Metric system

For a more accessible and less technical introduction tothis topic, see Introduction to the metric system.

For a topical guide to this subject, see Outline ofthe metric system.

Countries which have officially adopted the metric systemCountries which have not officially adopted the metric system(US, Myanmar (formerly Burma) and Liberia)

The metric system is an internationally agreed decimalsystem of measurement that was originally based on themètre des Archives and the kilogramme des Archives in-troduced by the French First Republic in 1799. Over theyears, the definitions of the metre and the kilogram havebeen refined, and the metric system has been extended toincorporate manymore units. Although a number of vari-ants of the metric system emerged in the late nineteenthand early twentieth centuries, the term is now often usedas a synonym for “SI”[Note 1] or the "International Systemof Units"—the official system of measurement in almostevery country in the world.The metric system has been officially sanctioned for usein the United States since 1866, but it remains the onlyindustrialised country that has not adopted the metric sys-tem as its official system of measurement. Many sourcesalso cite Liberia and Burma as the only other countries notto have done so. Although the United Kingdom uses themetric system for most official purposes, the use of theimperial system of measure, particularly for use at home,is widespread and is permitted by the law.Although the originators intended to devise a system thatwas equally accessible to all, it proved necessary to useprototype units in the custody of national or local au-thorities as standards. Control of the prototype units ofmeasure was maintained by the French government until1875, when it passed to an inter-governmental organisa-tion—the General Conference on Weights and Measures

“The metric system is for all people for all time.” (Condorcet,1791). Four everyday measuring devices that have metric cali-brations: a tapemeasure calibrated in centimetres, a thermometercalibrated in degrees Celsius, a kilogramweight, and an electricalmultimeter that measures volts, amperes and ohms.

(CGPM).[Note 1] It is now hoped that the last of these pro-totypes can be retired by 2014.From its beginning, the main features of the metric sys-tem were the standard set of inter-related base units anda standard set of prefixes in powers of ten. These baseunits are used to derive larger and smaller units that couldreplace a huge number of other units of measure in exis-tence. Although the system was first developed for com-mercial use, the development of coherent units of mea-sure made it particularly suitable for science and engi-neering.The uncoordinated use of the metric system by dif-ferent scientific and engineering disciplines, particularlyin the late 19th century, resulted in different choicesof fundamental units, even though all were based onthe same definitions of the metre and the kilogram.During the 20th century, efforts were made to ratio-nalise these units, and in 1960 the CGPM published theInternational System of Units which, since then, has been

1

2 1 FEATURES

the internationally recognised standard metric system.

1 Features

Although the metric system has changed and devel-oped since its inception, its basic concepts have hardlychanged. Designed for transnational use, it consisted ofa basic set of units of measurement, now known as baseunits. Derived units were built up from the base units us-ing logical rather than empirical relationships while mul-tiples and submultiples of both base and derived unitswere decimal-based and identified by a standard set ofprefixes.

1.1 Universality

Chinese road sign listing distances on an expressway in easternBeijing. Although the primary text is in Chinese, the distances useinternationally recognised characters.

At the outbreak of the French Revolution in 1789, mostcountries and even some cities had their own system ofmeasurement. Although different countries might haveused units of measure with the same name, such as thefoot, or local language equivalents such as pied, fuß andvoet, there was no consistency in the magnitude of thoseunits, nor in the relationships with their multiples and sub-multiples,[1] much like the modern-day differences be-tween the US and the UK pints and gallons.[2]

The metric system was designed to be universal—in thewords of the French philosopher Marquis de Condorcet itwas to be “for all people for all time”.[3]:1 It was designedfor ordinary people, for engineers who worked in human-related measurements and for astronomers and physicistswho worked with numbers both small and large, hencethe huge range of prefixes that have now been defined inSI.[4]

When the French Government first investigated the ideaof overhauling their system of measurement, the con-cept of universality was put into practice when, in 1789,

Maurice de Talleyrand, acting on Condorcet’s advice, in-vited John Riggs Miller, a British Parliamentarian andThomas Jefferson, the American Secretary of State toGeorge Washington, to work with the French in pro-ducing an international standard by promoting legisla-tion in their respective legislative bodies. However, theseovertures failed and the custody of the metric systemremained in the hands of the French government until1875.[3]:250–253

Unit names are ordinary nouns and although they use thecharacter set and follow the grammatical rules of the lan-guage concerned for example "kilometre", "kilómetro",each unit has a symbol that is independent of language,for example “km” for “kilometre”, “V” for “volts” etc.[5]

1.2 Decimal multiples

Main article: metric prefix

In the metric system, multiples and sub-multiples of unitsfollow a decimal pattern,[Note 2] a concept identified as apossibility in 1586 by Simon Stevin, the Flemish math-ematician who had introduced decimal fractions intoEurope.[6] This is done at the cost of losing the simplicityassociated with many traditional systems of units wheredivision by 3 or 4 does not result in awkward fractions;for example one third of a foot is four inches, a simplic-ity that in 1790 was debated, but rejected by the origina-tors of the metric system.[7] In 1854, in the introductionto the proceedings of the [British] Decimal Association,the mathematician Augustus de Morgan, summarised theadvantages of a decimal based system were over a non-decimal system thus: “In the simple rules of arithmetic,we practice a pure decimal system, nowhere interruptedby the entrance of any other system: from column to col-umn we never carry anything but tens".[8]

A common set of decimal-based prefixes that have the ef-fect multiplication or division by an integer power of tencan be applied to units which are too large or too smallfor practical use. The concept of using consistent classi-cal (Latin or Greek) names for the prefixes was first pro-posed in a report by the [French Revolutionary] Commis-sion on Weights and Measures in May 1793.[3]:89–96 Theprefix kilo, for example, is used to multiply the unit by1000, and the prefix milli is to indicate a one-thousandthpart of the unit. Thus the kilogram and kilometre are athousand grams and metres respectively, and a milligramand millimetre are one thousandth of a gram and metrerespectively. These relations can be written symbolicallyas:[4]

1 mg = 0.001 g1 km = 1000 m

In the early days, multipliers that were positive powersof ten were given Greek-derived prefixes such as kilo-

1.3 Realisability and replicable prototypes 3

and mega-, and those that were negative powers of tenwere given Latin-derived prefixes such as centi- andmilli-. However, 1935 extensions to the prefix system did notfollow this convention; the prefixes nano- and micro-, forexample used prefixes with Greek roots.[9] During the19th century the prefix myria-, derived from the Greekword μύριοι (mýrioi), was used as a multiplier for 10000(104).[10]

When applying prefixes to derived units of area and vol-ume that are expressed in terms of units of length squaredor cubed, the square and cube operators are applied to theunit of length including the prefix, as illustrated here:[4]

1mm2 (square millimetre) = (1mm)2 = (0.001m)2 = 0.000001 m2

1 km2 (square kilometre) = (1 km)2 = (1000m)2 = 1000000 m2

1 mm3 (cubic millimetre) = (1 mm)3 = (0.001m)3 = 0.000000001 m3

1 km3 (cubic kilometre) = (1 km)3 = (1000m)3 = 1000000000 m3

Prefixes are not usually used to indicate multiples of asecond greater than 1; the non-SI units of minute, hourand day are used instead. On the other hand, prefixes areused for multiples of the non-SI unit of volume, the litre(l, L) such as millilitres (ml).[4]

1.3 Realisability and replicable prototypes

Paris

The metre was originally defined to be one ten millionth ofthe distance between the North Pole and the Equator throughParis.[3]

Main article: Realisation (metrology)

The base units used in the metric system must berealisable, ideally with reference to natural phenomenarather than unique artefacts. Each of the base units in SIis accompanied by a mise en pratique [practical realisa-tion] published by the BIPM that describes in detail atleast one way in which the base unit can be measured.[11]Where possible, definitions of the base units were devel-oped so that any laboratory equipped with proper instru-ments would be able to realise a standard without relianceon an artefact held by another country. In practice, suchrealisation is done under the auspices of a mutual accep-tance arrangement (MAA). [12]

1.3.1 Metre and kilogram

In the original version of the metric system the base unitscould be derived from a specified length (the metre) andthe weight [mass] of a specified volume (1⁄1000 of a cubicmetre) of pure water. Initially the de facto French Gov-ernment of the day, the Assemblée nationale constituante,considered defining the metre as the length of a pendulumthat has a period of one second at 45°N and an altitudeequal to sea level. The altitude and latitude were specifiedto accommodate variations in gravity; the specified lati-tude was a compromise between the latitude of London(51° 30'N), Paris (48° 50'N) and the median parallel ofthe United States (38°N) to accommodate variations.[3]:94However the mathematician Borda persuaded the assem-bly that a survey having its ends at sea level and based ona meridian that spanned at least 10% of the earth’s quad-rant would be more appropriate for such a basis.[3]:96

10 cm

10 cm10 cm

One litre is equivalent to the volume of a cube with edges of 10cm and the kilogram was originally designed to be one litre ofwater at the melting point of ice.[13]

The available technology of the 1790s made it imprac-ticable to use these definitions as the basis of the kilo-gram and the metre, so prototypes that represented thesequantities insofar as was practicable were manufactured.On 22 June 1799 these prototypes were adopted as thedefinitive reference pieces, deposited in the Archives na-tionales and became known as the mètre des Archives and

4 1 FEATURES

the kilogramme des Archives. Copies were made and dis-tributed around France.[3]:266–269 These artefacts were re-placed in 1889 by the new prototypes manufactured un-der international supervision. Insofar as was possible, thenew prototypes were exact copies of the original proto-types, but used a later technology to ensure better stabil-ity. One of each of the kilogram and metre prototypeswere chosen by lot to serve as the definitive internationalreference piece with the remainder being distributed tosignatories of the Metre Convention.[14] In 1889 therewas no generally accepted theory regarding the nature oflight but by 1960 the wavelength of specific light spectracould give a more accurate and reproducible value than aprototype metre. In that year the prototype metre wasreplaced by a formal definition which defines the me-tre in terms of the wavelength of specified light spectra.By 1983 it was accepted that the speed of light in vac-uum was constant and that this constant provided a morereproducible procedure for measuring length. Thereforethe metre was redefined in terms of the speed of light.These definitions give a much better reproducibility andalso allow anyone, anywhere with a suitably equipped lab-oratory, to make a standard metre.[15]

1.3.2 Other base units

None of the other base units rely on a prototype – all arebased on phenomena that are directly observable and hadbeen in use for many years before formally becoming partof the metric system.The second first became a de facto base unit within themetric system when, in 1832, Carl Friedrich Gauss usedit, the centimetre and the gram to express the units associ-ated with values of absolute measurements of the Earth’smagnetic field.[16] The second, if based on the Earth’s ro-tation, is not a constant as the Earth’s rotation is slow-ing down—in 2008 the solar day was 0.002 s longer thanin 1820.[17] This had been known for many years; con-sequently in 1952 the International Astronomical Union(IAU) defined the second in terms of the Earth’s rota-tion in the year 1900. Measurements of time were madeusing extrapolation from readings based on astronomy.With the launch of SI in 1960, the 11th CGPM adoptedthe IAU definition.[18] In the years that followed, atomicclocks became significantly more reliable and preciseand in 1968 the 13th CGPM redefined the second interms of the frequency of a specific frequency from theemission spectrum of the caesium 133 atom, a compo-nent of atomic clocks. This provided the means to mea-sure the time associated with astronomical phenomenarather than using astronomical phenomena as the basisfrom which time measurements were made.[19][20]

The CGS absolute unit of electric current, the abampere,had been defined in terms of the force between two par-allel current-carrying wires in 1881.[21] In the 1940s, theInternational Electrotechnical Commission adopted anMKS variant of this definition for the ampere which was

adopted in 1948 by the CGPM.[22][23]

Temperature has always been based on observablephenomena—in 1744 the degree Centigrade[Note 3] wasbased on the freezing and boiling points of water.[24] In1948 the CGPM adopted the Centigrade scale, renamedit the “Celsius” temperature scale name and defined it interms of the triple point of water.[25]

When the mole and the candela were accepted by theCGPM in 1971 and 1975 respectively, both had been de-fined by third parties by reference to phenomena ratherthan artefacts.[26]

1.4 Coherence

Main article: Coherence (units of measurement)Each variant of the metric system has a degree of

James Clerk Maxwell played a major role in developing the con-cept of a coherent CGS system and in extending the metric systemto include electrical units.

coherence—the various derived units being directly re-lated to the base units without the need of intermediateconversion factors.[27] For example, in a coherent systemthe units of force, energy and power are chosen so thatthe equations

force = mass × acceleration

energy = force × distance

power = energy / time

hold without the introduction of constant factors. Once aset of coherent units have been defined, other relation-ships in physics that use those units will automatically

5

be true. Therefore Einstein’s mass-energy equation, E= mc2, does not require extraneous constants when ex-pressed in coherent units.[28]

The CGS system had two units of energy, the erg that wasrelated to mechanics and the calorie that was related tothermal energy so only one of them (the erg) could bear acoherent relationship to the base units. Coherence was adesign aim of SI resulting in only one unit of energy beingdefined – the joule.[19]

In SI, which is a coherent system, the unit of power is the"watt" which is defined as "one joule per second”.[19] Inthe US customary system of measurement, which is non-coherent, the unit of power is the "horsepower" which isdefined as “550 foot-pounds per second” (the pound inthis context being the pound-force).[29] Similarly, neitherthe US gallon nor the imperial gallon is one cubic foot orone cubic yard— the US gallon is 231 cubic inches andthe imperial gallon is 277.42 cubic inches.[30]

The concept of coherence was only introduced into themetric system in the third quarter of the nineteenthcentury;[31] in its original form themetric systemwas non-coherent—in particular the litre was 0.001 m3 and theare (from which the hectare derives) was 100 m2. A pre-cursor to the concept of coherence was however presentin that the units of mass and length were related to eachother through the physical properties of water, the gramhaving been designed as being the mass of one cubic cen-timetre of water at its freezing point.[32]

2 History

Main article: History of the metric systemSee also: MetricationIn 1586 the Flemish mathematician Simon Stevin pub-lished a small pamphlet called De Thiende (“the tenth”).Decimal fractions had been employed for the extrac-tion of square roots some five centuries before his time,but nobody used decimal numbers in daily life. Stevindeclared that using decimals was so important that theuniversal introduction of decimal weights, measures andcoinage was only a matter of time.[6]

One of the earliest proposals for a decimal system inwhich length, area, volume and mass were linked to eachother was made by John Wilkins, first secretary of theRoyal Society of London in his 1668 essay "An Essay to-wards a Real Character and a Philosophical Language".His proposal used a pendulum that had a beat of one sec-ond as the basis of the unit of length.[33][34][35] Two yearslater, in 1670, Gabriel Mouton, a French abbot and sci-entist, proposed a decimal system of length based on thecircumference of the Earth. His suggestion was that aunit, the milliare, be defined as a minute of arc along ameridian. He then suggested a system of sub-units, di-viding successively by factors of ten into the centuria, de-curia, virga, virgula, decima, centesima, and millesima.

John Wilkins who, in 1668, published an essay proposing a dec-imal system of measurement

His ideas attracted interest at the time, and were sup-ported by both Jean Picard and Christiaan Huygens in1673, and also studied at the Royal Society in London.In the same year, Gottfried Leibniz independently madeproposals similar to those of Mouton.[36]

In pre-revolutionary Europe, each state had its own sys-tem of units of measure.[1] Some countries, such as Spainand Russia, saw the advantages of harmonising their unitsof measure with those of their trading partners.[37] How-ever, vested interests who profited from variations in unitsof measure opposed this. This was particularly preva-lent in France where the huge inconsistency in the size ofunits of measure was one of the causes that, in 1789, ledto the outbreak of the French Revolution.[3]:2 During theearly years of the revolution, savants[Note 4] including theMarquis de Condorcet, Pierre-Simon Laplace, Adrien-Marie Legendre, Antoine Lavoisier and Jean-Charles deBorda set up a Commission of Weights and Measures.The commission was of the opinion that the countryshould adopt a completely new system of measure basedon the principles of logic and natural phenomena. Logicdictated that such a system should be based on the radixused for counting. Their report of March 1791 to theAssemblée nationale constituante considered but rejectedthe view of Lapace that a duodecimal system of count-ing should replace the existing decimal system; the viewsuch a system was bound to fail prevailed. The com-mission’s final recommendation was that the assemblyshould promote a decimal based system of measurement.The leaders of the assembly accepted the views of thecommission.[7][3]:99–100

Initially France attempted to work with other coun-tries towards the adoption of a common set of units of

6 2 HISTORY

measure.[3]:99–100 Among the supporters of such an in-ternational system of units was Thomas Jefferson who, in1790, presented a document Plan for Establishing Unifor-mity in the Coinage, Weights, and Measures of the UnitedStates to congress in which he advocated a decimal systemthat used traditional names for units (such as ten inchesper foot).[38] The report was considered but not adoptedby Congress.[3]: 249–250

Woodcut dated 1800 illustrating the new decimal units which be-came the legal norm across all France on 4 November 1800

2.1 Original metric system

The French law of 18 Germinal, Year III (7 April 1795)defined five units of measure:[32]

• The mètre for length

• The are (100 m2) for area [of land]

• The stère (1 m3) for volume of stacked[39] firewood

• The litre (1 dm3) for volumes of liquid

• The gramme for mass.

This system continued the tradition of having separatebase units for geometrically related dimensions, e.g.,mètre for lengths, are (100 m2) for areas, stère (1 m3)for dry capacities, and litre (1 dm3) for liquid capacities.The hectare, equal to a hundred ares, the area of a square100metres on a side (about 2.47 acres), is still in use. Theearlymetric system included only a few prefixes frommilli(one thousandth) to myria (ten thousand).[32]

Originally the kilogramme, defined as being one pinte(later renamed the litre) of water at the melting pointof ice, was called the grave; the gramme being an al-ternative name for a thousandth of a grave. However,the word grave, being a synonym for the title "count",had aristocratic connotations and was renamed the kilo-gramme.[13] The name mètre was suggested by Auguste-Savinien Leblond in May 1790.[3]: 92

France officially adopted the metric system on 10 De-cember 1799. Although it was decreed that its use was tobe mandatory in Paris that year and across the provincesthe following year, the decree was not universally ob-served across France.[40]

2.2 International adoption

Areas annexed by France during the Napoleonic era werethe first to inherit the metric system. In 1812 Napoleonintroduced a system known as mesures usuelles whichused the names of pre-metric units of measure, but de-fined them in terms ofmetric units – for example, the livremetrique (metric pound) was 500 g and the toise metrique(metric fathom) was 2 metres.[41] After the Congress ofVienna in 1815, France lost the territories that she hadannexed; some, such as the Papal States reverted to theirpre-revolutionary units of measure, others such as Badenadopted a modified version of the mesures usuelles, butFrance kept her system of measurement intact.[42]

In 1817 the Netherlands reintroduced the metric system,but used pre-revolutionary names—for example 1 cen-timetre became the duim (thumb), the ons (ounce) be-came 100 g and so on.[43] Certain German states adoptedsimilar systems[42][44] and in 1852 the German Zollverein(customs union) adopted the zollpfund (customs pound)of 500 g for intrastate commerce.[45] In 1872 the newlyformed German Empire adopted the metric system asits official system of weights and measures[46] and thenewly formed Kingdom of Italy likewise, following thelead given by Piedmont, adopted the metric system in1861.[47]

The Exposition Universelle (1867) (Paris Exhibition) de-voted a stand to the metric system and by 1875 two thirdsof the European population and close on half the world’spopulation had adopted the metric system. By 1872 theonly principal European countries not to have adopted themetric system were Russia and the United Kingdom.[48]

By 1920 countries comprising 22% of the world’s popula-

7

tion, mainly English-speaking, used the imperial system;25% used mainly the metric system and the remaining53% used neither.[40]

In 1927 several million people in the United States sentover 100,000 petitions backed by the Metric Associationand The General Federation of Women’s Clubs urgingCongress to adopt the metric system. The petition wasopposed by the manufacturing industry, citing the cost ofthe conversion.[49]

2.3 International standards

In 1861 a committee of the British Association for Ad-vancement of Science (BAAS) including William Thom-son (later Lord Kelvin), James Clerk Maxwell and JamesPrescott Joule introduced the concept of a coherent sys-tem of units based on the metre, gram and second which,in 1873, was extended to include electrical units.[50][51]

Seal of the International Bureau of Weights and Measures(BIPM)

On 20 May 1875 an international treaty known as theConvention du Mètre (Metre Convention)[52] was signedby 17 states. This treaty established the following organi-sations to conduct international activities relating to a uni-form system for measurements:[53]

• General Conference on Weights and Measures(CGPM),[Note 1] an intergovernmental conferenceof official delegates of member nations and thesupreme authority for all actions;

• International Committee for Weights and Measures(CIPM),[Note 1] consisting of selected scientists andmetrologists, which prepares and executes the deci-sions of the CGPM and is responsible for the super-vision of the International Bureau of Weights andMeasures (BIPM);

• International Bureau of Weights and Measures(BIPM),[Note 1] a permanent laboratory and worldcentre of scientific metrology, the activities of whichinclude the establishment of the basic standards andscales of the principal physical quantities and main-tenance of the international prototype standards.

In 1881 first International Electrical Congress adoptedthe BAAS recommendations on electrical units, followedby a series of congresses in which further units ofmeasurewere defined and the International Electrotechnical Com-mission (IEC) was set up with the specific task of over-seeing electrical units of measure.[54] This was followedby the International Congress of Radiology (ISR) who, attheir inaugural meeting in 1926, initiated the definitionof radiological-related units of measure.[55] In 1921 theMetre Convention was extended to cover all units of mea-sure, not just length and mass and in 1933 the 8th CGPMresolved to work with other international bodies to agreestandards for electrical units that could be related backto the international prototypes.[56] Since 1954 the CIPMcommittee that oversees the definition of units of mea-surement, the Consultative Committee for Units,[Note 5]has representatives frommany international organisationsincluding the ISR, IEC and ISO under the chairmanshipof the CIPM.[57]

3 Variants

A number of variants of the metric system evolved, allusing theMètre des Archives andKilogramme des Archives(or their descendants) as their base units, but differing inthe definitions of the various derived units.

3.1 Centimetre-gram-second systems

The centimetre gram second system of units (CGS) wasthe first coherent metric system, having been developedin the 1860s and promoted by Maxwell and Thomson. In1874, this system was formally promoted by the BritishAssociation for the Advancement of Science (BAAS).[16]The system’s characteristics are that density is expressedin g/cm3, force expressed in dynes and mechanical en-ergy in ergs. Thermal energy was defined in calories, onecalorie being the energy required to raise the tempera-ture of one gram of water from 15.5 °C to 16.5 °C. Themeeting also proposed two sets of units for electrical andmagnetic properties – the electrostatic set of units and theelectromagnetic set of units.[58]

3.2 Metre-kilogram-second systems

The CGS units of electricity were cumbersome to workwith. This was remedied at the 1893 International Elec-trical Congress held in Chicago by defining the “interna-

8 3 VARIANTS

tional” ampere and ohm using definitions based on themetre, kilogram and second.[59] In 1901, Giovanni Giorgishowed that by adding an electrical unit as a fourth baseunit, the various anomalies in electromagnetic systemscould be resolved. The metre-kilogram-second-coulomb(MKSC) and metre-kilogram-second-ampere (MKSA)systems are examples of such systems.[60]

The International System of Units (Système internationald’unités or SI) is the current international standard metricsystem and is also the system most widely used aroundthe world. It is an extension of Giorgi’s MKSA system—its base units are the metre, kilogram, second, ampere,kelvin, candela and mole.[19]

3.3 Metre-tonne-second systems

The metre-tonne-second system of units (MTS) wasbased on the metre, tonne and second – the unit of forcewas the sthène and the unit of pressure was the pièze.It was invented in France for industrial use and from1933 to 1955 was used both in France and in the SovietUnion.[54][61]

3.4 Gravitational systems

Gravitational metric systems use the kilogram-force(kilopond) as a base unit of force, with mass measured ina unit known as the hyl, Technische Mass Einheit (TME),mug or metric slug.[62] Although the CGPM passed a res-olution in 1901 defining the standard value of accelerationdue to gravity to be 980.665 cm/s2, gravitational units arenot part of the International System of Units (SI).[63]

3.5 International System of Units

Main articles: International System of Units and List ofphysical quantitiesThe 9th CGPM met in 1948, three years after the endof the Second World War and fifteen years after the8th CGPM. In response to formal requests made by theInternational Union of Pure and Applied Physics and bythe French Government to establish a practical systemof units of measure, the CGPM requested the CIPM toprepare recommendations for such a system, suitable foradoption by all countries adhering to the Metre Conven-tion. The recommendation also catalogued symbols forthe most important MKS and CGS units of measure andfor the first time the CGPMmade recommendations con-cerning derived units.[64] At the same time the CGPMformally adopted a recommendation for the writing andprinting of unit symbols and of numbers.[65]

The CIPM’s draft proposal, which was an extensive re-vision and simplification of the metric unit definitions,symbols and terminology based on the MKS system ofunits, was put to the 10th CGPM in 1954. In accordance

Cover of brochure The International System of Units

with Giorgi’s proposals of 1901, the CIPM also recom-mended that the ampere be the base unit fromwhich elec-tromechanical units would be derived. The definitionsfor the ohm and volt that had previously been in use werediscarded and these units became derived units based onthe metre, ampere, second and kilogram. After negotia-tions with the International Commission on Illumination(CIE)[Note 1] and IUPAP, two further base units, the de-gree kelvin and the candela were also proposed as baseunits.[66] The full system and name “Système Interna-tional d'Unités” were adopted at the 11th CGPM in Oc-tober 1960.[67] During the years that followed the defi-nitions of the base units and particularly the methods ofapplying these definitions have been refined.[68]

The formal definition of International System of Units(SI) along with the associated resolutions passed by theCGPM and the CIPM are published by the BIPM inbrochure form at regular intervals. The eighth edition ofthe brochure Le Système International d'Unités—The In-ternational System of Units was published in 2006 and isavailable on the internet.[69] In October 2011, at the 24thCGPM proposals were made to change the definitions offour of the base units. These changes should not affectthe average person.[70]

5.1 Variations in spelling 9

4 Relating SI to the real world

Main article: Non-SI units mentioned in the SI

Although SI, as published by the CGPM, should, in the-ory, meet all the requirements of commerce, science andtechnology, certain units of measure have acquired such aposition within the world community that it is likely theywill be used for many years to come. In order that suchunits are used consistently around the world, the CGPMcatalogued such units in Tables 6 to 9 of the SI brochure.These categories are:[71]

• Non-SI units accepted for use with the Interna-tional System of Units (Table 6). This list includesthe hour and minute, the angular measures (degree,minute and second of arc) and the historic [non-coherent] metric units, the litre, tonne and hectare(originally agreed by the CGPM in 1879)

• Non-SI units whose values in SI units must beobtained experimentally (Table 7). This list in-cludes various units of measure used in atomic andnuclear physics and in astronomy such as the dalton,the electron mass, the electron volt, the astronomicalunit and a number of other units of measure that arewell-established, but dependent on experimentally-determined physical quantities.

• Other non-SI units (Table 8). This list cataloguesa number of units of measure that have been used in-ternationally in certain well-defined spheres includ-ing the bar for pressure, the ångström for atomicphysics, the nautical mile and the knot in navigation.

• Non-SI units associated with the CGS and theCGS-Gaussian system of units (Table 9). Thistable catalogues a number of units of measure basedon the CGS system and dating from the nineteenthcentury. They appear frequently in the literature, buttheir continued use is discouraged by the CGPM.

5 Usage around the world

Further information: MetricationThe usage of the metric system varies around theworld. According to the USCentral Intelligence Agency’sFactbook (2007), the International System of Units hasbeen adopted as the official system of weights and mea-sures by all nations in the world except for Burma, Liberiaand the United States,[72] while the NIST has identi-fied the United States as the only industrialised countrywhere the metric system is not the predominant systemof units.[73] However, reports published since 2007 holdthis is no longer true of Liberia or Burma.[74] An AgenceFrance-Presse report from 2010 stated that Sierra Leonehad passed a law to replace the imperial system with the

1795 1815 1835 1855 1876 1896 1916 1937 1957 1977 1998

Countries by date of metrication. Colours red to green show thepattern of metrication from 1795 to 1998. Black identifies coun-tries that have not adopted the metric system as the primary mea-surement system. White identifies countries that already used themetric system at the time they gained their independence

metric system thereby aligning its system ofmeasurementwith that used by its Mano River Union (MRU) neigh-bours Guinea and Liberia.[Note 6][75] Reports from Burmasuggest that that country is also planning to adopt the met-ric system.[76]

In the United States metric units, authorised by Congressin 1866,[77] are widely used in science, military, and par-tially in industry, but customary units predominate inhousehold use. At retail stores the litre is a commonlyused unit for volume, especially on bottles of beverages,and milligrams are used to denominate the amounts ofmedications, rather than grains.[78][79] On the other handnon-metric units are used in certain regulated environ-ments such as nautical miles and knots in internationalaviation.In the countries of the Commonwealth of Nations themetric system has replaced the imperial system by vary-ing degrees: Australia, New Zealand and Commonwealthcountries in Africa are almost totally metric, India ismostly metric, Canada is partly metric while in the UnitedKingdom the metric system, the use of which was firstpermitted for trade in 1864, is used in much governmentbusiness, in most industries including building, health andengineering and for pricing by measure or weight in mosttrading situations, both wholesale and retail.[80] Howeverthe imperial system is widely used by the British publicand is legally mandated in various cases, such as road-signdistances must be in yards and miles.[3][81][82]

Some other jurisdictions, such as Hong Kong, have lawsmandating or permitting other systems ofmeasurement inparallel with the metric system in some or all contexts.[83]

5.1 Variations in spelling

The SI symbols for the metric units are intended tobe identical, regardless of the language used[5] but unitnames are ordinary nouns and use the character setand follow the grammatical rules of the language con-cerned. For example, the SI unit symbol for kilome-tre is “km” everywhere in the world, even though the

10 7 FUTURE DEVELOPMENTS

local language word for the unit name may vary. Lan-guage variants for the kilometre unit name include: chi-lometro (Italian), Kilometer (German),[Note 7] kilometer(Dutch), kilomètre (French), χιλιόμετρο (Greek), quiló-metro/quilômetro (Portuguese), kilómetro (Spanish) andкилометр (Russian).[84][85]

Variations are also found with the spelling of unit namesin countries using the same language, including differ-ences in American English and British spelling. Forexample meter and liter are used in the United Stateswhereasmetre and litre are used in other English-speakingcountries. In addition, the official US spelling for therarely used SI prefix for ten is deka. In American En-glish the term metric ton is the normal usage whereas inother varieties of English tonne is common. Gram is alsosometimes spelled gramme in English-speaking countriesother than the United States, though this older usage isdeclining.[86]

5.2 Conversion and calculation incidents

The dual usage of or confusion between metric and non-metric units has resulted in a number of serious incidents.These include:

• Flying an overloaded American International Air-ways aircraft from Miami, Florida to Maiquetia,Venezuela on 26 May 1994. The degree of over-loading was consistent with ground crew assum-ing that kilogram weight markings on cargo werepounds.[87]

• In 1999 the Institute for Safe Medication Practicesreported that confusion between grains and gramsled to a patient receiving phenobarbital 0.5 gramsinstead of 0.5 grains (0.03 grams) after the practi-tioner misread the prescription.[88]

• The Canadian "Gimli Glider" accident in 1983,when a Boeing 767 jet ran out of fuel in mid-flight because of two mistakes made when calculat-ing the fuel supply of Air Canada's first aircraft touse metric measurements: mechanics miscalculatedthe amount of fuel required by the aircraft as a resultof their unfamiliarity with metric units.[89]

• The root cause of the loss in 1999 of NASA'sUS$125 million Mars Climate Orbiter whichcrashed into Mars was a mismatch of units – thespacecraft engineers calculated the thrust forces re-quired for velocity changes using US customaryunits (lbf·s) whereas the teamwho built the thrusterswere expecting a value in metric units (N·s) as perthe agreed specification.[90][91]

6 Conversion between SI andlegacy units

Main article: Conversion of units

During its evolution, the metric system has adopted manyunits of measure. The introduction of SI rationalised boththe way in which units of measure were defined and alsothe list of units in use. These are now catalogued in theofficial SI Brochure.[19] The table below lists the units ofmeasure in this catalogue and shows the conversion fac-tors connecting them with the equivalent units that werein use on the eve of the adoption of SI.[92][93][94][95]

The SI Brochure also catalogues certain non-SI units thatare widely used with the SI in matters of everyday life orunits that are exactly defined values in terms of SI unitsand are used in particular circumstances to satisfy theneeds of commercial, legal, or specialised scientific in-terests. These units include:[19]

7 Future developments

Main article: Proposed redefinition of SI base unitsAfter the metre was redefined in 1960, the kilogram was

Relations between proposed SI units definitions (in colour) andwith seven fundamental constants of nature (in grey) with fixednumerical values in the proposed system.

the only SI base unit that relied on a specific artefact.After the 1996–1998 recalibrations a clear divergencebetween the international and various national prototypekilograms was observed.[96]

At the 23rd CGPM (2007), the CIPM was mandated toinvestigate the use of natural constants as the basis forall units of measure rather than the artefacts that werethen in use. At a meeting of the CCU held in Reading,

11

United Kingdom in September 2010, a resolution[97] anddraft changes to the SI brochure that were to be presentedto the next meeting of the CIPM in October 2010 wereagreed to in principle.[70] The CCU proposed to

• in addition to the speed of light, define four con-stants of nature—Planck’s constant, an elementarycharge, Boltzmann constant and Avogadro constant– to have exact values

• retire the international prototype kilogram

• revise the current definitions of the kilogram,ampere, kelvin and mole to make use of the abovefour constants of nature

• tighten the wording of the definitions of all the baseunits

The CIPMmeeting of October 2010 found that “the con-ditions set by the General Conference at its 23rd meet-ing have not yet been fully met. For this reason theCIPM does not propose a revision of the SI at the presenttime”.[98] The CIPM did however sponsor a resolution atthe 24th CGPM inwhich the changes were agreed in prin-ciple and which were expected to be finalised at the 25thCGPM in 2014.[99]

8 See also

• Binary prefix, used in computer science

• Conversion of units

• History of measurement

• ISO/IEC 80000, style manual for measurementsmetric and non-metric, superseding ISO 31

• Metrication, the process of introducing the SImetricsystem as the worldwide standard for physical mea-surements

• Metrology

• Units of measurement

9 Notes[1] The following abbreviations are taken from the French

rather than the English texts:

• SI: Le Système international d'unités• CGPM: Conférence générale des poids et mesures• CIPM: Comité international des poids et mesures• BIPM: Bureau international des poids et mesures• CIE: Commission Internationale de l'Eclairage

[2] Non-SI units for time and plane angle measurement, in-herited from existing systems, are an exception to thedecimal-multiplier rule

[3] Now called the degree Celsius

[4] An extremely learned or scholarly person – Oxford En-glish Dictionary

[5] The CCU was set up in 1964 to replace the Commis-sion for the System of Units—a commission establishedin 1954 to advise on the definition of SI.

[6] According to the Agence France-Presse report (2010)Liberia was metric, but Sierra Leone was not metric—astatement that conflicted with the CIA statement (2007).

[7] In German all nouns start with an upper-case letter

[8] Roentgen is a measure of ionization (charge per mass),not of absorbed dose, so there is no well-defined conver-sion factor. However, a radiation field of gamma rays thatproduces 1 roentgen of ionization in dry air would de-posit 0.0096 gray in soft tissue, and between 0.01 and 0.04grays in bone. Since this unit was often used in radiationdetectors, a factor of 0.01 can be used to convert the de-tector reading in roentgens to the approximate absorbeddose in grays.

10 References[1] Palaiseau, JFG (October 1816). Métrologie universelle,

ancienne et moderne: ou rapport des poids et mesures desempires, royaumes, duchés et principautés des quatre par-ties du monde. Bordeaux. pp. 71–460. Retrieved October30, 2011.

[2] “pint”. Encyclopaedia Britannica. 2013. Retrieved 4April 2013.

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[4] International Bureau of Weights and Measures (2006),The International System of Units (SI) (8th ed.), pp.121,122, ISBN 92-822-2213-6

[5] International Bureau of Weights and Measures (2006),The International System of Units (SI) (8th ed.), p. 130,ISBN 92-822-2213-6

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[7] Glaser, Anton (1981) [1971]. History of Binary and otherNondecimal Numeration (Revised ed.). Tomash. pp. 71–72. ISBN 0-938228-00-5. Retrieved 5 April 2013.

[8] de Morgan, Augustus (1854). Decimal Association(formed Jun 12, 1854)—Proceedings with an introductionby Professor de Morgan. London. p. 2. Retrieved 21April 2012.

12 10 REFERENCES

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[43] Jacob de Gelder (1824). Allereerste Gronden der Cijfer-kunst [Introduction to Numeracy] (in Dutch). 's Graven-hage andAmsterdam: deGebroeders van Cleef. pp. 163–176. Retrieved 2 March 2011.

[44] FerdinandMalaisé (1842). Theoretisch-practischer Unter-richt im Rechnen [Theoretical and practical instruction inarithmetic] (in German). München. pp. 307–322. Re-trieved 26 March 2011.

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[48] Secretary, the Metric committee (1873). “Report on thebest means of providing a Uniformity of Weights andMeasures, with reference to the Interests of Science”. Re-port of the forty second meeting of the British Associationfor the Advancement of Science held at Brighton, August1872 (British Association for the Advancement of Sci-ence): 25–28. Retrieved 12 May 2011.

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[51] Professor Everett et al, ed. (1874). “First Report of theCommittee for the Selection and Nomenclature of Dy-namical and Electrical Units”. Report on the Forty-thirdMeeting of the British Association for the Advancement ofScience held at Bradford in September 1873 (British Asso-ciation for the Advancement of Science): 222–225. Re-trieved 2011-05-10.

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11 External links• CBC Radio Archives For Good Measure: CanadaConverts to Metric

15

12 Text and image sources, contributors, and licenses

12.1 Text• Metric system Source: http://en.wikipedia.org/wiki/Metric%20system?oldid=638356931 Contributors: Damian Yerrick, The Anome,

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Parrot, JHunterJ, BillFlis, Beetstra, Boomshadow, Optakeover, Michael Greiner, Peter Horn, BranStark,Iridescent, Igoldste, Richard75, Courcelles, Rhetth, Tawkerbot2, ILikeThings, Dlohcierekim, Chetvorno, Powerslide, SkyWalker, JFor-get, Eric, RoboCafaz, CWY2190, R9tgokunks, Zolcos, Green caterpillar, El aprendelenguas, Requestion, FlyingToaster, Fandoo, KenGallager, MrFish, Senorelroboto, Fnlayson, Perfect Proposal, Mato, Nick Wilson, Gogo Dodo, Zginder, JFreeman, Tawkerbot4, Gvil,DumbBOT, Chrislk02, Krouic, Casliber, Thijs!bot, Epbr123, N5iln, Headbomb, Marek69, John254, Frank, Gerry Ashton, James086,Swinginruss, Philippe, Nick Number, Msaditi, Engr.student, Mentifisto, AntiVandalBot, Majorly, Luna Santin, Widefox, Rolgiati, Billscot-tbob, Bladestorm, Scepia, NByz, Res2216firestar, JAnDbot, Husond, Harryzilber, Sean7341, Mcorazao, Db099221, Nicholas Tan, Drmindbender, Acroterion, SteveSims, Bongwarrior, VoABot II, P64, Fusionmix, JamesBWatson, Jay Gatsby, Mclay1, Harel, CTF83!, John-bibby, 28421u2232nfenfcenc, St.Jimmy666, EstebanF, Glen, DerHexer, Philryan, Pax:Vobiscum, Taborgate, MartinBot, STBot, Arjun01,Samibellina, Jim.henderson, Rettetast, Anaxial, Zouavman Le Zouave, Mschel, R'n'B, AlexiusHoratius, Jarhed, Rlarocco, Tgeairn, Ssol-bergj, J.delanoy, Captain panda, Pharaoh of the Wizards, Trusilver, Rlsheehan, Uncle Dick, Suviljan, Extransit, Horst, Xyzt1234, It Is MeHere, Katalaveno, DarkFalls, Eosin-Y, Clfin62, Msny824, AntiSpamBot, Girl2k, Jcwf, NewEnglandYankee, SJP, Minesweeper.007, Gen-joke, KylieTastic, Jamesontai, Natl1, Useight, CardinalDan, Funandtrvl, Xenonice, MetricGuy, RoseTech, VolkovBot, That-Vela-Fella,Jeff G., Grammarmonger, WOSlinker, Dougie monty, Philip Trueman, Jkeene, Crohnie, Seraphim, Allyhazell, Martin451, Marbe166,Jackfork, LeaveSleaves, Amog, DieBuche, Modal Jig, Cremepuff222, Greenprince, Fasouzafreitas, Mwilso24, Rhopkins8, Falcon8765,Enviroboy, Nagy, Symane, Logan, PokeYourHeadOff, Qwazywabbit, S.Örvarr.S, Demmy, Biscuittin, Quietpanther, EJF, Industrializa-tion, Technion, SieBot, Whiteboard123, Jim77742, Moonriddengirl, Martin Kealey, Dawn Bard, Squiffycat, Bruceleefan189, Erier2003,Smsarmad, Yintan, Wing gundam, Jason Patton, LeadSongDog, Srushe, Jp314159, Perspicacite, Theaveng, Syst3m3rr0r, Allmightyduck,Superflameb, Oxymoron83, Antonio Lopez, Canislupusarctos, Jdaloner, Steven Zhang, Lightmouse, Iain99, Maelgwnbot, BillShurts, C'estmoi, Iknowyourider, StaticGull, Adamtester, Scouten, Caeden1966, Pinkadelica, DJFreestyler, Randy Kryn, ClueBot, Trojancowboy, Go-rillaWarfare, Fyyer, The Thing That Should Not Be, AldoNadi, Tanglewood4, Testi123, Buonaparte69, Drmies, Razimantv, Mild BillHiccup, Awnmwad, Bucketdude, Markstuart44, LizardJr8, Ojbaby2, Puchiko, NuclearVacuum, Excirial, Quercus basaseachicensis, Jus-dafax, Resoru, Eeekster, Lartoven, Sun Creator, Rao Ravindra, Jroovers, Hans Adler, Razorflame, Mikaey, Audaciter, Thingg, Kslall8765,Aitias, Richardlw, Wcp07, Yoman82, SoxBot III, Vigilius, Crowsnest, Bücherwürmlein, Glacier Wolf, DarkTilde, XLinkBot, Pichpich,Rror, Kettie25, PL290, Subversive.sound, JinJian, Rounddot5827, Nas777, Good Olfactory, Osarius, Enigmocracy, Hoplophile, The-Codeman4, M1ch1ganst8, Willking1979, Little sawyer, Jojhutton, Friginator, CL, Ronhjones, Fieldday-sunday, Fluffernutter, Noozgroop,Chamal N, Bassbonerocks, Doniago, 5 albert square, 68Yut, 68Yuto, Ehrenkater, Tide rolls, Lightbot, Cameraslovedones, LuK3, En-viro999, Whatismetric, TheSuave, Yobot, Fraggle81, TaBOT-zerem, Cflm001, Rsquire3, Benito, THEN WHO WAS PHONE?, Eric-Wester, Tempodivalse, Magog the Ogre, Synchronism, AnomieBOT, XL2D, Floquenbeam, Jim1138, Galoubet, Emb09, Rambo5000,Ipatrol, AdjustShift, Ulric1313, MultK, Flewis, Materialscientist, Limideen, ImperatorExercitus, Citation bot, Eumolpo, Apollo, Arthur-Bot, B. Fairbairn, Xqbot, Sionus, Transity, JimVC3, Capricorn42, Drilnoth, Silvermen, Grim23, NFD9001, Freeonlinegames, The SanestMad Hatter, Br77rino, K1004, AbigailAbernathy, Elideb, GrouchoBot, Morten Isaksen, Shirik, RibotBOT, Locobot, Fobos92, A. di M.,Peter Buch, Erik9, Fotaun, A.amitkumar, BoomerAB, George2001hi, MayFlowerNorth, FrescoBot, Limelightmaster, Findiver, Jc3s5h,KerryO77, Recognizance, Cntrational, Dirtlawyer1, ClickRick, Potatis invalido, Pinethicket, Elockid, 5Celcious, LittleWink, Martinvl,Calmer Waters, Moonraker, BRUTE, Stoiko Stoilov, RedBot, Mediatech492, SpaceFlight89, RandomStringOfCharacters, Monkeyman-man, Dac04, SkyMachine, Abc518, Robvanvee, FoxBot, Q Illespont, Ottawaresident, DixonDBot, RXRX, Rpt0, Vrenator, Deleter of info,777sms, Aiken drum, Youtube92, ThinkEnemies, Cazzchazz, Reach Out to the Truth, BrightBlackHeaven, DARTH SIDIOUS 2, Whiskydrinker, Mean as custard, RjwilmsiBot, Vtstarin, Jackehammond, TGCP, Felipe1966, WikitanvirBot, GA bot, Ajraddatz, I win boom, Leamolly, The Mysterious El Willstro, Wikipelli, K6ka, Susfele, Maxviwe, LincMad, Chryed, WikipedianD, Unreal7, Pingu.dbl96, Make-cat, Wayne Slam, Underrated1 17, Markus031098, L Kensington, Quantumor, Peckoduck, Mayur, Donner60, Puffin, Nzacdp, CGPGrey,DarkXWeatherX, , Patrolboat, G-13114, Sven Manguard, DASHBotAV, Teh.Cyrus, Cgtdk, ResearchRave, Xanchester, ClueBot NG,Bernisman, TCMjunkie, Gareth Griffith-Jones, Hellsassasindemon, Tetracapillactomist, Wilcoxst, Chester Markel, Selvasivagurunathanm, Braincricket, Go Phightins!, Alexhangartner, Super renzy benzy, Widr, Exurbis67, Thistledome, Theopolisme, MerlIwBot, Odd-bodz, Helvitica Bold, Curb Chain, Techhead0, Thekingsisbest, YouMakeMeFeel:, Lowercase sigmabot, Mouloud47, Vagobot, Juro2351,Northamerica1000, SemanticEngine, Dan653, Jon emmets, Chris292, Zeus6play, HazelGHC, LowJoe999, Klilidiplomus, ArchieCrane,Shibingeorge, Agent 78787, Pratyya Ghosh, Tonyxc600, ChrisGualtieri, GoShow, Williamaperry67, Garamond Lethe, Healablemarrow4,

16 12 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

Gobmy, Kelvinsong, JJ 65, EdithLovely, Mogism, MeasureIT, Xeryus rouge, Burzuchius, Lugia2453, Herve Reex, 93, LMANSH, Reatlas,Clayton 0033, Imaeditertrol, Likeaboss444, Nerlost, Epicgenius, Camyoung54, Curatrice, Tentinator, QuantoAltoPossoVolare, AnnieLess,Beckhamdavidson, Ugog Nizdast, Eagle3399, Ginsuloft, Tomkyd1964, Anderino, Totalforce8, Fukdatshet, Urbaninformative, Monkbot,Goldwannern, JojoBunny0523, Health Planner, The Chemistry Bookworm and Anonymous: 1230

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