The International System of Units^[1] (abbreviated SI from French: Système international d'unités^[2]) is the modern form of the metric system and is generally a system of units of measurement devised around seven 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, which, in turn, had a few variants. The SI is declared as an evolving system, thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves.

SI is the world's most widely used system of measurement, which is used both in everyday commerce and in science.^[3][4][5] The system has been nearly globally adopted with the United States being the only industrialised nation that does not mainly use the metric system in its commercial and standards activities.^[6] The United Kingdom has officially adopted a partial metrication policy, with no intention of replacing imperial units entirely. Canada has adopted it for many purposes but imperial/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.^[7][8]

History[link]

The metric system was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier, who is known as the "father of modern chemistry") who had been commissioned by the Assemblée nationale and Louis XVI of France to create a unified and rational system of measures.^[9] 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 gramme and kilogramme replaced the former terms gravet (correctly milligrave) and 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 Napoleon's coup d'état), the metric system was definitively adopted in France.

The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty that established three international organisations to oversee the keeping of metric standards:

• 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 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 (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 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, Le Système international d'unités. The seventh base unit, the 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.^[10] The CIPM meeting of October 2010 found that the proposal was not complete,^[11] and it is expected that the CGPM will consider the full proposal in 2015.

Units and prefixes[link]

The International System of Units consists of a set of units together with a set of prefixes. The units are divided into two classes—base units and derived units. There are seven base units, each representing, by convention, different kinds of physical quantities.

Derived units are formed from multiplication and division of the seven base units and other derived units^[14] and are unlimited in number;^[15] 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 = m²·kg·s⁻³·A⁻², which follows from the definition of the quantity electrical resistance. The radian and steradian, once given special status, are now considered dimensionless derived units.^[14]

A 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.

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.

[edit] Writing unit symbols and the values of quantities

• 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", "7.3×10² m²", "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.^[16][17]
• Symbols for derived units formed by multiplication are joined with a 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 (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s⁻¹, m·s⁻¹, or Failed to parse (Missing texvc executable; please see math/README to configure.): \textstyle\frac{\mathrm{m}}{\mathrm{s}}

. Only one solidus should be used; e.g., kg/(m·s²) and kg·m⁻¹·s⁻² are acceptable, but kg/m/s² 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 (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.^[18]
• 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 unit itself is written "pascal".^[19]
  • 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 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 CGPM since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any standards body. For more information, see litre. The litre is not an SI unit per se and is expressed in SI terms as a cubic decimetre, i.e., dm³.
• 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 10³ (kilo) are uppercase.^[20]
• Symbols of units are not pluralised; e.g., "25 kg", not "25 kgs".^[18]
• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European languages.^[21]
• Spaces may be used as a thousands separator (1000000) 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. In print, the space used for this purpose is typically narrower than that between words (commonly a 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, Japanese, and Korean language computing (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 CJK Compatibility and Letterlike Symbols subranges for back compatibility, without necessarily recommending future usage. These are summarised in Unicode System of Units.
• When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) are recognised as language-dependent terms, since the value of billion and trillion can vary from language to language. SI, therefore, recommends avoiding these terms.^[16] However, no alternative is suggested by the International Bureau of Weights and Measures (BIPM).

Writing the unit names[link]

• Names of units follow the grammatical rules associated with common nouns - 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.^[22]
• Names of units are pluralised using the normal English grammar rules;^[23][24] e.g., "henries" is the plural of "henry".^[23]:31 The units lux, hertz, and 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.^[25]

Realisation of units[link]

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.^[26] However, "any method consistent with the laws of physics could be used to realise any SI unit."^[27] (p. 111).

Related systems[link]

The definitions of the terms 'quantity', 'unit', 'dimension' etc. used in measurement, are given in the International Vocabulary of Metrology.^[28]

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 Quantities and Units.

"New SI"[link]

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

When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artifact. Moreover, after the 1996-1998 recalibration a clear divergence between the various prototype kilograms was observed.

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in Reading, United Kingdom in September 2010, a resolution^[29] and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle.^[10] The proposals that the CCU put forward were:

• In addition to the speed of light, four constants of nature - Planck's constant, an elementary charge, Boltzmann constant and Avogadro's number be defined to have exact values.
• The international prototype kilogram be retired
• The current definitions of the kilogram, ampere, kelvin and mole be revised.
• The wording of the definitions of all the base units be tightened up

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time".^[30] The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principal and which were expected to be finalised at the CGPM's next meeting in 2014.^[31]

Conversion factors[link]

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 factor. There are several compilations of conversion factors; see, for example, Appendix B of NIST SP 811.^[23]

Cultural issues[link]

Three nations have not officially adopted the International System of Units as their primary or sole system of measurement: Myanmar (Burma), Liberia, and the United States

The near-worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardise the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. For use in science, the SI prefixes simplify dealing with very large and small quantities.

Many units in everyday and scientific use are not SI units. In some cases these units have been designated by the BIPM as "non-SI units accepted for use with the SI". ^{[32] [33]} Some examples include:

• The units of time (minute, min; hour, h; day, d) in use besides the SI second, are specifically accepted for use according to table 6.^[34]
• The year is specifically not included but has a recommended conversion factor.^[35]
• The Celsius temperature scale; kelvins are rarely employed in everyday use.
• Electric energy is often billed in kilowatt-hours, instead of megajoules. Similarly, battery charge is often measured as milliampere-hours (mA·h), instead of coulombs.
• The nautical mile and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 International nautical mile = 1852 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 for altitude.
• Astronomical distances measured in astronomical units, parsecs, and light-years instead of, for example, petametres (a light-year is about 9.461 Pm or about 9461000000000000 m).
• Atomic scale units used in physics and chemistry, such as the ångström, electron volt, atomic mass unit and barn.
• Some physicists prefer the centimetre-gram-second (CGS) units, or systems based on physical constants, such as Planck units, atomic units, or geometric units.
• In some countries, the informal cup measurement has become 250 mL. Likewise, a 500 g metric pound is used in many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (for example, pints for beer and cider in glasses in the UK —although pint means 568 mL; Jeroboams for champagne in France).
• A metric mile of 10 km is used in Norway and Sweden. The term metric mile is also used in some countries for the 1500 m foot race.
• In the US, blood glucose measurements are recorded in milligrams per decilitre (mg/dL), which normalises to cg/L. In Canada, Australia, New Zealand, Oceania, and Europe the standard is millimole per litre (mmol/L) or mM (millimolar).
• Blood pressure is usually measured in mmHg(≈Torr).
• Atmospheric pressure in government weather reports is measured in inHg in the USA,^[36] and in the SI unit hPa in Australia,^[37] UK^[38] and most other countries.

The fine-tuning that has happened to the metric base-unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the US customary units, are defined in SI units,^[39] any change in the definition of the SI units results in a change of the definition of the older units, as well.

International trade[link]

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 units of measurement directives, which catalogued the units of measure that might be used for, amongst other things, trade: the first was Directive 71/354/EEC^[40] issued in 1971, which required member states to standardise on SI rather than use the variety of cgs and mks units then in use. The second was Directive 80/181/EEC^{[41][42][43][44][45]} issued in 1979, which replaced the first and gave the United Kingdom and the Republic of Ireland a number of derogations from the original directive.

The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty, or were in universal use in worldwide trade. They also permitted the use of supplementary indicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, supplementary indicators have been allowed indefinitely.

Chinese characters[link]

Chinese expressway distances road sign in eastern Beijing. Although the primary text is in Chinese, the distances use internationally recognised characters.

In Japanese: Individual Chinese characters exist for some SI units, namely metre, litre, and gram, with the prefixes from kilo- (1000) to milli- (1/1000), yielding 21 (3×7) characters. These were created in Japan in the late 19th century (Meiji period) by choosing characters for the basic units – 米 "metre", 升 "litre", and 克 "gram" – and for the prefixes – 千 "kilo-, 1000", 百 "hecto-, 100", 十 "deca-, 10", 分 "deci-, 1/10", 厘 "centi-, 1/100", and 毛 "milli-, 1/1000" – and then combining them to form a single character, such as 粁 (米+千) for kilometre (in the case of no prefix, the base character alone is used). The entire metre series, for example, is 粁, 粨, 籵, 米, 粉, 糎, 粍. The symbols for the metric units are internationally-recognised Latin characters.

In Chinese: The basic units are 米 mǐ "metre", 升 shēng "litre", 克 kè "gram", and 秒 mǐao "second". Some sample prefixes are 分 fēn "deci", 厘 lí "centi", 毫 háo "milli", and 微 wēi "micro". These are not combined into a single character, so for example centimetres are simply 厘米 límǐ.

See also[link]

References[link]

Further reading[link]

• International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. Electronic version.
• BW Petley (2004). Symbols, Units, Nomenclature, & Fundamental Physical Constants.IUPAP-39. [1]
• Unit Systems in Electromagnetism
• MW Keller et al. Metrology Triangle Using a Watt Balance, a Calculable Capacitor, and a Single-Electron Tunneling Device
• “The Current SI Seen From the Perspective of the Proposed New SI”. Barry N. Taylor. Journal of Research of the National Institute of Standards and Technology, Vol. 116, No. 6, Pgs. 797-807, Nov-Dec 2011.

External links[link]

Official

• BIPM Bureau International des Poids et Mesures (SI maintenance agency) (home page)
  • BIPM brochure (SI reference)
• ISO 80000-1:2009 Quantities and units -- Part 1: General
• NIST Official Publications
  • NIST Special Publication 330, 2008 Edition: The International System of Units (SI)
  • NIST Special Publication 811, 2008 Edition: Guide for the Use of the International System of Units
  • NIST Special Pub 814: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy
• Weights and Measures Act, Canada
• IEEE/ASTM SI 10-2002 Standard for Use of the International System of Units (SI): The Modern Metric System (ANSI approved, joint IEEE/ASTM standard)
• Rules for SAE Use of SI (Metric) Units
• National Physical Laboratory, UK

Information

• International System of Units at the Open Directory Project
• EngNet Metric Conversion Chart Online Categorised Metric Conversion Calculator
• U.S. Metric Association. 2008. A Practical Guide to the International System of Units

History

• LaTeX SIunits package manual gives a historical background to the SI system.

Research

• The metrological triangle
• Recommendation of ICWM 1 (CI-2005)

Pro-metric advocacy groups

• The UK Metric Association
• The US Metric Association
• Canadian Metric Association
• Metrication US

Pro-customary measures pressure groups

• Pro-customary measures groups at the Open Directory Project

v t e SI units Base units Ampere · Candela · Kelvin · Kilogram · Metre · Mole · Second Derived units Becquerel · Coulomb · Degree Celsius · Farad · Gray · Henry · Hertz · Joule · Katal · Lumen · Lux · Newton · Ohm · Pascal · Radian · Siemens · Sievert · Steradian · Tesla · Volt · Watt · Weber Accepted for use with SI Dalton (Atomic mass unit) · Astronomical unit · Day · Decibel · Degree Celsius · Degree of arc · Electronvolt · Hectare · Hour · Litre · Minute · Minute of arc · Neper · Second of arc · Tonne Atomic units · Natural units See also SI prefixes · Systems of measurement · Conversion of units · New SI definitions · History of the metric system Book:International System of Units  · Category:SI base units

A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce. Scientifically, when later analyzed, some quantities are designated as fundamental units meaning all other needed units can be derived from them, whereas in the early and most historic eras, the units were given by fiat (See Statutory law) by the ruling entities and were not necessarily well inter-related or self-consistent.

History[link]

Although we might suggest that the Egyptians had discovered the art of measurement, it is only with the Greeks that the science of measurement begins to appear. The Greek's knowledge of geometry, and their early experimentation with weights and measures, soon began to place their measurement system on a more scientific basis. By comparison, Roman science, which came later, was not as advanced...^[1]

The French Revolution gave rise to the metric system, and this has spread around the world, replacing most customary units of measure. In most systems, length (distance), weight, and time are fundamental quantities; or as has been now accepted as better in science, the substitution of mass for weight, as a better more basic parameter. Some systems have changed to recognize the improved relationship, notably the 1824 legal changes to the imperial system.

Later science developments showed that either electric charge or electric current must be added to complete the minimum set of fundamental quantities by which all other metrological units may be defined. Other quantities, such as power, speed, etc. are derived from the fundamental set; for example, speed is distance per unit time. Historically a wide range of units was used for the same quantity, in several cultural settings, length was measured in inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, stadia, leagues, with conversion factors which were not simple powers of ten or even simple fractions within a given customary system.

Nor were they necessarily the same units (or equal units) between different members of similar cultural backgrounds. It must be understood by the modern reader that historically, measurement systems were perfectly adequate within their own cultural milieu, and the understanding that a better more universal system (based on more rationale and fundamental units) only gradually spread with the maturation and appreciation of the rigor characteristic of Newtonian physics. Moreover, changing a measurement system has real fiscal and cultural costs as well as the advantages that accrue from replacing one measuring system with a better one.

Once the analysis tools within that field were appreciated and came into widespread use in the emerging sciences, especially in the applied sciences like civil and mechanical engineering, pressure built up for conversion to a common basis of measurement. As people increasingly appreciated these needs and the difficulties of converting between numerous national customary systems became more widely recognised there was an obvious justification for an international effort to standardise measurements. The French Revolutionary spirit took the first significant and radical step down that road.

In antiquity, systems of measurement were defined locally, the different units were defined independently according to the length of a king's thumb or the size of his foot, the length of stride, the length of arm or per custom like the weight of water in a keg of specific size, perhaps itself defined in hands and knuckles. The unifying characteristic is that there was some definition based on some standard, however egocentric or amusing it may now seem viewed with eyes used to modern precision. Eventually cubits and strides gave way under need and demand from merchants and evolved to customary units.

In the metric system and other recent systems, a single basic unit is used for each fundamental quantity. Often secondary units (multiples and submultiples) are used which convert to the basic units by multiplying by powers of ten, i.e., by simply moving the decimal point. Thus the basic metric unit of length is the metre; a distance of 1.234 m is 1234.0 millimetres, or 0.001234 kilometres.

Current practice[link]

Metrication is complete or nearly complete in almost all countries of the world. US customary units are heavily used in the United States and to some degree Liberia. Traditional Burmese units of measurement are used in Burma. U.S. units are used in limited contexts in Canada due to a high degree of trade.

A number of other jurisdictions have laws mandating or permitting other systems of measurement in some or all contexts, such as the United Kingdom – where for example its road signage legislation only allows distance signs displaying imperial units (miles or yards)^[2] – or Hong Kong.^[3]

In the United States, metric units are widely used in science, military, and partially in industry, but customary units predominate in household use. At retail stores, the liter is a commonly used unit for volume, especially on bottles of beverages, and milligrams are used to denominate the amounts of medications, rather than grains. Also, other standardized measuring systems other than metric are still in universal international use, such as nautical miles and knots in international aviation.

Metric system[link]

Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795. During this evolution the use of these systems has spread throughout the world, first to non-English-speaking countries, and then to English speaking countries.

Multiples and submultiples of metric units are related by powers of ten and their names are formed with prefixes. This relationship is compatible with the decimal system of numbers and it contributes greatly to the convenience of metric units.

In the early metric system there were two fundamental or base units, the metre for length and the gram for mass. The other units of length and mass, and all units of area, volume, and compound units such as density were derived from these two fundamental units.

Mesures usuelles (French for customary measurements) were a system of measurement introduced to act as a compromise between the metric system and traditional measurements. It was used in France from 1812 to 1839.

A number of variations on the metric system have been in use. These include gravitational systems, the centimetre-gram-second systems (cgs) useful in science, the metre-tonne-second system (mts) once used in the USSR and the metre-kilogram-second system of units (mks) most commonly used today.

The current international standard metric system is the International System of Units (Système international d'unités or SI) It is an mks system based on the metre, kilogram and second as well as the kelvin, ampere, candela, and mole.

The SI includes two classes of units which are defined and agreed internationally. The first of these classes are the seven SI base units for length, mass, time, temperature, electric current, luminous intensity and amount of substance. The second of these are the SI derived units. These derived units are defined in terms of the seven base units. All other quantities (e.g. work, force, power) are expressed in terms of SI derived units.

Imperial and US customary units[link]

Both imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former British Empire but in most Commonwealth countries they have been largely supplanted by the metric system. They are still used for some applications in the United Kingdom but have been mostly replaced by the metric system in commercial, scientific, and industrial applications.

US customary units, however, are still the main system of measurement in the United States. While some steps towards metrication have been made (mainly in the late 1960s and early 1970s), the customary units have a strong hold due to the vast industrial infrastructure and commercial development. The effort is proceeding slowly due to the overwhelming financial cost of converting the existing infrastructure. US companies which trade internationally are more likely to use the metric system due to international standards and certifications such as ISO9000. The metric system is preferred in certain fields such as science, medicine, technology and the military. The building profession uses US customary units, though architects working internationally are increasingly adapting to the metric system.

While imperial and US customary systems are closely related, there are a number of differences between them. Units of length and area (the inch, foot, yard, mile etc.) are identical except for surveying purposes. The Avoirdupois units of mass and weight differ for units larger than a pound (lb.). The imperial system uses a stone of 14 lb., a long hundredweight of 112 lb. and a long ton of 2240 lb. The stone is not used in the US and the hundredweights and tons are short being 100 lb. and 2000 lb. respectively.

Where these systems most notably differ is in their units of volume. A US fluid ounce (fl oz) c. 29.6 millilitres (ml) is slightly larger than the imperial fluid ounce (28.4 ml). However, as there are 16 US fl oz to a US pint and 20 imp fl oz per imperial pint, these imperial pint is about 20% larger. The same is true of quarts, gallons, etc. Six US gallons are a little less than five imperial gallons.

The Avoirdupois system served as the general system of mass and weight. In addition to this there are the Troy and the Apothecaries' systems. Troy weight was customarily used for precious metals, black powder and gemstones. The troy ounce is the only unit of the system in current use; it is used for precious metals. Although the troy ounce is larger than its Avoirdupois equivalent, the pound is smaller. The obsolete troy pound was divided into twelve ounces opposed to the sixteen ounces per pound of the Avoirdupois system. The Apothecaries' system; traditionally used in pharmacology, now replaced by the metric system; shares the same pound and ounce as the troy system but with different further subdivisions.

Natural units[link]

Natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. Natural units are natural because the origin of their definition comes only from properties of nature and not from any human construct. Various systems of natural units are possible. Below are listed some examples.

• Geometric unit systems are useful in relativistic physics. In these systems the base physical units are chosen so that the speed of light and the gravitational constant are set equal to unity.
• Planck units are a form of geometric units obtained by also setting Boltzmann's constant, the Coulomb force constant and the reduced Planck constant to unity. They might be considered unique in that they are based only on properties of free space rather than any prototype, object or particle.
• Stoney units are similar to Planck units but set the elementary charge to unity and allow Planck's constant to float.
• "Schrödinger" units are also similar to Planck units and set the elementary charge to unity too but allow the speed of light to float.
• Atomic units (au) are a convenient system of units of measurement used in atomic physics, particularly for describing the properties of electrons. The atomic units have been chosen such that the fundamental electron properties are all equal to one atomic unit. They are similar to "Schrödinger" units but set the electron mass to unity and allow the gravitational constant to float. The unit energy in this system is the total energy of the electron in the Bohr atom and called the Hartree energy. The unit length is the Bohr radius.
• Electronic units are similar to Stoney units but set the electron mass to unity and allow the gravitational constant to float. They are also similar to Atomic units but set the speed of light to unity and allow Planck's constant to float.
• Quantum electrodynamical units are similar to the electronic system of units except that the proton mass is normalised rather than the electron mass.

Non-standard units[link]

Non-standard measurement units, sometimes found in books, newspapers etc., include:

Area[link]

• The American football field, which has a playing area 100 yards (91.4 m) long by 160 feet (48.8 m) wide. This is often used by the American public media for the sizes of large buildings or parks: easily walkable but non-trivial distances. Note that it is used both as a unit of length (100 yd/91.4 m, the length of the playing field excluding goal areas) and as a unit of area (57,600 sq ft/5,350 m²), about 1.32 acres (0.53 ha).
• British media also frequently uses the football pitch for equivalent purposes, although Association Football (Soccer) pitches are not of a fixed size, but instead can vary within defined limits (100–130 yd/91.4–118.9 m long, and 50–100 yd/45.7–91.4 m wide, giving an area of 5,000 to 13,000 sq yd/4,181 to 10,870 m²). However the UEFA Champions League field must be exactly 105 by 68 m (114.83 by 74.37 yd) giving an area of 7,140 m² (0.714 ha) or 8,539 sq yd (1.764 acres). Example: HSS vessels are aluminium catamarans about the size of a football pitch... - Belfast Telegraph 23 June 2007

Energy[link]

• A ton of TNT equivalent, and its multiples the kiloton, the megaton, and the gigaton. Often used in stating the power of very energetic events such as explosions and volcanic events and earthquakes and asteroid impacts. A gram of TNT as a unit of energy has been defined as 1000 thermochemical calories (1,000 cal/4,184 J).
• The atom bomb dropped on Hiroshima. Its force is often used in the public media and popular books as a unit of energy. (Its yield was roughly 13 kilotons, or 60 TJ.)
• One stick of dynamite

Units of currency[link]

A unit of measurement that applies to money is called a unit of account. This is normally a currency issued by a country or a fraction thereof; for instance, the US dollar and US cent (1/100 of a dollar), or the euro and euro cent.

ISO 4217 is the international standard describing three letter codes (also known as the currency code) to define the names of currencies established by the International Organization for Standardization (IOS).

Historical systems of measurement[link]

Throughout history, many official systems of measurement have been used. While no longer in official use, some of these customary systems are occasionally used in day to day life, for instance in cooking.

Afroasia[link]

• Arabic^[4]
• Egyptian
• Hebrew
• Maltese
• Mesopotamian

Asia[link]

• Chinese
• Hindu
• Japanese
• Persian
• Taiwanese
• Tamil
• Thai

Europe[link]

See also[link]

• Megalithic yard
• Pseudoscientific metrology
• Units of measurement
• Weights and measures

Conversion tables[link]

• Approximate conversion of units
• Conversion of units

Notes[link]

References[link]

• Tavernor, Robert (2007), Smoot's Ear: The Measure of Humanity, ISBN 0-300-12492-9

External links[link]

• A utility to Convert Different Units
• CLDR - Unicode localization of currency, date, time, numbers
• A Dictionary of Units of Measurement
• Old units of measure
• Measures from Antiquity and the Bible Antiquity and the Bible
• Reasonover's Land Measures A Reference to Spanish and French land measures (and their English equivalents with conversion tables) used in North America
• The Unified Code for Units of Measure

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The term international system may refer to:

• In politics, international relations
• In the sciences, the International System of Units (SI)

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