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{{Short description|Collection of units of measurement and rules relating them to each other}}
{{more citations needed|date=August 2015}}
{{redirect|Customary system|the system of measurement used in the United States, also known as the customary system|United States customary system}}

A '''system of units of measurement''', also known as a '''system of units''' or '''system of measurement''', is a collection of [[units of measurement]] and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and [[wikt:commerce|commerce]]. Instances in use include the [[International System of Units]] or {{Abbr|SI|Système international}} (the modern form of the [[metric system]]), the [[British imperial system]], and the [[United States customary system]].

==History==
{{see also|Units of measurement#History}}
{{further|History of measurement}}

In antiquity, ''systems of measurement'' were defined locally: the different units might be 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 maybe 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. Eventually ''[[cubit]]s'' and ''[[yard|strides]]'' gave way to "customary units" to meet the needs of merchants and scientists.

The preference for a more universal and consistent system only gradually spread with the growth of international trade and science. Changing a measurement system has costs in the near term, which often results in resistance to such a change. The substantial benefit of conversion to a more rational and internationally consistent system of measurement has been recognized and promoted by scientists, engineers, businesses and politicians, and has resulted in most of the world adopting a commonly agreed metric system.

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), [[mass]], and [[time]] are ''base quantities''.

Later, science developments showed that an electromagnetic quantity such as [[electric charge]] or electric current could be added to extend the set of base quantities. [[Gaussian units]] have only length, mass, and time as base quantities, with no separate electromagnetic dimension. Other quantities, such as [[Power (physics)|power]] and [[speed]], are derived from the base quantities: for example, speed is distance per unit time. Historically, a wide range of units was used for the same type of quantity.  In different contexts length was measured in [[inch]]es, [[Foot (length)|feet]], [[yards]], [[fathom]]s, [[Rod (unit)|rods]], [[Chain (unit)|chains]], [[furlong]]s, [[mile]]s, [[nautical mile]]s, [[stadia (length)|stadia]], [[League (unit)|leagues]], with conversion factors that were not based on power of ten.

In the metric system and other recent systems, underlying relationships between quantities, as expressed by formulae of physics such as [[Newton's laws of motion]], is used to select a small number of base quantities for which a unit is defined for each, from which all other units may be derived. Secondary units (multiples and submultiples) are derived from these base and derived units by multiplying by powers of ten.  For example, where the unit of length is the [[metre]]; a distance of 1&nbsp;metre is 1,000&nbsp;millimetres, or 0.001&nbsp;kilometres.

===Current practice===
{{main article|Metrication}}
Metrication is complete or nearly complete in most countries.

However, [[US customary units]] remain heavily used in the [[United States]] and to some degree in [[Liberia]]. Traditional [[Burmese units of measurement]] are used in [[Burma]], with partial transition to the metric system. U.S. units are used in limited contexts in Canada due to the large volume of trade with the U.S.  There is also considerable use of imperial weights and measures, despite ''de jure'' Canadian conversion to metric.

A number of other jurisdictions have laws mandating or permitting other systems of measurement in some or all contexts, such as the United Kingdom whose [[road signage legislation (UK)|road signage legislation]], for instance, only allows distance signs displaying [[imperial units]] (miles or yards)<ref name=TSRGD>{{cite web
|url = http://www.opsi.gov.uk/si/si2002/20023113.htm
|title = Statutory Instrument 2002 No. 3113 The Traffic Signs Regulations and General Directions 2002
|publisher = Her Majesty's Stationery Office (HMSO)
|year = 2002
|access-date = 18 March 2010}}</ref> or Hong Kong.<ref name="HK">[http://www.legislation.gov.hk/blis_ind.nsf/d2769881999f47b3482564840019d2f9/ca7c0e7895c7f088c82564760077b0c9?OpenDocument HK Weights and Measures Ordinance]</ref>

In the United States, metric units are virtually always used in science, frequently in the military, and partially in industry.  U.S. customary units are primarily used in U.S. households. At retail stores, the litre (spelled 'liter' in the U.S.) is a commonly used unit for volume, especially on bottles of beverages, and milligrams, rather than [[Grain (unit)|grains]], are used for medications. 

Some other non-[[SI]] units are still in international use, such as [[nautical mile]]s and [[knot (unit)|knots]] in aviation and shipping, and [[Foot (unit)|feet]] for aircraft altitude.

==Metric system==
{{Main article|Metric system|International System of Units}}
[[File:MetricImperialUSCustomaryUnits.jpg|thumb|upright|A baby bottle that measures in three measurement systems—metric, imperial (UK), and US customary]]

[[Metric system]]s 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 [[SI prefix|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 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 derived units such as density were derived from these two base units.

[[Mesures usuelles]] ([[French language|French]] for ''customary measures'') were a system of measurement introduced 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 metric system|gravitational systems]], the [[centimetre–gram–second system of units|centimetre–gram–second systems]] (cgs) useful in science, the [[metre–tonne–second system of units|metre–tonne–second system]] (mts) once used in the USSR and the [[metre–kilogram–second system of units|metre–kilogram–second system]] (mks). In some engineering fields, like [[computer-aided design]], millimetre–gram–second (mmgs) is also used.<ref>{{Cite web |title=Units and Dimension Standard - 2021 - SOLIDWORKS Help |url=https://help.solidworks.com/2021/english/SolidWorks/sldworks/hidd_units_dim_std.htm |access-date=2024-01-11 |website=help.solidworks.com}}</ref>

The current international standard for the metric system is the [[International System of Units]] ({{Lang|fr|Système international d'unités}} or SI). It is a system in which all units can be expressed in terms of seven units.  The units that serve as the [[SI base unit]]s are the [[metre]], [[kilogram]], [[second]], [[ampere]], [[kelvin]], [[mole (unit)|mole]], and [[candela]].

==British imperial and US customary units==
{{Main article|Imperial and US customary measurement systems|Imperial units|US customary units}}
Both [[British imperial units]] and [[United States customary units|US customary units]] derive from earlier [[English unit]]s. Imperial units were mostly used in the former [[British Empire]] and the [[Commonwealth of Nations|British Commonwealth]], but in all these 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 [[commerce|commercial]], [[scientific]], and [[Industrial sector|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.

While British imperial and US customary systems are closely related, there are a number of [[Comparison of the imperial and US customary measurement systems|differences between them]]. Units of length and area (the [[inch]], [[foot (unit)|foot]], [[yard]], [[mile]], etc.) have been identical since the adoption of the [[International Yard and Pound Agreement]]; however, the US and, formerly, India retained older definitions for surveying purposes. This gave rise to the US [[survey foot]], for instance. The [[avoirdupois]] units of mass and weight differ for units larger than a [[pound (mass)|pound]] (lb). The British imperial system uses a stone of 14&nbsp;lb, a [[long hundredweight]] of 112&nbsp;lb and a [[long ton]] of 2,240&nbsp;lb. The [[Stone (unit)|stone]] is not a measurement of weight used in the US. The US customary system uses the [[short hundredweight]] of 100&nbsp;lb and [[short ton]] of 2,000&nbsp;lb.

Where these systems most notably differ is in their units of volume. An imperial fluid ounce of 28.4130625&nbsp;ml is 3.924% smaller than the US [[fluid ounce]] (fl&nbsp;oz) of  29.5735295625 [[millilitre]]s (ml). However, as there are 16&nbsp;US&nbsp;fl&nbsp;oz to a US [[pint]] and 20&nbsp;imp&nbsp;fl&nbsp;oz to an imperial pint, the imperial pint is 20.095% larger than a US pint, and the same is true for [[gill (unit)|gill]]s, [[quart]]s, and [[gallon]]s: six US gallons (22.712470704 L) is only 0.08% less than five imperial gallons (22.73045 L).

The [[avoirdupois]] system served as the general system of mass and weight. In addition to this, there are the [[Troy weight|troy]] and the [[apothecaries' system]]s. Troy weight was customarily used for [[precious metal]]s, [[black powder]], and [[gemstone]]s. 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 12 ounces, rather than the 16 ounces per pound of the avoirdupois system. The apothecaries' system was traditionally used in [[pharmacology]], but has now been replaced by the metric system; it shared the same pound and ounce as the troy system but with different further subdivisions.

==Natural units==
[[Natural units]] are [[units of measurement]] defined in terms of universal [[physical constants]] in such a manner that selected physical constants take on the numerical value of one when expressed in terms of those units.  Natural units are so named because their definition relies on only properties of [[nature]] and not on any human construct. Varying systems of natural units are possible, depending on the choice of constants used.

Some examples are as follows:
* [[Geometrized unit system]]s are useful in [[Theory of relativity|relativistic physics]]. In these systems, [[speed of light]] and the [[gravitational constant]] are among the constants chosen.
* [[Planck units]] is system of geometrized units in which the [[reduced Planck constant]] is included in the list of defining constants. It is based on only properties of [[free space]] rather than of any object or particle.
* [[Stoney units]] is a system of geometrized units in which the [[Coulomb constant]] and the [[elementary charge]] are included.
* [[Atomic units]] are a system of units used in [[atomic physics]], particularly for describing the properties of [[electron]]s. The atomic units have been chosen to use several constants relating to the electron: the [[electron mass]], the [[elementary charge]], the [[Coulomb constant]] and the [[reduced Planck constant]]. The unit of [[energy]] in this system is the total energy of the [[electron]] in the [[Bohr atom]] and called the [[Hartree energy]]. The unit of length is the [[Bohr radius]].

==Non-standard units==
[[List of unusual units of measurement|Non-standard measurement units]] also found in books, newspapers etc., include:

===Area===
* The [[American football#Field and players|American football field]], which has a playing area {{convert|100|yd|m|1|lk=in}} long by {{convert|160|ft|m|1}} wide. This is often used by the [[United States|American]] public media for the sizes of large buildings or parks. It is used both as a unit of length ({{convert|100|yd|m|1|abbr=on|disp=or}}, the length of the playing field excluding goal areas) and as a unit of area ({{convert|57600|sqft|m2|abbr=on|disp=or}}), about {{convert|1.32|acre|ha|lk=on}}.
* British media also frequently uses the [[Association football pitch|football pitch]] for equivalent purposes, although [[soccer]] pitches are not of a fixed size, but instead can vary within defined limits ({{convert|100|-|130|yd|m|1|abbr=on|disp=or}} long, and {{convert|50|-|100|yd|m|1|abbr=on|disp=or}} wide, giving an area of {{convert|5000|to|13000|sqyd|m2|0|abbr=on|disp=or}}). However the [[UEFA Champions League]] field must be exactly {{convert|105|by|68|m|yd|2|abbr=on}} giving an area of {{convert|7140|m2|ha|abbr=on}} or {{convert|8539|sqyd|acre|abbr=on|lk=on}}. For example, "[[High-speed Sea Service|HSS vessels]] are aluminium catamarans '''about the size of a football pitch'''."<ref>{{Cite web|last=Henry|first=Lesley-Anne|date=23 June 2007|title=Sad sight of a superferry laid up due to soaring jet fuel bills|url=http://www.belfasttelegraph.co.uk/news/local-national/article2698634.ece|url-status=dead|archive-url=https://web.archive.org/web/20081006162911/http://www.belfasttelegraph.co.uk/news/local-national/article2698634.ece|archive-date=2008-10-06|website=The [[Belfast Telegraph]]}}</ref>
* Larger areas are also expressed as a multiple of the areas of states and countries understood to be familiar to the reader.

===Energy===
* 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 [[explosion]]s and [[volcanic]] events and [[earthquakes]] and [[asteroid]] impacts. A [[gram]] of TNT as a unit of [[energy]] has been defined as 1000 thermochemical calories ({{convert|1000|cal|J|0|abbr=on|lk=on|disp=or}}).
* The [[Little Boy|atom bomb dropped on Hiroshima]]. Its energy yield 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==
A unit of measurement that applies to [[money]] is called a [[unit of account]] in economics and unit of measure in accounting.<ref>[http://fasri.net/wp-content/uploads/2009/12/Johnso2007n--Unit-of-Acct-Paper.pdf Financial Accounting Standards Research Initiative: The Unit of Account Issue]{{Dead link|date=June 2018 |bot=InternetArchiveBot |fix-attempted=no }}</ref> This is normally a [[currency]] issued by a [[country]] or a fraction thereof; for instance, the [[United States dollar|US dollar]] and US cent ({{frac|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 (ISO).

==Historical systems of measurement==
{{Main article|History of measurement}}

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]].

===Africa===
{{div col|colwidth=22em}}
* [[Algerian units of measurement|Algerian]]
* [[Egyptian units of measurement|Egyptian]]
* [[Ethiopian units of measurement|Ethiopian]]
* [[Eritrean units of measurement|Eritrean]]
* [[Guinean units of measurement|Guinean]]
* [[Libyan units of measurements|Libyan]]
* [[Malagasy units of measurement|Malagasy]]
* [[Mauritian units of measurement|Mauritian]]
* [[Moroccan units of measurement|Moroccan]]
* [[Seychellois units of measurement|Seychellois]]
* [[Somalian units of measurement|Somalian]]
* [[Tunisian units of measurement|Tunisian]]
* [[South African units of measurement|South African]]
* [[Tanzanian units of measurement|Tanzanian]]
{{div col end}}

===Asia===
{{see also|History of measurement systems in India}}
{{div col|colwidth=22em}}
* [[Ancient Arabic weights and measures|Arabic]]<ref>M. Ismail Marcinkowski, ''Measures and Weights in the Islamic World. An English Translation of Professor Walther Hinz's Handbook "Islamische Maße und Gewichte"'', with a foreword by Professor Bosworth, F.B.A. Kuala Lumpur, ISTAC, 2002, {{ISBN|983-9379-27-5}}. This work is an annotated translation of a work in German by the late German orientalist Walther Hinz, published in the ''Handbuch der Orientalistik'', erste Abteilung, Ergänzungsband I, Heft 1, Leiden, The Netherlands: E. J. Brill, 1970.</ref>
* [[Afghan units of measurement|Afghan]]
* [[Cambodian units of measurement|Cambodian]]
* [[Chinese units of measurement|Chinese]]
** [[Hong Kong units of measurement|Hong Kong]]
* [[Ancient Hebrew weights and measures|Hebrew]] ([[Biblical and Talmudic units of measurement|Biblical and Talmudic]])
* [[Indian units of measurement|Indian]]
* [[Indonesian units of measurement|Indonesian]]
* [[Japanese units of measurement|Japanese]]
* [[Korean units of measurement|Korean]]
* [[Omani units of measurement|Omani]]
* [[History of measurement systems in Pakistan|Pakistani]]
* [[Philippine units of measurement|Philippine]]
* [[Ancient Mesopotamian weights and measures|Mesopotamian]]
* [[Ancient Persian weights and measures|Persian]]
* [[Singaporean units of measurement|Singaporean]]
* [[Sri Lankan units of measurement|Sri Lankan]]
* [[Syrian units of measurement|Syrian]]
* [[Taiwanese units of measurement|Taiwanese]]
* [[Tamil units of measurement|Tamil]]
* [[Thai units of measurement|Thai]]
* [[Vietnamese units of measurement|Vietnamese]]
* [[Nepalese units of measurement|Nepalese]]

Still in use:
* [[Myanmar units of measurement|Myanmar]]
{{div col end}}

===Europe===
{{div col|colwidth=22em}}

* [[Ancient Greek units of measurement|Ancient Greek]]
* [[Belgian units of measurement|Belgian]]
* [[Byzantine units of measurement|Byzantine]]
* [[Czech units of measurement|Czech]]
* [[Cypriot units of measurement|Cypriot]]
* [[Danish unit|Danish]]
* [[Dutch unit|Dutch]]
* [[English unit|English]]
* [[Estonian units of measurement|Estonian]]
* [[Finnish unit|Finnish]]
* [[French units of measurement|French]] (now)
* [[Units of measurement in France before the French Revolution|French]] (to 1795)
* [[German unit|German]]
* [[Greek units of measurement|Greek]]
* [[Hungarian units of measurement|Hungary]]
* [[Icelandic units of measurement|Icelandic]]
*[[Old Irish units of measurement|Irish]]
* [[Italian units of measurement|Italian]]
* [[Latvian units of measurement|Latvian]]
* [[Luxembourgian units of measurement|Luxembourgian]]
* [[Maltese units of measurement|Maltese]]
* [[Norwegian units of measure|Norwegian]]
* [[Old Polish units of measurement|Polish]]
* [[Portuguese customary units|Portuguese]]
* [[Ancient Roman weights and measures|Roman]]
* [[Romanian units of measurement|Romanian]]
* [[Obsolete Russian weights and measures|Russian]]
* [[Obsolete Scottish units of measurement|Scottish]]
* [[Serbian units of measurement|Serbian]]
* [[Slovak units of measurement|Slovak]]
* [[Spanish customary units|Spanish]]
* [[Swedish unit|Swedish]]
* [[Swiss units of measurement|Switzerland]]
* [[Ottoman units of measurement|Turkish]]
* [[Obsolete Tatar weights and measures|Tatar]]
* [[Welsh units of measurement|Welsh]]
{{div col end}}

===North America===

{{div col |colwidth=22em}}

* [[Costa Rican units of measurement|Costa Rican]]
* [[Cuban units of measurement|Cuban]]
* [[Haitian units of measurement|Haitian]]
* [[Honduran units of measurement|Honduran]]
* [[Mexican units of measurement|Mexico]]
* [[Nicaraguan unit of measurement|Nicaraguan]]
*[[Puerto Rican units of measurement|Puerto Rican]]
{{div col end}}

===South America===

{{div col|colwidth=22em}}
*[[Argentine units of measurement|Argentine]]
*[[Bolivian units of measurement|Bolivian]]
*[[Brazilian units of measurement|Brazilian]]
*[[Chilean units of measurement|Chilean]]
*[[Colombian units of measurement|Colombian]]
*[[Paraguayan units of measurement|Paraguayan]]
*[[Peruvian units of measurement|Peruvian]]
*[[Uruguayan units of measurement|Uruguayan]]
*[[Venezuelan units of measurement|Venezuelan]]
{{div col end}}

==Ancient==

{{div col|colwidth=22em}}
*[[Ancient Arabic units of measurement|Arabic]]
*[[Biblical and Talmudic units of measurement|Biblical and Talmudic]]
*[[Ancient Egyptian units of measurement|Egyptian]]
*[[Ancient Greek units of measurement|Greek]]
*[[Hindu units of time|Hindu (time)]]
*[[History of measurement systems in India|Indian]]
*[[Ancient Mesopotamian units of measurement|Mesopotamian]]
*[[Persian units of measurement|Persian]]
*[[Ancient Roman units of measurement|Roman]]
{{div col end}}

==See also==
* [[Conversion of units]]
* [[History of the metric system]]
* [[ISO 31]]
* [[Level of measurement]]
* [[Medieval weights and measures]]
* [[Megalithic yard]]
* [[Petrograd Standard]]
* [[Pseudoscientific metrology]]
* [[Unified Code for Units of Measure]]
* [[Weights and measures]]

== Notes and references ==
{{Reflist|30em}}

==Bibliography==
* Tavernor, Robert (2007), ''Smoot's Ear: The Measure of Humanity'', {{ISBN|0-300-12492-9}}

==External links==
{{Commons category|Customary units of measurement}}
*[https://www.unicode.org/cldr/index.html CLDR – Unicode localization of currency, date, time, numbers]
*[http://www.unc.edu/~rowlett/units A Dictionary of Units of Measurement]
*[https://web.archive.org/web/20041210085422/http://www.du.edu/~jcalvert/tech/oldleng.htm Old units of measure]
*[http://members.aol.com/JackProot/met/antbible.html Measures from Antiquity and the Bible] {{webarchive |url=https://web.archive.org/web/20080510212126/http://members.aol.com/JackProot/met/antbible.html |date=May 10, 2008 |title=Antiquity and the Bible }}
*Reasonover's Land Measures [http://www.booksontexas.com/Reasonover_s_Land_Measures_p/reas05.htm A Reference to Spanish and French land measures (and their English equivalents with conversion tables) used in North America]
*[https://web.archive.org/web/20060226162744/http://aurora.regenstrief.org/~schadow/units/UCUM/ucum.html The Unified Code for Units of Measure]

{{Systems of measurement}}
{{SI units}}

[[Category:Systems of units|*]]
[[Category:Measurement]]