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| − | [[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'''(abbreviated '''SI''') is the modern form of the metric system, according to a resolution of the International Bureau of Weights and Measures. It is generally a system of units of measurement devised around seven SI 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 metre-kilogram-second system, rather than the Centimetre–gram–second system of units 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. |
| − | 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. | + | |
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| − | 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. | + | SI is the world's most widely used system of measurement, which is used both in everyday commerce and in science.Definitions of the basic units can be found at the sites bottom, 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. |
| − | <blockquote>In the International System of Units (SI) (BIPM, 2006), the definition of the metre fixes the speed of light in vacuum ''c''<sub>0</sub>, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) ''μ''<sub>0</sub>, and the definition of the mole fixes the molar mass of the carbon 12 atom ''M''(<sup>12</sup>C) to have the exact values given in the table [Table 1, p.7]. Since the electric constant (also called the permittivity of vacuum) is related to ''μ''<sub>0</sub> by ''ε''<sub>0</sub> = 1/''μ''<sub>0</sub>''c''<sub>0</sub><sup>2</sup>, it too is known exactly.</blockquote> – CODATA report</ref> The system has been nearly [[Metrication|globally adopted]] with the United States being the only industrialized nation that does not mainly use the metric system in its commercial and standards activities.<ref>{{cite web
| + | In the International System of Units, the definition of the metre fixes the speed of light in vacuum ''c''<sub>0</sub>, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) ''μ''<sub>0</sub>, and the definition of the mole fixes the molar mass of the carbon 12 atom ''M''(<sup>12</sup>C) to have the exact values given in the bottom table. Since the electric constant is related to ''μ''<sub>0</sub> by ''ε''<sub>0</sub> = 1/''μ''<sub>0</sub>''c''<sub>0</sub><sup>2</sup>, it too is known exactly. |
| − | |url = http://en.wikipedia.org/w/index.php?title=International_System_of_Units&action=edit
| + | |
| − | |title = Appendix G : Weights and Measures
| + | |
| − | |work = [[The World Factbook]]
| + | |
| − | |publisher = [[Central Intelligence Agency]]
| + | |
| − | |accessdate =3 September 2011}}</ref> The United Kingdom has officially [[Metrication in the United Kingdom|partially adopted metrication]], with no intention of replacing [[imperial units]] entirely. [[Metrication in Canada|Canada]] has adopted it for many purposes but [[Imperial units|imperial]]/[[United States customary units|US]] units are still legally permitted and remain in common use throughout many sectors of Canadian society, particularly in the retail food, buildings trades, and railways sectors.<ref>''[http://laws-lois.justice.gc.ca/eng/acts/W-6/page-14.html/ Weights and Measures Act]''</ref><ref>''[http://laws-lois.justice.gc.ca/eng/acts/W-6/page-2.html#h-4/ Weights and Measures Act], accessed January 2012, Act current to 18 January 2012. Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefor are as added pursuant to subparagraph 6(1)(b)(ii).</ref>
| + | |
| | | | |
| | ==History== | | ==History== |
| − | {{main|History of the metric system}}
| + | The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty that established three international organizations to oversee the keeping of metric standards: |
| − | The [[metric system]] was conceived by a group of scientists (among them, [[Antoine Lavoisier|Antoine-Laurent Lavoisier]], who is known as the "father of modern chemistry") who had been commissioned by the ''[[Assemblee Nationale|Assemblée nationale]]'' and [[Louis XVI]] of France to create a unified and rational system of measures.<ref>{{Cite web|url=http://www1.bipm.org/en/si/history-si/name_kg.html|title=The name "kilogram"|accessdate=25 July 2006}}</ref> On 1 August 1793, the National Convention adopted the new decimal ''[[metre]]'' with a provisional length as well as the other decimal units with preliminary definitions and terms. On 7 April 1795 (''Loi du 18 germinal, an III'') the terms ''[[gram]]me'' and ''[[kilogram]]me'' replaced the former terms ''gravet'' (correctly ''milligrave'') and ''[[grave (unit)|grave]]'' and on 22 June 1799, after [[Pierre Méchain]] and [[Jean-Baptiste Delambre]] completed their survey, the definitive standard metre was deposited in the French National Archives. On 10 December 1799 (a month after [[coup of 18 Brumaire|Napoleon's coup d'état]]), the metric system was definitively adopted in France.
| + | * General Conference on Weights and Measures – a meeting every four to six years of delegates from all member states; |
| | + | * International Bureau of Weights and Measures - an international metrology centre in France; and |
| | + | * International Committee for Weights and Measures —an administrative committee that meets annually at the BIPM. |
| | | | |
| − | The desire for international cooperation on [[metrology]] led to the signing in 1875 of the [[Metre Convention]], a treaty that established three international organizations to oversee the keeping of metric standards: | + | The history of the metric system has seen a number of variations, and has spread around the world, to replace many traditional measurement systems. At 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, whereas others were based on customary 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, in 1948, asked the International Committee for Weights and Measures to conduct an international study of the measurement needs of the scientific, technical, and educational communities. |
| − | * [[General Conference on Weights and Measures]] (''Conférence générale des poids et mesures'' or CGPM) – a meeting every four to six years of delegates from all member states;
| + | |
| − | * [[International Bureau of Weights and Measures]] (''Bureau international des poids et mesures'' or BIPM) – an international metrology centre at [[Sèvres]] in France; and
| + | |
| − | * [[International Committee for Weights and Measures]] (''Comité international des poids et mesures'' or CIPM)—an administrative committee that meets annually at the BIPM.
| + | |
| | | | |
| − | The [[Metric system#History|history of the metric system]] has seen a number of variations, and has spread around the world, to replace many traditional [[Systems of measurement|measurement systems]]. At 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, whereas others were based on customary systems. It was recognised that additional steps were needed to [[metrication|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 that were <!--"that were" expresses the preterit, and the following predicate "are" connotes the non-changing entity no matter where in time of the complements "metre," "kilogram," "second," "ampere," "kelvin," "candela"-->recommended are the metre, kilogram, second, ampere, degree Kelvin (later renamed kelvin), and candela. In 1960, the 11th CGPM named the system the ''International System of Units. The seventh base unit, the mole mole, was added in 1971 by the 14th CGPM. |
| | | | |
| − | 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 [[SI electromagnetism units|electromagnetic]] quantities. The six base units that were <!--"that were" expresses the preterit, and the following predicate "are" connotes the non-changing entity no matter where in time of the complements "metre," "kilogram," "second," "ampere," "kelvin," "candela"-->recommended are the [[metre]], [[kilogram]], [[second]], [[ampere]], degree Kelvin (later renamed [[kelvin]]), and [[candela]]. In 1960, the 11th CGPM named the system the ''International System of Units'', abbreviated SI from the French name, {{lang|fr|''Le Système international d'unités''}}. The seventh base unit, the [[mole (unit)|mole]], was added in 1971 by the 14th CGPM.
| + | One of the CIPM committees, the CCU, has proposed a number of changes to the definitions of the base units used in SI. |
| − | | + | |
| − | One of the CIPM committees, the CCU, has proposed a number of [[new SI definitions|changes]] to the definitions of the base units used in SI.<ref name="draft">{{cite web | + | |
| − | |url = http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf
| + | |
| − | |title = Draft Chapter 2 for SI Brochure, following redefinitions of the base units
| + | |
| − | |author = Ian Mills
| + | |
| − | |publisher = CCU
| + | |
| − | |date = 29 September 2010
| + | |
| − | |accessdate =1 January 2011}}</ref> The CIPM meeting of October 2010 found that the proposal was not complete,<ref>{{cite web
| + | |
| − | |url = http://www.bipm.org/utils/en/pdf/BIPM_Bulletin.pdf
| + | |
| − | |title = BIPM Bulletin
| + | |
| − | |author = Anon
| + | |
| − | |publisher = BIPM
| + | |
| − | |date = November 2010
| + | |
| − | |accessdate =5 January 2011}}</ref> and it is expected that the CGPM will consider the full proposal in 2015.
| + | |
| | | | |
| | ==Units and prefixes== | | ==Units and prefixes== |
| − | {{Main|SI base unit|SI derived unit|SI prefix}}
| + | The International System of Units consists of a set of units together with a set of SI. The units are divided into two classes—'''base units''' and '''derived units'''. There are seven SI, each representing, by convention, different kinds of physical quantities. |
| − | The International System of Units consists of a set of units together with a set of [[SI prefix|prefixes]]. The units are divided into two classes—'''base units''' and '''derived units'''. There are seven [[SI base unit|base units]], each representing, by convention, [[Dimensional analysis|different kinds of physical quantities]]. | + | |
| | | | |
| | {| class="wikitable" style="margin:1em auto 1em auto" | | {| class="wikitable" style="margin:1em auto 1em auto" |
| − | |+ SI base units<ref name=sp330>{{Cite book|author=Barry N. Taylor & Ambler Thompson Ed. |title= The International System of Units (SI) |url=http://physics.nist.gov/Pubs/SP330/sp330.pdf |accessdate=18 June 2008|publisher=National Institute of Standards and Technology|location= Gaithersburg, MD|pages=23|year= 2008}}</ref><ref>[http://old.iupac.org/publications/books/author/mills.html Quantities Units and Symbols in Physical Chemistry], IUPAC</ref> | + | |+ SI base units |
| | |- | | |- |
| | !Unit name | | !Unit name |
| Line 48: |
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| | !Quantity name | | !Quantity name |
| | !Quantity symbol | | !Quantity symbol |
| − | ![[Dimensional analysis|Dimension symbol]] | + | !Dimension symbol |
| | |- | | |- |
| − | ![[metre]] | + | !metre |
| | |m | | |m |
| − | |[[length]] | + | |length |
| | |''l'' (a lowercase L), ''x'', ''r'' | | |''l'' (a lowercase L), ''x'', ''r'' |
| | |L | | |L |
| | |- | | |- |
| − | ![[kilogram]] <ref group=note>Despite the prefix "kilo-", the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units.</ref> | + | !kilogram |
| | |kg | | |kg |
| − | |[[mass]] | + | |mass |
| | |''m'' | | |''m'' |
| | |M | | |M |
| | |- | | |- |
| − | ![[second]] | + | !second |
| | |s | | |s |
| − | |[[time]] | + | |time |
| | |''t'' | | |''t'' |
| | |T | | |T |
| | |- | | |- |
| − | ![[ampere]] | + | !ampere |
| | |A | | |A |
| − | |[[electric current]] | + | |electric current |
| | |''I'' (an uppercase i) | | |''I'' (an uppercase i) |
| | |I | | |I |
| | |- | | |- |
| − | ![[kelvin]] | + | !kelvin |
| | |K | | |K |
| − | |[[thermodynamic temperature]] | + | |thermodynamic temperature |
| | |''T'' | | |''T'' |
| | |Θ | | |Θ |
| | |- | | |- |
| − | ![[candela]] | + | !candela |
| | |cd | | |cd |
| − | |[[luminous intensity]] | + | |luminous intensity |
| | |''I''<sub>v</sub> (an uppercase i with lowercase non-italicized v subscript) | | |''I''<sub>v</sub> (an uppercase i with lowercase non-italicized v subscript) |
| | |J | | |J |
| | |- | | |- |
| − | ![[Mole (unit)|mole]] | + | !Mole |
| | |mol | | |mol |
| − | |[[amount of substance]] | + | |amount of substance |
| | |''n'' | | |''n'' |
| | |N | | |N |
| | |- | | |- |
| | |colspan=5| | | |colspan=5| |
| − | ;Note
| |
| − | {{reflist|group=note}}
| |
| | |} | | |} |
| | | | |
| − | [[SI derived unit|Derived units]] are formed from multiplication and division of the seven base units and other derived units<ref name=SI>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]], p. 3.</ref> and are unlimited in number;<ref>{{SIBrochure8th|page=103}}</ref> for example, the SI derived unit of speed is metre per second, m/s. Some derived units have special names; for example, the unit of resistance, the ohm, symbol Ω, is uniquely defined by the relation Ω = m<sup>2</sup>·kg·s<sup>−3</sup>·A<sup>−2</sup>, which follows from the definition of the quantity [[electrical resistance]]. The [[radian]] and [[steradian]], once given special status, are now considered dimensionless derived units.<ref name=SI/>
| + | 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. |
| − | | + | |
| − | 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==
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| − | 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).
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| − | ==Related systems==
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| − | 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>
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| − | 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'']].
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| − | ==Conversion factors==
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| − | 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/>
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| − | ==Cultural issues==
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| − | [[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]]]]
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| − | 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.
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| − | 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".
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| − | <ref>[http://www.bipm.org/en/si/si_brochure/chapter4/table6.html BIPM - Table 6<!-- Bot generated title -->]</ref>
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| − | <ref>[http://www.bipm.org/en/si/si_brochure/chapter4/table8.html BIPM - Table 8<!-- Bot generated title -->]</ref> Some examples include:
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| − | * 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>
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| − | * 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>
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| − | * The [[Celsius]] temperature scale; kelvins are rarely employed in everyday use.
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| − | * [[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.
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| − | * 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]].
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| − | * [[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).
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| − | * Atomic scale units used in physics and chemistry, such as the [[ångström]], [[electron volt]], [[atomic mass unit]] and [[barn (unit)|barn]].
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| − | * 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 -->
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| − | * 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).
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| − | * 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.
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| − | * 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).
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| − | * [[Blood pressure]] is usually measured in [[mmHg]](≈[[Torr]]).
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| − | * [[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.
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| − | 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.
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| − | </ref> any change in the definition of the SI units results in a change of the definition of the older units, as well.
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| − | ===International trade===
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| − | 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.
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| − | 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.
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| − | [[Category:UBIK]] | + | [[Category:UBIK|System of units]] |
SI is the world's most widely used system of measurement, which is used both in everyday commerce and in science.Definitions of the basic units can be found at the sites bottom, as well as the 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.
In the International System of Units, the definition of the metre fixes the speed of light in vacuum c0, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) μ0, and the definition of the mole fixes the molar mass of the carbon 12 atom M(12C) to have the exact values given in the bottom table. Since the electric constant is related to μ0 by ε0 = 1/μ0c02, it too is known exactly.
The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty that established three international organizations to oversee the keeping of metric standards:
The history of the metric system has seen a number of variations, and has spread around the world, to replace many traditional measurement systems. At 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, whereas others were based on customary 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, in 1948, asked the International Committee for Weights and Measures 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 that were recommended are the metre, kilogram, second, ampere, degree Kelvin (later renamed kelvin), and candela. In 1960, the 11th CGPM named the system the International System of Units. The seventh base unit, the mole mole, was added in 1971 by the 14th CGPM.
One of the CIPM committees, the CCU, has proposed a number of changes to the definitions of the base units used in SI.
The International System of Units consists of a set of units together with a set of SI. The units are divided into two classes—base units and derived units. There are seven SI, each representing, by convention, different kinds of physical quantities.
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.
