Units of measurement

{{short description|Quantity standard}} {{distinguish|Level of measurement}} {{redirect|Unit of measure}} {{redirect|Weights and measures}} {{pp-move}} {{use dmy dates|date=December 2020}}

[[File:Weights and Measures office.jpg|thumb|upright=1.5|right|The former Weights and Measures office in [[Seven Sisters, London]]]] [[File:Unità di misura - Palazzo della Ragione - Padova.jpg|thumb|upright=1.5|right|Units of measurement, [[Palazzo della Ragione, Padua]]]]

A '''unit of measurement''', or '''unit of measure''', is a definite [[magnitude (mathematics)|magnitude]] of a [[quantity]], defined and adopted by convention or by law, that is used as a standard for measurement of the same [[kind of quantity]].{{VIM3rd|term=measurement unit|pages=6–7}}. Any other quantity of that kind can be expressed as a multiple of the unit of measurement,{{Cite web|url=http://www.ibiblio.org/units/|title=Units of Measurement|website=www.ibiblio.org}} For example, a length is a [[physical quantity]]. The [[metre]] (symbol: m) is a [[unit of length]] that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is meant is 10 times the definite predetermined length called "metre".

The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present. A multitude of [[System of measurement|systems of units]] used to be very common. Now there is a global standard, the [[International System of Units]] (SI), which is the modern form of the [[metric system]], replacing the [[Centimetre–gram–second system of units|cgs system]].

In trade, '''weights and measures''' are often a subject of governmental regulation, to ensure fairness and transparency. The [[International Bureau of Weights and Measures]] (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the [[International System of Units|International System of Units (SI)]].{{Cite web |title=1-Mission Role and Objectives |url=https://www.bipm.org/en/-/mission-role-objectives |access-date=2025-01-23 |website=BIPM |language=en-US}}

[[Metrology]] is the science of developing nationally and internationally accepted units of measurement.{{cite web |title=''What is metrology?'' Celebration of the signing of the Metre Convention, World Metrology Day 2004 |url=http://www.bipm.org/en/convention/wmd/2004/ |publisher=BIPM |year=2004 |access-date=2025-01-22 |url-status=dead |archive-url=https://web.archive.org/web/20110927012931/http://www.bipm.org/en/convention/wmd/2004/ |archive-date=2011-09-27 }} In [[physics]] and metrology, units are standards for [[measurement]] of physical quantities that need clear definitions to be useful. [[Reproducibility]] of experimental results is central to the [[scientific method]]. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures historically developed for commercial purposes.{{Cite web|url=https://www.texasgateway.org/resource/13-language-physics-physical-quantities-and-units|title=1.3 The Language of Physics: Physical Quantities and Units | Texas Gateway|website=www.texasgateway.org}}

[[Science]], [[medicine]], and [[engineering]] often use larger and smaller units of measurement than those used in everyday life. The judicious selection of the units of measurement can aid researchers in [[problem solving]] (see, for example, [[dimensional analysis]]).

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

A unit of measurement is a standardized [[quantity]] of a physical property, used as a factor to express occurring quantities of that property. Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks, some of those tasks are: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Before the establishment of the decimal [[metric system]] in France during the [[French Revolution]] in the late [[18th century]],{{cite journal |last1=Débarbat |first1=Suzanne |author-link=Suzanne Débarbat |last2=Quinn |first2=Terry |date=1 January 2019 |title=Les origines du système métrique en France et la Convention du mètre de 1875, qui a ouvert la voie au Système international d'unités et à sa révision de 2018 |journal=Comptes Rendus Physique |series=The new International System of Units / Le nouveau Système international d’unités |language=fr |volume=20 |issue=1 |pages=6–21 |bibcode=2019CRPhy..20....6D |doi=10.1016/j.crhy.2018.12.002 |issn=1631-0705 |doi-access=free}} many units of length were determined by the size of parts of the [[human body]].{{cite journal |last1=Kaaronen |first1=Roope O. |last2=Manninen |first2=Mikael A. |last3=Eronen |first3=Jussi T. |date=2023-06-02 |title=Body-based units of measure in cultural evolution |url=https://www.science.org/doi/10.1126/science.adf1936 |journal=Science |volume=380 |issue=6648 |pages=948–954 |doi=10.1126/science.adf1936|pmid=37262170 |bibcode=2023Sci...380..948K |url-access=subscription }}

The earliest known uniform systems of measurement seem to have all been created sometime in the [[4th millennium BC|4th]] and [[3rd millennium BC|3rd millennia BC]] among the ancient peoples of [[Mesopotamia]], [[Ancient Egypt|Egypt]] and the [[Indus Valley civilisation|Indus Valley]], and perhaps also [[Elam]] in [[Iran|Persia]] as well.{{cite web |date=2019-12-09 |title=Ancient units of measurement {{!}} Ancient Ports - Ports Antiques |url=https://www.ancientportsantiques.com/ancient-measures/units-of-measure/ |access-date=2025-11-22 |language=en-GB}}{{Cite journal |last=Stein |first=Ben P. |date=2022-03-30 |title=From the Noggin to the Butt: Quirky Measurement Units Throughout Human History |url=https://www.nist.gov/blogs/taking-measure/noggin-butt-quirky-measurement-units-throughout-human-history |journal=NIST |language=en}}

Weights and measures are mentioned in the [[Bible]] (Leviticus 19:35–36). It is a commandment to be honest and have fair measures.

In the ''[[Magna Carta]]'' of 1215 (The Great Charter) with the seal of [[John, King of England|King John]], put before him by the Barons of England, King John agreed in Clause 35 "There shall be one measure of wine throughout our whole realm, and one measure of ale and one measure of corn—namely, the London quart;—and one width of dyed and russet and [[hauberk]] cloths—namely, two ells below the selvage..."

As of the 21st century, the International System is predominantly used in the world. There exist other unit systems which are used in many places such as the [[United States customary units|United States Customary System]] and the [[Imperial units|Imperial System]]. The United States is the only industrialized country that has not yet at least mostly converted to the metric system.{{cite book |last=Giunta |first=Carmen J. |title=A Brief History of the Metric System |chapter-url=https://link.springer.com/10.1007/978-3-031-28436-6_6 |chapter=The Metric System and the United States |series=SpringerBriefs in Molecular Science |date=2023 |publisher=Springer International Publishing |isbn=978-3-031-28435-9 |location=Cham |pages=69–78 |language=en |doi=10.1007/978-3-031-28436-6_6}} The systematic effort to develop a universally acceptable system of units dates back to 1790 when the [[National Assembly (France)|French National Assembly]] charged the French Academy of Sciences to come up such a unit system. This system was the precursor to the metric system which was quickly developed in France but did not take on universal acceptance until 1875 when The Metric Convention Treaty was signed by 17 nations. After this treaty was signed, a [[General Conference on Weights and Measures|General Conference of Weights and Measures]] (CGPM) was established. The CGPM produced the current SI, which was adopted in 1954 at the 10th Conference of Weights and Measures. Currently, the United States is a dual-system society which uses both the SI and the US Customary system.{{cite book |author=Yunus A. Çengel |author2=Michael A. Boles|title=Thermodynamics: An Engineering Approach|publisher=McGraw Hill |isbn=9780073398174|pages=996|edition=Eighth|date=2002}}{{cite book |last1=Dodd |first1=Richard |title=Using SI Units in Astronomy |date=2012 |publisher=Cambridge University Press |isbn=9780521769174 |pages=246 |doi=10.1017/CBO9781139019798}}

== Definition == The formal definition of ''unit of measurement'' (or ''measurement unit'') is

== Systems of units == {{main|System of measurement}} The use of a single unit of measurement for some quantity has obvious drawbacks. For example, it is impractical to use the same unit for the distance between two cities and the length of a needle. Thus, historically they would develop independently. One way to make large numbers or small fractions easier to read, is to use [[unit prefixes]].

At some point in time though, the need to relate the two units might arise, and consequently the need to choose one unit as defining the other or vice versa. For example, an [[inch]] could be defined in terms of a [[Barleycorn (unit)|barleycorn]]. A system of measurement is a collection of units of measurement and rules relating them to each other.

As [[science]] progressed, a need arose to relate the measurement systems of different quantities, like length and weight and volume. The effort of attempting to relate different traditional systems between each other exposed many inconsistencies, and brought about the development of new units and systems.

Systems of units vary from country to country. Some of the different systems include the [[Centimetre–gram–second system of units|centimetre–gram–second]], [[Foot–pound–second system of units|foot–pound–second]], [[MKS system of units|metre–kilogram–second]] systems, and the [[International System of Units]], SI. Among the different systems of units used in the world, the most widely used and internationally accepted one is SI. The [[SI base unit|base SI unit]]s are the second, metre, kilogram, ampere, kelvin, mole and candela; all [[SI derived unit|other SI units]] are derived from these base units.{{Cite web|url=https://www.helpyoubetter.com/measurement-in-physics-and-si-units-of-measurement/|title=Measurement in Physics & SI units of Measurement|date=15 November 2018|website=HelpYouBetter|language=en-US|access-date=15 August 2019|archive-date=16 January 2021|archive-url=https://web.archive.org/web/20210116211910/https://www.helpyoubetter.com/measurement-in-physics-and-si-units-of-measurement/|url-status=dead}} {{cite web |title = 9th edition of the SI Brochure |publisher = BIPM |date = 2019 |url = https://www.bipm.org/en/publications/si-brochure/ |access-date = 2019-05-20 }}{{rp|132}}

Systems of measurement in modern use include the [[metric system]], the [[imperial system]], and [[United States customary units]].

=== Traditional systems === Historically many of the systems of measurement which had been in use were to some extent based on the dimensions of the human body. Such units, which may be called [[anthropic units]], include the [[cubit]], based on the length of the forearm; the [[Pace (unit)|pace]], based on the length of a stride; and the [[Foot (unit)|foot]] and [[Hand (unit)|hand]].Crease, Robert P. World in the balance: The historic quest for an absolute system of measurement. WW Norton & Company, 2011.{{rp|25}} As a result, units of measure could vary not only from location to location but from person to person. Units not based on the human body could be based on agriculture, as is the case with the [[furlong]], [[acre]] and [[carucate]], each based on the amount of land able to be worked by a team of [[oxen]].[[Brampton, Norfolk|Brampton]] Parish Council, [https://brampton-norfolk.norfolkparishes.gov.uk/2010/11/28/a-caracute-and-a-virgate/ Brampton, Norfolk], accessed on 18 February 2025

=== Metric systems === {{main|International System of Units}} [[Metric system]]s of units have [[History of the metric system|evolved since the adoption of the original metric system]] in [[France]] in 1791. The current international standard metric system is the [[SI|International System of Units]] (abbreviated to SI). An important feature of modern systems is [[standardization]]. Each unit has a universally recognized size. [[File:Tabella conversione metrica 1860 MG 7771.jpg|thumb|An example of [[metrication]] in 1860 when Tuscany became part of modern Italy (ex. one "libbra" = 339.54 grams)]]

Both the [[imperial units]] and [[US customary units]] derive from earlier [[English units of measurement|English unit]]s. Imperial units were mostly used in the [[Commonwealth of Nations|British Commonwealth]] and the former [[British Empire]]. US customary units are still the main system of measurement used in the [[United States]] outside of science, medicine, many sectors of industry, and some of government and military, and despite Congress having legally authorised metric measure on 28 July 1866. {{cite web |url = http://lamar.colostate.edu/~hillger/laws/metric-act.html |title = US Metric Act of 1866 |url-status = dead |archive-url = https://web.archive.org/web/20141010211054/http://lamar.colostate.edu/~hillger/laws/metric-act.html |archive-date = 10 October 2014 |df = dmy-all }} as amended by Public Law 110–69 dated 9 August 2007 Some steps towards US [[metrication]] have been made, particularly the redefinition of basic US and imperial units to derive exactly from SI units. Since the [[international yard and pound]] agreement of 1959 the US and imperial inch is now defined as exactly {{val|0.0254|ul=m}}, and the US and [[Avoirdupois|imperial avoirdupois pound]] is now defined as exactly {{val|0.45359237|ul=kg}}.{{cite web |url = http://ts.nist.gov/WeightsAndMeasures/h44-04.cfm |title = NIST Handbook 44 Appendix B |year = 2002 |publisher = [[National Institute of Standards and Technology]] |url-status = dead |archive-url = https://web.archive.org/web/20070213121133/http://ts.nist.gov/WeightsAndMeasures/h44-04.cfm |archive-date = 13 February 2007 |df = dmy-all |access-date = 18 February 2007 }}

=== Natural systems === {{main | Natural units}} While the above systems of units are based on arbitrary unit values, formalised as standards, [[natural units]] in physics are based on physical principle or are selected to make physical equations easier to work with. For example, [[atomic units]] (au) were designed to simplify the wave equation in [[atomic physics]].{{Cite journal|last=Hartree|first=D. R.|title=The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods|year=1928|journal = [[Mathematical Proceedings of the Cambridge Philosophical Society]] | publisher = Cambridge University Press | volume = 24 | issue = 1 | pages = 89–110 | url = http://journals.cambridge.org/action/displayAbstract?aid=1733252 | doi = 10.1017/S0305004100011919|bibcode = 1928PCPS...24...89H |url-access = subscription }}

Some [[List of unusual units of measurement|unusual and non-standard units]] may be encountered in sciences. These may include the [[solar mass]] ({{val|2|e=30|u=kg}}), the [[TNT equivalent|megaton]] (the energy released by detonating one million tons of [[trinitrotoluene]], TNT) and the [[electronvolt]].

=== Legal control of weights and measures === To reduce the incidence of retail fraud, many national [[statutes]] have standard definitions of weights and measures that may be used (hence "[[statute measure]]"), and these are verified by legal officers.{{citation needed|date=November 2019}}

=== Informal comparison to familiar concepts === {{main|List of non-coherent units of measurement}} In informal settings, a quantity may be described as multiples of that of a familiar entity, which can be easier to contextualize than a value in a formal unit system. For instance, a publication may describe an area in a foreign country as a number of multiples of the area of a region local to the readership. The propensity for certain concepts to be used frequently can give rise to loosely defined "systems" of units.{{cite news |last1=Marsh |first1=David |title=Mind your language: Wales, Belgium and other units of measurement |url=https://www.theguardian.com/media/mind-your-language/2010/may/17/mind-your-language-david-marsh |access-date=30 August 2018 |work=the Guardian |date=17 May 2010 |language=en}}{{cite news |title=Size of Wales |url=https://www.economist.com/johnson/2010/06/11/size-of-wales |access-date=30 August 2018 |newspaper=The Economist |language=en}}

== Base and derived units == {{main|Base unit of measurement}}

For most quantities, a unit is necessary to communicate values of that physical quantity. For example, it is necessary to use some form of unit to convey to someone a particular length, because a length can be described only in relation to an understood defined quantity, such as another length that is known to both people.

Not all quantities require a dedicated unit. Using physical laws, units of quantities can be expressed in terms of a combination of unit for other quantities. This allows a small set of units to be used to define all others. These units are taken as the ''base units'' and the other units are ''derived units''. Thus, base units are the units of the quantities that are independent of other quantities. In the SI, these are the units of length, mass, time, electric current, temperature, luminous intensity and amount of substance. Derived units are the units of the quantities that are derived from the base quantities and some of the derived units are the units of speed, work, acceleration, energy, pressure, etc.

Different systems of units are based on different choices of a set of related units including fundamental and derived units.

== Physical quantity components == {{excerpt|Physical quantity#Value}}

==Dimensional homogeneity== {{main|Dimensional homogeneity}}

Units can only be added or subtracted if they are the same type; however units can always be multiplied or divided, as [[George Gamow]] used to explain. Let Z be "2 metres" and W "3 seconds", then{{fact|date=December 2025}} : 2,\mathrm{metres} \times 3,\mathrm{seconds} = {Z}{W} \times [Z][W] = 6 , \mathrm{metres} \times \mathrm{seconds}.

There are certain rules that apply to units:{{fact|date=December 2025}}

• Only like terms may be added. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied or divided, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metre per second (m/s). See [[dimensional analysis]]. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m2/s2). Put simply, units obey the laws of indices. (See [[Exponentiation]].)
• Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to 1 kg⋅m/s2. Thus a quantity may have several unit designations, for example: the unit for [[surface tension]] can be referred to as either N/m (newton per metre) or kg/s2 (kilogram per second squared).

== Converting units of measurement == {{excerpt|Conversion of units}}

== In software development ==

Software developers in a wide variety of fields including scientific, healthcare and financial applications have sought to adopt approaches that reduce bugs and mistakes involving units of measurement. In object-oriented programming, this is often achieved using the Quantity [[Software design pattern|pattern]] to pair together the value and the unit.{{Cite book |last=Fowler |first=Martin |title=Analysis patterns: reusable object models |date=1997 |publisher=Addison Wesley |isbn=978-0-201-89542-1 |series=The Addison-Wesley series in object-oriented software engineering |location=Menlo Park, California|pages=36–38}} (In financial applications, it is common to represent monetary values by storing them with the currency—this is often known as the 'Money pattern'.){{Cite web |title=Money |url=https://www.martinfowler.com/eaaCatalog/money.html |access-date=2025-03-23 |website=martinfowler.com}} The programming language [[F Sharp (programming language)|F#]] has syntactic support for representing units of measure, converting between them, and checking their type safety at compile-time.{{Cite web | date=2023-10-14 |title=Units of Measure - F# |url=https://learn.microsoft.com/en-us/dotnet/fsharp/language-reference/units-of-measure |access-date=2025-03-23 |website=learn.microsoft.com |language=en-us}}

== Real-world implications == One example of the importance of agreed units is the failure of the [[NASA]] [[Mars Climate Orbiter]], which was accidentally destroyed on a mission to Mars in September 1999 (instead of entering orbit) due to miscommunications about the value of forces: different computer programs used different units of measurement ([[Newton (unit)|newton]] versus [[pound force]]). Considerable amounts of effort, time, and money were wasted. {{cite web |url = http://lamar.colostate.edu/~hillger/unit-mixups.html |title = Unit Mixups |publisher = US Metric Association |url-status = dead |archive-url = https://web.archive.org/web/20100923105150/http://lamar.colostate.edu/~hillger/unit-mixups.html |archive-date = 23 September 2010 |df = dmy-all }} {{cite web |url = ftp://ftp.hq.nasa.gov/pub/pao/reports/1999/MCO_report.pdf |publisher = NASA |date = 10 November 1999 |archive-url = https://web.archive.org/web/20151213144352/ftp://ftp.hq.nasa.gov/pub/pao/reports/1999/MCO_report.pdf |archive-date = 2015-12-13 |url-status = dead |title = Mars Climate Orbiter Mishap Investigation Board Phase I Report }}

On 15 April 1999, [[Korean Air]] cargo [[Korean Air Cargo Flight 6316|flight 6316]] from [[Shanghai]] to [[Seoul]] was lost due to the crew confusing tower instructions (in metres) and altimeter readings (in feet). Three crew and five people on the ground were killed. Thirty-seven were injured. {{cite press release |url = https://www.ntsb.gov/pressrel/1999/990427.htm |title = Korean Air Flight 6316 |publisher = [[NTSB]] |url-status = live |archive-url = https://web.archive.org/web/20061006234603/https://www.ntsb.gov/Pressrel/1999/990427.htm |archive-date= 6 October 2006 |df = dmy-all }} {{cite web |url = http://aviation-safety.net/database/record.php?id=19990415-0 |title = Korean Air incident |publisher = Aviation Safety Net |url-status = live |archive-url = https://web.archive.org/web/20130731090810/http://aviation-safety.net/database/record.php?id=19990415-0 |archive-date= 31 July 2013 |df = dmy-all }}

In 1983, a Boeing 767 (which thanks to its pilot's gliding skills landed safely and became known as the [[Gimli Glider]]) ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of [[Air Canada]]'s first aircraft to use metric measurements. {{cite news |first=Richard |last=Witkin |title=Jet's Fuel Ran Out After Metric Conversion Errors |url=https://select.nytimes.com/search/restricted/article?res=F00F17F73B5D0C738FDDAE0894DB484D81 |quote=Air Canada said yesterday that its Boeing 767 jet ran out of fuel in mid-flight last week because of two mistakes in figuring the fuel supply of the airline's first aircraft to use metric measurements. After both engines lost their power, the pilots made what is now thought to be the first successful emergency ''dead stick'' landing of a commercial jetliner. |work=[[The New York Times]] |date=30 July 1983 |access-date=21 August 2007 }} This accident was the result of both confusion due to the simultaneous use of metric and Imperial measures and confusion of mass and volume measures.

When planning his journey across the Atlantic Ocean in the 1480s, [[Christopher Columbus|Columbus]] mistakenly assumed that the [[mile]] referred to in the Arabic estimate of {{sfrac|56|2|3}} miles for the size of a [[Degree (angle)|degree]] was the same as the much shorter Italian mile of 1,480 metres. His estimate for the size of the degree and for the circumference of the Earth was therefore about 25% too small.Nunn, George Emra. "The geographical conceptions of Columbus: a critical consideration of four problems". No. 14. New York: American Geographical Society, 1924.[https://archive.org/stream/geographicalconc00nunn#page/n14/mode/1up 1–2][https://archive.org/stream/geographicalconc00nunn#page/n14/mode/1up 17-18]{{rp|1}}{{rp|17}}

== See also == {{main|Outline of metrology and measurement}}

• [[Dimensional metrology]]
• [[Forensic metrology]]
• [[Smart Metrology]]
• [[Time metrology]]
• [[Quantum metrology]]
• [[GNU Units]]
• [[List of humorous units of measurement]]
• [[List of obsolete units of measurement]]
• [[List of unusual units of measurement]]
• [[Measure word]]
• [[List of metric units]]
• [[Numerical-value equation]]
• [[Scottish units of measurement|Scottish units]]
• [[Seconds pendulum]]
• [[Space (punctuation)#Unit symbols and numbers]]
• [[System of measurement]]
• [[Unified Code for Units of Measure]]
• [[United States customary units]]
• [[Unit of account]]
• [[Units of information]]

== References == {{reflist|30em}}

==External links== {{commons category|Units of measure}}

• Rowlett, Russ (2018) [https://www.ibiblio.org/units/ How Many? A Dictionary of Units of Measurement]
• [https://web.archive.org/web/20111017035501/http://ts.nist.gov/WeightsAndMeasures/Publications/H44-09.cfm NIST Handbook 44], ''Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices''
• [http://www.bipm.org/en/measurement-units/ Official SI website]
• [https://web.archive.org/web/20160729171456/http://quantitysystem.codeplex.com/ Quantity System Framework] – Quantity System Library and Calculator for Units Conversions and Quantities predictions
• [http://www.tritechresearch.com/conversions.html List of units with selected conversion factors]

'''Historical'''

• [http://www.wdl.org/en/item/2847 "Arithmetic Conventions for Conversion Between Roman [i.e. Ottoman] and Egyptian Measurement"] is a manuscript from 1642, in Arabic, which is about units of measurement.
• {{cite NIE|wstitle=Weights and Measures|short=x}}

'''Legal'''

• [https://web.archive.org/web/20150402104216/http://www.irishstatutebook.ie/1996/en/act/pub/0027/ Ireland – Metrology Act 1996]
• {{UK-LEG|type=uksi|path=uksi/1995/1804|title=Units of Measurement Regulations 1995}}

'''Metric information'''

• [http://www.bipm.org/en/measurement-units/ BIPM] (official site)
• [https://ucum.org/trac The Unified Code for Units of Measure] (UCUM)

{{systems of measurement}} {{authority control}}

{{DEFAULTSORT:Units of Measurement}} [[Category:Units of measurement|*]]