[[Image:SI Brochure Cover.jpg|frame|right|Cover of brochure ''[http://www.bipm.org/en/publications/brochure/ The International System of Units]'']]The '''International System of Units'''<ref>{{SIbrochure8th}}</ref> (abbreviated '''SI''' from {{lang-fr|Système international d'unités}}<ref>[http://www.bipm.org/en/CGPM/db/11/12/ Resolution of the International Bureau of Weights and Measures establishing the International System of Units]</ref>) is the modern form of the [[metric system]] and is generally a system of [[units of measurement]] devised around seven [[SI base unit|base units]] and the convenience of the number ten. The older metric system included several groups of units. The SI was established in 1960, based on the [[Mks system of units|metre-kilogram-second]] system, rather than the [[Centimetre–gram–second system of units|centimetre-gram-second]] system, which, in turn, had a few variants. The SI is declared as an evolving system, thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves.
SI is the world's most widely used [[Systems of measurement|system of measurement]], which is used both in everyday [[commerce]] and in [[science]].<ref>[http://www.bipm.org/en/si/base_units/ Official BIPM definitions]</ref><ref>[http://www.physics.nist.gov/cuu/Units/introduction.html Essentials of the SI: Introduction]</ref><!--English units are still used in some scientific applications, but note also that parsecs in astronomy, calories and mmHg in the medical sciences, and electron volts in physics are not part of the specific system of units known as SI, to just scratch the surface--><ref>An extensive presentation of the SI units is maintained on line by [http://www.physics.nist.gov/cuu/Units/units.html NIST], including a [http://www.physics.nist.gov/cuu/Units/SIdiagram.html diagram] of the interrelations between the derived units based upon the SI units. Definitions of the basic units can be found on this site, as well as the [http://physics.nist.gov/cuu/Constants/codata.pdf CODATA report] listing values for special constants such as the [[electric constant]], the [[magnetic constant]] and the [[speed of light]], all of which have defined values as a result of the definition of the metre and ampere.
A [[SI prefix|prefix]] may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten, and beyond a hundred(th) all are integer powers of a thousand. For example, ''kilo-'' denotes a multiple of a thousand and ''milli-'' denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, and multiples of the kilogram are named as if the gram was the base unit. Thus a millionth of a metre is a ''micrometre'', not a millimillimetre, and a millionth of a kilogram is a ''milligram'', not a microkilogram.
{{SI-Prefixes}}
In addition to the SI units, there is also a set of [[non-SI units accepted for use with SI]], which includes some commonly used non-coherent units such as the [[litre]].
==Writing unit symbols and the values of quantities {{anchor|SI_writing_style}}==
* The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., "2.21 kg", "{{val|7.3|e=2|u=m<sup>2</sup>}}", "22 K". This rule explicitly includes the percent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.<ref name='BIPM style'>{{Cite book |url= http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |title= The International System of Units (SI) |publisher= International Bureau of Weights and Measures (BIPM) |pages=134–135 |year=2006 |edition=8}}<!-- alternative URL: http://www.bipm.org/en/si/si_brochure/chapter5/5-3-7.html --></ref><ref name='nist style'>{{Cite web|url=http://physics.nist.gov/Pubs/SP811/sec07.html |title=NIST Guide to SI Units — Rules and Style Conventions |accessdate=29 December 2009|last1=Thompson|first1=A.|date=July 2008 |last2=Taylor |first2=B. N. |publisher=National Institute of Standards and Technology }}</ref>
* Symbols for derived units formed by multiplication are joined with a [[interpunct|centre dot]] (·) or a non-break space; e.g., N·m or N m.
* Symbols for derived units formed by division are joined with a [[solidus (punctuation)|solidus]] (/), or given as a negative [[exponent]]. E.g., the "metre per second" can be written m/s, m s<sup>−1</sup>, m·s<sup>−1</sup>, or <math>\textstyle\frac{\mathrm{m}}{\mathrm{s}}</math>. Only one solidus should be used; e.g., kg/(m·s<sup>2</sup>) and kg·m<sup>−1</sup>·s<sup>−2</sup> are acceptable, but kg/m/s<sup>2</sup> is ambiguous and unacceptable.
* Symbols are mathematical entities, not abbreviations, and do not have an appended period/full stop (.).
* Symbols are written in upright ([[Roman type|Roman]]) type (m for metres, s for seconds), so as to differentiate from the [[italic type]] used for quantities (''m'' for mass, ''s'' for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.<ref name=BIPM2006Ch5>{{Cite book |url= http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |title= The International System of Units (SI) |publisher= International Bureau of Weights and Measures (BIPM) |chapter=Chapter 5. Writing unit symbols and names, and expressing the values of quantities |year=2006 |edition=8}}</ref>
* Symbols for units are written in [[lower case]] (e.g., "m", "s", "mol"), 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 [[units of measurement|unit]] itself is written "[[pascal (unit)|pascal]]".<ref>Ambler Thompson and Barry N. Taylor, (2008), [http://physics.nist.gov/cuu/pdf/sp811.pdf ''Guide for the Use of the International System of Units (SI)''], (Special publication 811), Gaithersburg, MD: [[National Institute of Standards and Technology]], section 6.1.2</ref>
** The one exception is the [[litre]], whose original symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many [[List of countries where English is an official language|English-speaking countries]]. The American [[National Institute of Standards and Technology]] recommends that "L" be used instead, a usage common in the US, Canada, and Australia (but not elsewhere). This has been accepted as an alternative by the [[General Conference on Weights and Measures|CGPM]] since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any [[Standards organization|standards body]].<!--there are lots of standards organisations and I'm pretty sure at least some of them did recommend this in the past; I think South Africa was also big on this--> For more information, see [[litre]]. The litre is not an SI unit per se and is expressed in SI terms as a cubic decimeter, i.e., dm<sup>3</sup>.
* A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km", "M" in "MPa", "G" in "GHz"). Compound prefixes are not allowed.
* All symbols of prefixes larger than 10<sup>3</sup> (kilo) are uppercase.<ref>Ambler Thompson and Barry N. Taylor, (2008), [http://physics.nist.gov/cuu/pdf/sp811.pdf ''Guide for the Use of the International System of Units (SI)''], (Special publication 811), Gaithersburg, MD: [[National Institute of Standards and Technology]], section 4.3.</ref>
* Symbols of units are not pluralised; e.g., "25 kg", not "25 kgs".<ref name="BIPM2006Ch5" />
* The 10th resolution of [[CGPM]] in 2003 declared that "the symbol for the [[Decimal separator|decimal marker]] shall be either the [[full stop|point]] on the line or the [[comma]] on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most continental [[Languages of Europe|European languages]].
* Spaces may be used as a [[thousands separator]] (''{{gaps|1|000|000}}'') in contrast to commas or periods (''1,000,000'' or ''1.000.000'') in order to reduce confusion resulting from the variation between these forms in different countries. [[Space (punctuation)|In print]], the space used for this purpose is typically narrower than that between words (commonly a [[Space (punctuation)#Table of spaces|''thin space'']]).
* Any line-break inside a number, inside a compound unit, or between number and unit should be avoided, but, if necessary, the last-named option should be used.
* In [[Chinese language|Chinese]], [[Japanese language|Japanese]], and [[Korean language]] computing ([[CJK characters|CJK]]), some of the commonly used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its [http://www.unicode.org/charts/PDF/U3300.pdf CJK Compatibility] and [http://www.unicode.org/charts/PDF/U2100.pdf Letterlike Symbols] subranges for back compatibility, without necessarily recommending future usage.
* When writing dimensionless quantities, the terms 'ppb' (parts per [[Billion (word)|billion]]) and 'ppt' (parts per [[long and short scales|trillion]]) are recognised as language-dependent terms, since the value of billion and trillion can [[Long and short scales|vary from language to language]]. SI, therefore, recommends avoiding these terms.<ref name='BIPM style'/> However, no alternative is suggested by the [[International Bureau of Weights and Measures]] (BIPM).
==Writing the unit names==
* Names of [[units of measurement|units]] follow the grammatical rules associated with [[common noun]]s - in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to 'degrees Celsius', since 'degree' is the unit. In German however, names of units, in common with all nouns, start with a capital letter.<ref>{{cite book
|title = Wörterbuch Englisch Dictionary German
|publisher = Eurobuch/Eurobooks
|year = 1988
|location = [[Limassol]]}}</ref>
* Names of units are pluralised using the normal [[English grammar]] rules;<ref name=Taylor>{{Cite journal|author=Ambler Thompson & Barry N. Taylor|year=2008|url=http://physics.nist.gov/cuu/pdf/sp811.pdf|title=NIST Special Publication 811: Guide for the Use of the International System of Units (SI)|publisher=National Institute of Standards and Technology|accessdate=18 June 2008}}</ref><ref>{{Cite journal |date=9 May 2008 |url=http://edocket.access.gpo.gov/2008/pdf/E8-11058.pdf |title=Interpretation of the International System of Units (the Metric System of Measurement) for the United States |publisher=National Archives and Records Administration |journal=Federal Register |volume=73 |issue=96 |pages=28432–3 |id=FR Doc number E8-11058 |accessdate=28 October 2009}}</ref> e.g., "henries" is the plural of "[[Henry (unit)|henry]]".<ref name=Taylor/>{{rp|31}} The units [[lux]], [[hertz]], and [[Siemens (unit)|siemens]] are exceptions from this rule: they remain the same in singular and plural form. Note that this rule applies only to the full names of units, not to their symbols.
* The official US spellings for ''deca'', ''metre'', and ''litre'' are ''deka'', ''meter'', and ''liter'', respectively.<ref name='deka'>{{Cite web|url=http://physics.nist.gov/Pubs/SP330/sp330.pdf |title=The International System of Units | pages=iii |accessdate=27 May 2008 }}</ref>
==Realisation of units==
Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of how the definitions of some important units are realised in practice is given on the BIPM website.<ref>[http://www.bipm.org/en/si/si_brochure/appendix2/ SI ''Practical Realization'' brochure]</ref> However, "any method consistent with the laws of physics could be used to realise any SI unit."<ref>{{SIbrochure8th|page=111}}</ref> (p. 111).
==Related systems==
The definitions of the terms 'quantity', 'unit', 'dimension' etc. used in measurement, are given in the [[International vocabulary of metrology|International Vocabulary of Metrology]].<ref>{{Cite web|url=http://www.bipm.org/en/publications/guides/vim.html|title=The International Vocabulary of Metrology (VIM)}}</ref>
The quantities and equations that define the SI units are now referred to as the ''International System of Quantities'' (ISQ), and are set out in the ISO/IEC 80000 [[ISO/IEC 80000|''Quantities and Units'']].
==Conversion factors==
The relationship between the units used in different systems is determined by convention or from the basic definition of the units. Conversion of units from one system to another is accomplished by use of a [[Conversion of units|conversion factor]]. There are several compilations of conversion factors; see, for example, Appendix B of NIST SP 811.<ref name=Taylor/>
==Cultural issues==
[[Image:Non-Metric User.svg|thumb|right|upright=1.5|Three nations have not officially adopted the International System of Units as their primary or sole system of measurement: [[Burmese units of measurement|Myanmar (Burma)]], [[Liberia#Weights_and_measures|Liberia]], and the [[United States customary units|United States]]]]
The near-worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardise the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. For use in science, the SI prefixes simplify dealing with very large and small quantities.
Many units in everyday and scientific use are not SI units. In some cases these units have been designated by the BIPM as "non-SI units accepted for use with the SI".
<ref>[http://www.bipm.org/en/si/si_brochure/chapter4/table6.html BIPM - Table 6<!-- Bot generated title -->]</ref>
<ref>[http://www.bipm.org/en/si/si_brochure/chapter4/table8.html BIPM - Table 8<!-- Bot generated title -->]</ref> Some examples include:
* The units of time ([[minute]], min; [[hour]], h; [[day]], d<!--- the only three in table 6 --->) in use besides the SI second, are specifically accepted for use according to table 6.<ref>[http://www.bipm.org/en/si/si_brochure/chapter4/table6.html BIPM - Table 6<!-- Bot generated title -->]</ref>
* The year is specifically not included but has a recommended conversion factor.<ref>[http://physics.nist.gov/Pubs/SP811/appenB9.html#TIME NIST Guide to SI Units - Appendix B9. Conversion Factors<!-- Bot generated title -->]</ref>
* The [[Celsius]] temperature scale; kelvins are rarely employed in everyday use.
* [[Electrical energy|Electric energy]] is often billed in [[watt-hour|kilowatt-hours]], instead of megajoules. Similarly, battery charge is often measured as milliampere-hours (mA·h), instead of [[coulomb]]s.
* The [[nautical mile]] and [[knot (unit)|knot]] (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 International nautical mile = {{gaps|1|852}} m or approximately 1 minute of latitude). In addition to these, Annex 5 of the [[Convention on International Civil Aviation]] permits the "temporary use" of the [[foot (length)|foot]] for [[altitude]].
* [[Astronomical distance]]s measured in [[astronomical unit]]s, [[parsec]]s, and [[light-year]]s instead of, for example, petametres (a light-year is about 9.461 Pm or about {{gaps|9|461|000|000|000|000}} m).
* Atomic scale units used in physics and chemistry, such as the [[ångström]], [[electron volt]], [[atomic mass unit]] and [[barn (unit)|barn]].
* Some [[physicist]]s prefer the [[centimetre gram second system of units|centimetre-gram-second]] (CGS) units, or systems based on [[physical constant]]s, such as [[Planck units]], [[atomic units]], or [[Geometrized unit system|geometric units]].<!-- these are natural units which are not similar to cgs units -->
* In some countries, the informal [[cup (unit)|cup]] measurement has become 250 mL. Likewise, a 500 g [[Pound (mass)#Metric pounds|metric pound]] is used in many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (for example, [[pint]]s for beer and cider in glasses in the UK —although ''pint'' means 568 mL; [[Wine bottle#Sizes|Jeroboams]] for champagne in France).
* A [[Mile#Other miles|metric mile]] of 10 km is used in Norway and Sweden. The term metric mile is also used in some countries for the 1500 m foot race.
* In the US, [[Blood sugar|blood glucose]] measurements are recorded in milligrams per decilitre (mg/dL), which normalises to cg/L. In Canada, Australia, New Zealand, Oceania, and Europe the standard is millimole per litre (mmol/L) or mM (millimolar).
* [[Blood pressure]] is usually measured in [[mmHg]](≈[[Torr]]).
* [[Atmospheric pressure]] in government weather reports is measured in [[inHg]] in the USA,<ref>[http://weather.noaa.gov/weather/current/KDEN.html Current Weather Conditions: DENVER INTERNATIONAL AIRPORT]</ref> and in the SI unit hPa in Australia,<ref>[http://www.bom.gov.au/australia/charts/synoptic_col.shtml Australia Mean Sea Level Pressure Analysis]</ref> UK<ref>[http://www.metoffice.gov.uk/weather/uk/guide/key.html#units Met Office Weather Units]</ref> and most other countries.
The fine-tuning that has happened to the metric base-unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the [[US customary units]], are defined in SI units,<ref>Mendenhall, T. C. (1893). "Fundamental Standards of Length and Mass". Reprinted in Barbrow, Louis E. and Judson, Lewis V. (1976). ''Weights and measures standards of the United States: A brief history (NBS Special Publication 447).'' Washington D.C.: Superintendent of Documents. Viewed 23 August 2006 at [http://physics.nist.gov/Pubs/SP447/ http://physics.nist.gov/Pubs/SP447/] pp. 28–29.
</ref> any change in the definition of the SI units results in a change of the definition of the older units, as well.
===International trade===
One of the European Union's (EU) objectives is the creation of a single market for trade. To achieve this objective, the EU standardised on using SI as the legal units of measure. As of 2009, it has issued two [[Unit of measurement|units of measurement]] [[Directive (European Union)|directives]], which catalogued the units of measure that might be used for, amongst other things, trade: the first was [[European units of measurement directives|Directive 71/354/EEC]]<ref>{{Cite web| url = http://eur-lex.europa.eu/Notice.do?mode=dbl&lang=en&lng1=en,nl&lng2=da,de,el,en,es,fr,it,nl,pt,&val=22924:cs&page=1&hwords= | title=Council Directive of 18 October 1971 on the approximation of laws of the member states relating to units of measurement, (71/354/EEC) | accessdate=7 February 2009}}</ref> issued in 1971, which required member states to standardise on SI rather than use the variety of [[Centimetre gram second system of units|cgs]] and [[Mks system of units|mks]] units then in use. The second was [[European units of measurement directives|Directive 80/181/EEC]]<ref>{{Cite web| url = http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:19791221:EN:PDF | author = The Council of the European Communities | title = Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC | date=21 December 1979 | accessdate=7 February 2009}}</ref><ref>{{Cite web| url = http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:19841220:EN:PDF | author = The Council of the European Communities | title = Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC | date=20 December 1984 | accessdate=7 February 2009}}</ref><ref>{{Cite web| url = http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:19891130:EN:PDF | author = The Council of the European Communities | title = Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC | date=30 November 1989 | accessdate=7 February 2009}}</ref><ref>{{Cite web| url = http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:20000209:EN:PDF | author = The Council of the European Communities | title = Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC | date=9 February 2000 | accessdate=7 February 2009}}</ref><ref>{{Cite web| url = http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:20090527:EN:PDF| author = The Council of the European Communities | title = Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC | date=27 May 2009 | accessdate=14 September 2009}}</ref> issued in 1979, which replaced the first and gave the United Kingdom and the Republic of Ireland a number of [[derogation]]s from the original directive.
The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty, or were in universal use in worldwide trade. They also permitted the use of ''supplementary indicators'' alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, ''supplementary indicators'' have been allowed indefinitely.
[[Category:UBIK]]