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A unit of measurement is a definite magnitude of a
quantity Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a u ...
, defined and adopted by convention or by law, that is used as a standard for
measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determi ...
of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a
length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most Measurement system, systems of measurement a Base unit (measurement), base unit f ...
is a
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
. The
metre The metre (British English, British spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek language, Greek noun , "m ...
(symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is actually 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 systems of units used to be very common. Now there is a global standard, the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
(SI), the modern form of the
metric system The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
. In trade, weights and measures is often a subject of governmental regulation, to ensure fairness and transparency. The
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an List of intergovernmental organizations, intergovernmental organisation, through which its 59 member-states act together on measur ...
(BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI).
Metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
is the science of developing nationally and internationally accepted units of measurement. In
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
and metrology, units are standards for
measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determi ...
of physical quantities that need clear definitions to be useful.
Reproducibility Reproducibility, also known as replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a ...
of experimental results is central to the
scientific method The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article hist ...
. 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.
Science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...
,
medicine Medicine is the science and Praxis (process), practice of caring for a patient, managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, and Health promotion ...
, and
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
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 Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business an ...
(see, for example,
dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...
). In the
social sciences Social science is one of the branches of science, devoted to the study of society, societies and the Social relation, relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the o ...
, there are no standard units of measurement and the theory and practice of measurement is studied in
psychometrics Psychometrics is a field of study within psychology Psychology is the science, scientific study of mind and behavior. Psychology includes the study of consciousness, conscious and Unconscious mind, unconscious phenomena, including fe ...
and the theory of conjoint measurement.

# History

A unit of measurement is a standardised
quantity Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a u ...
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: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. The earliest known uniform systems of measurement seem to have all been created sometime in the 4th and 3rd millennia BC among the ancient peoples of
Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the F ...
,
Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a List of transcontinental countries, transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via a land bridg ...
and the
Indus Valley The Indus ( ) is a transboundary river of Asia and a trans-Himalayan river of South and Central Asia Central Asia, also known as Middle Asia, is a region of Asia Asia (, ) is one of the world's most notable geographical reg ...
, and perhaps also
Elam Elam (; Linear Elamite: ''hatamti''; Elamite cuneiform, Cuneiform Elamite: ; Sumerian language, Sumerian: ; Akkadian language, Akkadian: ; he, עֵילָם ''ʿēlām''; peo, 𐎢𐎺𐎩 ''hūja'') was an ancient civilization centered i ...
in
Persia Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...
as well. Weights and measures are mentioned in the
Bible The Bible (from Koine Greek , , 'the books') is a collection of religious texts or scriptures that are held to be sacredness, sacred in Christianity, Judaism, Samaritanism, and many other religions. The Bible is an anthologya compilation of ...
(Leviticus 19:35–36). It is a commandment to be honest and have fair measures. In the ''
Magna Carta (Medieval Latin for "Great Charter of Freedoms"), commonly called (also ''Magna Charta''; "Great Charter"), is a royal charter of rights agreed to by King John of England at Runnymede, near Windsor, Berkshire, Windsor, on 15 June 1215. ...
'' of 1215 (The Great Charter) with the seal of 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, multiple unit systems are used all over the world such as the United States Customary System, the British Customary System, and the International System. However, the United States is the only industrialized country that has not yet at least mostly converted to the Metric System. The systematic effort to develop a universally acceptable system of units dates back to 1790 when the 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 of Weights and Measures (CGPM) was established. The CGPM produced the current SI system 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 system and the US Customary system.

# Systems of units

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 Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelf ...
could be defined in terms of a barleycorn. A system of measurement is a collection of units of measurement and rules relating them to each other. As
science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...
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. The system of units varies from country to country and some of the different system of units are CGS system of units, FPS system of units, MKS system of units and SI system of units. Among the different systems of units used in the world, the most widely used and internationally accepted one is the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
, or SI system of units. In this SI units system, there are seven
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which a ...
s and three supplementary units. The base SI units are metre, kilogram, second, kelvin, ampere, candela and the mole and the three supplementary SI units are radian, steradian and becquerel. All other SI units can be derived from these base units. Systems of measurement in modern use include the
metric system The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
, the
imperial system The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed thro ...
, and
United States customary units United States customary units form a system of measurement units commonly used in the United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental Unit ...
.

Historically many of the systems of measurement which had been in use were to some extent based on the dimensions of the human body. As a result, units of measure could vary not only from location to location but from person to person.

## Metric systems

Metric system The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
s of units have evolved since the adoption of the original metric system in
France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
in 1791. The current international standard metric system is the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
(abbreviated to SI). An important feature of modern systems is
standardization Standardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, users, interest groups, standards organizations and governments. Standardization ...
. Each unit has a universally recognized size. Both the
imperial units The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed thro ...
and US customary units derive from earlier English units. Imperial units were mostly used in the
British Commonwealth The Commonwealth of Nations, simply referred to as the Commonwealth, is a political association of 56 member states, the vast majority of which are former territories of the British Empire. The chief institutions of the organisation are the C ...
and the former
British Empire The British Empire was composed of the dominions, Crown colony, colonies, protectorates, League of Nations mandate, mandates, and other Dependent territory, territories ruled or administered by the United Kingdom and its predecessor states. I ...
. US customary units are still the main system of measurement used in the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...
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. Some steps towards US
metrication Metrication or metrification is the act or process of converting to the metric system of measurement. All over the world, countries have transitioned from local and traditional units of measurement to the metric system. This process began in Fr ...
have been made, particularly the redefinition of basic US and imperial units to derive exactly from SI units. Since the
international yard and pound The international yard and pound are two units of measurement that were the subject of an agreement among representatives of six nations signed on 1 July 1959: the United States, United Kingdom, Canada, Australia, New Zealand, and South Africa. T ...
agreement of 1959 the US and imperial inch is now defined as exactly , and the US and imperial avoirdupois pound is now defined as exactly .

## Natural systems

While the above systems of units are based on arbitrary unit values, formalised as standards, some unit values occur naturally in science. Systems of units based on these are called
natural units In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a Coherence (units of measurement), coherent unit of a quantity. For e ...
. Similar to natural units, atomic units (au) are a convenient system of units of measurement used in
atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
. Also a great number of unusual and non-standard units may be encountered. These may include the
solar mass The solar mass () is a standard mass#Units of mass, unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as star cluster, stellar clusters, nebulae, galaxy, galaxies and Black hole, b ...
(), the megaton (the energy released by detonating one million tons of trinitrotoluene, TNT) and the
electronvolt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an Voltage, electric potential difference of one volt i ...
.

## Legal control of weights and measures

To reduce the incidence of retail fraud, many national
statutes A statute is a formal written enactment of a legislative authority that governs the legal entities of a city A city is a human settlement of notable size.Goodall, B. (1987) ''The Penguin Dictionary of Human Geography''. London: Penguin.Kuper ...
have standard definitions of weights and measures that may be used (hence " statute measure"), and these are verified by legal officers.

## Informal comparison to familiar concepts

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.

# Base and derived units

For most quantities a unit is necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given. But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the ''base units'' and the other units are ''derived units''. Thus base units are the units of the quantities which are independent of other quantities and they are the units of length, mass, time, electric current, temperature, luminous intensity and the amount of substance. Derived units are the units of the quantities which 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.

# Calculations with units of measurement

## Units as dimensions

Any value of a
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
is expressed as a comparison to a unit of that quantity. For example, the value of a physical quantity ''Z'' is expressed as the product of a unit 'Z''and a numerical factor: : For example, let $Z$ be "2 candlesticks", then candlestick. The multiplication sign is usually left out, just as it is left out between variables in the scientific notation of formulas. The convention used to express quantities is referred to as quantity calculus. In formulas the unit 'Z''can be treated as if it were a specific magnitude of a kind of physical
dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
: see ''
Dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...
'' for more on this treatment. 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 $Z_1$ be "2 candlesticks" and $Z_2$ "3 cabdrivers", then :"2 candlesticks" times "3 cabdrivers" candlestick $\times$ cabdriver. A distinction should be made between units and standards. A unit is fixed by its definition and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit and realizes that unit only under certain physical conditions. For example, a metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be exactly one metre long only at a certain temperature. There are certain rules that have to be used when dealing with units: * Treat units algebraically. Only add like terms. 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 metres per second (m/s). See
dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...
. 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 Exponentiation is a mathematics, mathematical operation (mathematics), operation, written as , involving two numbers, the ''Base (exponentiation), base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". W ...
.) * 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 Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
can be referred to as either N/m (newton per metre) or kg/s2 (kilogram per second squared).

## Expressing a physical value in terms of another unit

Conversion of units Conversion of units is the conversion between different units of measurement A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for ...
involves comparison of different standard physical values, either of a single physical quantity or of a physical quantity and a combination of other physical quantities. Starting with: : replace the original unit with its meaning in terms of the desired unit , e.g. if , then: : Now $n_i$ and $c_$ are both numerical values, so just calculate their product. Or, which is just mathematically the same thing, multiply ''Z'' by unity, the product is still ''Z'': : For example, you have an expression for a physical value ''Z'' involving the unit ''feet per second'' () and you want it in terms of the unit ''miles per hour'' (): Or as an example using the metric system, you have a value of fuel economy in the unit ''litres per 100 kilometres'' and you want it in terms of the unit ''microlitres per metre'': :$\mathrm = \mathrm \mathrm \mathrm = \frac \,\mathrm = 90\,\mathrm$

# Real-world implications

One example of the importance of agreed units is the failure of the
NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the US federal government responsible for the civil List of government space agencies, space program ...
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 versus pound force). Considerable amounts of effort, time, and money were wasted. On 15 April 1999,
Korean Air Korean Air Co., Ltd. (), trade name, operating as Korean Air (Korean Air Lines before 1984), is the flag carrier of South Korea and its largest airline based on fleet size, international destinations and international flights. The present-da ...
cargo flight 6316 from
Shanghai Shanghai (; , , Standard Mandarin pronunciation: ) is one of the four direct-administered municipalities of the People's Republic of China (PRC). The city is located on the southern estuary of the Yangtze River, with the Huangpu River flow ...
to
Seoul Seoul (; ; ), officially known as the Seoul Special City, is the Capital city, capital and largest metropolis of South Korea.Before 1972, Seoul was the ''de jure'' capital of the North Korea, Democratic People's Republic of Korea (North Korea ...
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. 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 Air Canada is the flag carrier and the largest airline of Canada Canada is a country in North America. Its Provinces and territories of Canada, ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean ...
's first aircraft to use metric measurements. 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, Columbus mistakenly assumed that the
mile The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a imperial unit, British imperial unit and United States customary unit of distance; both are based on the older English unit of Unit of length, ...
referred to in the Arabic estimate of 56⅔ miles for the size of a degree was the same as the actually 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.

* GNU Units * List of humorous units of measurement * List of obsolete units of measurement * List of unusual units of measurement *
Measure word In linguistics, measure words are words (or morphemes) that are used in combination with a numeral to indicate an amount of something represented by some noun. Description Measure words denote a unit or measurement and are used with mass nouns ( ...
* List of metric units * Numerical-value equation *
Scottish units Scottish or Scots units of measurement are the weights and measures peculiar to Scotland which were nominally replaced by English units in 1685 but continued to be used in unofficial contexts until at least the late 18th century. The system was ...
* Seconds pendulum * Space (punctuation)#Unit symbols and numbers *
System of measurement A 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 commerce. Systems of measurement i ...
* Unified Code for Units of Measure *
United States customary units United States customary units form a system of measurement units commonly used in the United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental Unit ...
*
Unit of account In economics, unit of account is one of the money functions. A unit of account is a standard numerical monetary unit of measurement of the market value of goods, services, and other transactions. Also known as a "measure" or "standard" of rela ...
*
Units of information In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information ar ...

# Notes

* Rowlett, Russ (2018
How Many? A Dictionary of Units of Measurement

NIST Handbook 44
''Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices''
Official SI website

Quantity System Framework
– Quantity System Library and Calculator for Units Conversions and Quantities predictions

Historical
"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. * Legal
Ireland – Metrology Act 1996
* Metric information
BIPM
(official site)
The Unified Code for Units of Measure
(UCUM) {{DEFAULTSORT:Units of Measurement * * Measurement * *