS). SI is sometimes referred to as the metric system (especially in the United States, which has not widely adopted it, although it has been used more commonly in recent years, and the UK, where conversion is incomplete). However, not all metric units of measurement are accepted as SI units.

There are seven base units and several derived units, together with a set of prefixes. Non-SI units can be converted to SI units (or vice versa) according to the conversion of units.

Origin

The units of the SI are decided by a series of international conferences organised by the standards organization Bureau International des Poids et Mesures (International Office of Weights and Measures). The SI was first given its name in 1960, and last added to in 1971.

The true origins of the SI or metric system date back to approximately 1640. It was invented by French scientists, and was given a huge boost in popularity by the French Revolution of 1789. The metric system tried to choose units which were non-arbitrary, merging well with the revolution's official ideology of "Pure Reason". The layout of the metric system may have been based on the idealistic world-view of ancient Greeks, who theorized that there were four basic elements: earth, water, fire and air.

The most important unit is that of length: one metre was intended to be equal to 1/10,000,000^thof the distance from the pole to the equator along the meridian through Paris. 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. However, due to a miscalculation by researchers of the flattening effect the earth's rotation had on its circumference, the first platinum prototype was short by 0.2 millimetres. Then a multiple of a specific radiation wavelength was introduced to abstractly define the (unchanged) length of the metre unit, and finally the metre was defined as the distance travelled by light in a vacuum in a specific period of time.

The unit of mass is the kilogram, which was defined by a cube filled with distilled pure water at its densest (+4° Celsius) and having sides equal to 1/10th of a metre. This volume contains one kilogram of water. One kilogram is about 10% heavier than two pounds (2 lb). The cubic space is also known as one litre so volume of different liquids can be compared. Later on, a platinum-iridium metal cylinder was manufactured to serve as the one kilogram weight standard and remained so ever since.

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 and the boiling point of pure, distilled water. Boiling water thus becomes one hundred degrees centigrade hot and freezing is zero degrees. This is the metric unit of temperature in everyday use. A hundred years later, scientists discovered there is an absolute minimum temperature and nothing can be colder than that. This prompted experts to relocate the zero place to mark this temperature, thus creating the Kelvin scale.

The metric unit of time remained the second. One definition of day is 86,400 seconds. The formal definition of the second has been changed several times for enhanced scientific requirements (astronomic observations, tuning fork clock, quartz clock and then caesium atomic clock) but wristwatch users remain relatively unaffected.

The swift worldwide adoption of the metric system as a tool of economy and everday 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 politics also factored into the choice as many countries made the industrial shift when Britain still had empire status, and had various feelings related to its position in the world. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our 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.

Non-scientific people should not be put off by the fine-tuning that has happened to the metric base units over the past two hundred years, as experts regularly tried to refine the metric system to fit the best scientific researcher (e.g. MKG to CGS to SI system changes or the invention of Kelvin scale). These changes seldom affect the everyday use of metric units. The presence of these adjustments has been one reason advocates of the U.S. customary units have used against metrication.

Basis

SI is built on seven SI base units, the kilogram, metre, second, ampere, kelvin, mole, and candela. These are used to define various SI derived units.

SI also defines a number of SI prefixes to be used with the units: these combine with any unit name to give subdivisions and multiples. For example, the prefix kilo denotes a multiple of a thousand, so the kilometre is 1 000 metres, the kilogram 1 000 grams, and so on. Note that a millionth of a kilogram is a milligram, not a microkilogram.

SI writing style

Symbols are written in lower case, except the symbols that are derived from the name of a person. This means that the symbol for the SI unit for pressure, named after Blaise Pascal, is Pa, whereas the unit itself is written pascal. The official SI brochure lists the symbol for the litre as an allowed exception to the capitalization rules: either capital or lowercase L is acceptable.
Symbols are written in singular, e.g. 25 kg (not "25 kgs").
It is preferable to keep the symbol in upright roman type (for example, m for metres, l for litres), so as to differentiate from mathematical and physical variables (for example, m for mass, l for length).
A space is left between the numbers and the symbols: 2.21 kg, 7.3·10² m²
SI uses spaces to separate decimal digits in sets of three. 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).
SI used only a comma as the separator for decimal fractions until 1997. The number "twenty four and fifty one hundredths" would be written as "24,51". In 1997 the CIPM decided that the British full stop (the "dot on the line", or period) would be the decimal separator in text whose main language is English ("24.51"); the comma remains the decimal separator in all other 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, e.g. m/s, m s^-1, m�s^-1 or <math>\frac{\mbox{m}}{\mbox{s}}<math>. A solidus should not be used if the result is ambiguous, e.g. kg�m^-1�s^-2, not "kg/m/s²".

The system can legally be used in every country in the world, and many countries do not maintain definitions of other units. Those countries that still give official recognition to non-SI units (e.g. the US and UK) have defined the modern in terms of SI units; for example, the common inch is defined to be exactly 0.0254 metres. Survey distances have, however, not been redefined due to the accumulation of error it would entail. It was adopted by the 11th General Conference on Weights and Measures (CGPM) in 1960. (See weights and measures for a history of the development of units of measurement.)

Units

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.

SI Base units Edit (http://www.mywiseowl.com/index.php?title=Template:SI_base_units&action=edit)
Name	Symbol	Quantity	Definition
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). This number is exact; the metre is defined this way.
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), S�vres, 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 1/1 000 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 (but 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).
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 metre apart in a vacuum, would produce a force between these conductors equal to 2×10 ⁻⁷ newton per metre 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	Amount of substance	The unit of amount of substance is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kilogram of pure carbon-12 (14th CGPM (1971) Resolution 3, CR 78). (Elementary entities may be atoms, molecules, ions, electrons, or particles.) It is approximately equal to 6.02214199×10²³ units.
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).

Dimensionless derived units

The following SI units are derived from the base units and are dimensionless.

SI Dimensionless derived units Edit (http://www.mywiseowl.com/index.php?title=Template:SI_dimensionless_units&action=edit)
Name	Symbol	Quantity	Definition
radian	rad	Angle	The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are <math>2\pi<math> radians in a circle.
steradian	sr	Solid angle	The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r². There are <math>4\pi<math> steradians in 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.

SI derived units with special names Edit (http://www.mywiseowl.com/index.php?title=Template:SI_special_units&action=edit)
Name	Symbol	Quantity	Expressed in base units
hertz	Hz	Frequency	s^-1
newton	N	Force	kg m s ^-2
joule	J	Energy	N m = kg m² s^-2
watt	W	Power	J/s = kg m² s^-3
pascal	Pa	Pressure	N/m² = kg m ^-1 s^-2
lumen	lm	Luminous flux	cd sr
lux	lx	Illuminance	cd sr m^-2
coulomb	C	Electric Charge	A s
volt	V	Electrical potential difference	J/C = kg m² A^-1 s^-3
ohm	Ω	Electric resistance	V/A = kg m² A^-2 s^-3
farad	F	Electric capacitance	Ω^-1 s = A² s⁴ kg^-1 m^-2
weber	Wb	Magnetic flux	kg m² s^-2 A^-1
tesla	T	Magnetic flux density	Wb/m² = kg s^-2 A^-1
henry	H	Inductance	Ω s = kg m² A^-2 s^-2
siemens	S	Electric conductance	Ω^-1 = kg^-1 m^-2 A² s³
degree Celsius	�C	Celsius temperature	K
becquerel	Bq	Radioactivity (decays per unit time)	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 = mol s^-1

Non-SI units accepted for use with SI

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

Non-SI units accepted for use with SI Edit (http://www.mywiseowl.com/index.php?title=Template:SI_acceptable_units&action=edit)
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
litre	l or L	volume	0.001 m³
tonne	t	mass	1 t = 10³ kg
neper	Np	Ratio (dimensionless)	1 Np = 1 (The Neper has not yet been formally adopted by the CGPM)
bel	B	Ratio (dimensionless)	1 B = (1/2) ln(10)
Experimental Non-SI units accepted for use with SI
electronvolt	eV	energy	1eV = 1.60217733 (49) &times 10^-19 J
atomic mass unit	u	mass	1u = 1.6605402 (10) &times 10^-27 kg
astronomical unit	au	length	1au = 1.49597870691 (30) &times 10¹¹ m
Other Non-SI units currently accepted for use with SI
nautical mile	nautical mile	length	1 nautical mile = 1852 m
knot	knot	speed	1 knot = 1 nautical mile per hour = (1852/3600) m/s
are	a	area	1a = 1dam² = 100 m²
hectare	ha	area	1ha = 100a = 10000 m²
bar	bar	pressure	1 bar = 10⁵Pa
Ångström	Å	length	1 Å = 0.1 nm = 10^-10 m
barn	b	area	1b = 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.

SI prefixes Edit (http://www.mywiseowl.com/index.php?title=Template:SI_prefixes&action=edit)
(Sub)multiple	Prefix	Symbol	Short scale Name	Long scale Name
10²⁴	yotta	Y	Septillion	Quadrillion
10²¹	zetta	Z	Sextillion	Thousand trillion (Trilliard)
10¹⁸	exa	E	Quintillion	Trillion
10¹⁵	peta	P	Quadrillion	Thousand billion (Billiard)
10¹²	tera	T	Trillion	Billion
10⁹	giga	G	Billion	Thousand million (Milliard)
10⁶	mega	M	Million
10³	kilo	k	Thousand
10²	hecto	h	Hundred
10¹	deca	da	Ten
10^-1	deci	d	Tenth
10^-2	centi	c	Hundredth
10^-3	milli	m	Thousandth
10^-6	micro	µ	Millionth
10^-9	nano	n	Billionth	Milliardth
10^-12	pico	p	Trillionth	Billionth
10^-15	femto	f	Quadrillionth	Billiardth
10^-18	atto	a	Quintillionth	Trillionth
10^-21	zepto	z	Sextillionth	Trilliardth
10^-24	yocto	y	Septillionth	Quadrillionth

Obsolete SI prefixes

The following SI prefixes are no longer in use.

Obsolete SI prefixes Template:Ed
(Sub)multiple	Prefix	Symbol	Short scale Name	Long scale Name
10⁴	myria	ma	Ten thousand, Myriad
10^-4	myrio	mo	Ten thousandth, Myriadth(?)

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'; see also American and British English differences). In addition, the official US spelling for the SI prefix 'deca' is 'deka' (again, a variation not recognized by the BIPM).

The US government has approved these spellings for official use, but the BIPM only recognizes the British English spellings as official names for the units. 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) (http://www.bipm.fr/en/si/) (home page)
BIPM reference (http://www.bipm.org/en/publications/brochure/) (SI reference)

Information

US NIST reference on SI (http://physics.nist.gov/cuu/Units/index.html)
SI - Its history and use in science and industry (http://www.aticourses.com/international_system_units.htm)
A Dictionary of Units of Measurement (http://www.unc.edu/~rowlett/units/)
Calculation of many metric and American and English units (http://www.sengpielaudio.com/Calculations03.htm)

SI