A

**unit of measurement** is a definite

magnitudeMagnitude Is A Part Of An EarthquakesMagnitude may refer to:In mathematics:*Magnitude , the relative size of a mathematical object*Magnitude , a term for the size or length of a vector...

of a

physical quantityA physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.

For example,

lengthIn geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

is a physical quantity. The

metreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 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 this day. Different systems of units used to be very common. Now there is a global standard, the

International System of UnitsThe International System of Units 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...

(SI), the modern form of the

metric systemThe metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

.

In trade,

**weights and measures** is often a subject of governmental regulation, to ensure fairness and transparency. The Bureau international des poids et mesures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI).

MetrologyMetrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

is the science for developing nationally and internationally accepted units of weights and measures.

In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

and

metrologyMetrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

, units are standards for

measurementMeasurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

of

physical quantitiesA physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

that need clear definitions to be useful.

ReproducibilityReproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

of experimental results is central to the

scientific methodScientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...

. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures developed long ago for commercial purposes.

ScienceScience is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

,

medicineMedicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....

, and

engineeringEngineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in

problem solvingProblem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping. Consideredthe most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of...

(see, for example,

dimensional analysisIn physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

).

In the

social sciencesSocial science is the field of study concerned with society. "Social science" is commonly used as an umbrella term to refer to a plurality of fields outside of the natural sciences usually exclusive of the administrative or managerial sciences...

, there are no standard units of measurement and the theory and practice of measurement is studied in

psychometricsPsychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...

and the

theory of conjoint measurementThe theory of conjoint measurement is a general, formal theory of continuous quantity. It was independently discovered by the French economist Gerard Debreu and by the American mathematical psychologist R...

.

## History

A unit of measurement is a standardised

quantityQuantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...

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 weights and measures seem to have all been created sometime in the

4thThe 4th millennium BC saw major changes in human culture. It marked the beginning of the Bronze Age and of writing.The city states of Sumer and the kingdom of Egypt were established and grew to prominence. Agriculture spread widely across Eurasia...

and

3rd millennia BCThe 3rd millennium BC spans the Early to Middle Bronze Age.It represents a period of time in which imperialism, or the desire to conquer, grew to prominence, in the city states of the Middle East, but also throughout Eurasia, with Indo-European expansion to Anatolia, Europe and Central Asia. The...

among the ancient peoples of

MesopotamiaMesopotamia is a toponym for the area of the Tigris–Euphrates river system, largely corresponding to modern-day Iraq, northeastern Syria, southeastern Turkey and southwestern Iran.Widely considered to be the cradle of civilization, Bronze Age Mesopotamia included Sumer and the...

,

EgyptAncient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...

and the

Indus ValleyThe Indus Valley Civilization was a Bronze Age civilization that was located in the northwestern region of the Indian subcontinent, consisting of what is now mainly modern-day Pakistan and northwest India...

, and perhaps also

ElamElam was an ancient civilization located in what is now southwest Iran. Elam was centered in the far west and the southwest of modern-day Iran, stretching from the lowlands of Khuzestan and Ilam Province, as well as a small part of southern Iraq...

in

PersiaIran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...

as well.

In "The

Magna CartaMagna Carta is an English charter, originally issued in the year 1215 and reissued later in the 13th century in modified versions, which included the most direct challenges to the monarch's authority to date. The charter first passed into law in 1225...

" of 1215 (The Great Charter) with the seal of

King JohnThe Life and Death of King John, a history play by William Shakespeare, dramatises the reign of John, King of England , son of Henry II of England and Eleanor of Aquitaine and father of Henry III of England...

, 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…."

Many systems were based on the use of parts of the body and the natural surroundings as measuring instruments. Our present knowledge of early weights and measures comes from many sources.

### 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 according to the proportions described by Marcus Vitruvius Pollio.{cn}} As a result, units of measure could vary not only from location to location, but from person to person.

### Metric systems

A number of

metric systemThe metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

s of units have

evolved since the adoption of the original metric systemThe origins of the metric system date back to the sixteenth century when Simon Stevin published details of his decimal notation and the seventeenth century when John Wilkins published a proposal for a decimal system of measurement based on natural units...

in

FranceThe French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

in 1791. The current international standard metric system is the

International System of UnitsSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

. An important feature of modern systems is

standardizationStandardization is the process of developing and implementing technical standards.The goals of standardization can be to help with independence of single suppliers , compatibility, interoperability, safety, repeatability, or quality....

. Each unit has a universally recognized size.

Both the

Imperial unitThe system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The system came into official use across the British Empire...

s and US customary units derive from earlier

English unitEnglish units are the historical units of measurement used in England up to 1824, which evolved as a combination of the Anglo-Saxon and Roman systems of units...

s. Imperial units were mostly used in the

British CommonwealthThe Commonwealth of Nations, normally referred to as the Commonwealth and formerly known as the British Commonwealth, is an intergovernmental organisation of fifty-four independent member states...

and the former

British EmpireThe British Empire comprised the dominions, colonies, protectorates, mandates and other territories ruled or administered by the United Kingdom. It originated with the overseas colonies and trading posts established by England in the late 16th and early 17th centuries. At its height, it was the...

. US customary units are still the main system of measurement used in the

United StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...

despite Congress having legally authorized metric measure on 28 July 1866. Some steps towards US

metricationMetrication refers to the introduction and use of the SI metric system, the international standard for physical measurements. This has involved a long process of independent and systematic conversions of countries from various local systems of weights and measures. Metrication began in France in...

have been made, particularly the redefinition of basic US units to derive exactly from SI units, so that in the US the inch is now defined as 0.0254 m (exactly), and the avoirdupois pound is now defined as 453.59237 g (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 unitsIn physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...

. Similar to natural units,

atomic unitsAtomic units form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, which one might name Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article...

(au) are a convenient system of units of measurement used in

atomic physicsAtomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

.

Also a great number of

unusual and non-standard units may be encountered. These may include the

Solar massThe solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

, the

MegatonTNT equivalent is a method of quantifying the energy released in explosions. The ton of TNT is a unit of energy equal to 4.184 gigajoules, which is approximately the amount of energy released in the detonation of one ton of TNT...

(1,000,000 tons of

TNT).

### 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.

## Base and derived units

Different systems of units are based on different choices of a set of

fundamental unitA set of fundamental units is a set of units for physical quantities from which every other unit can be generated.In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe...

s.

The most widely used system of units is the International System of Units, or

SISi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

. There are seven

SI base unitThe International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

s. All

other SI unitsThe International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...

can be derived from these base units.

For most quantities a unit is absolutely 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*. Other units are

*derived units*. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Which units are considered base units is a matter of choice.

The base units of SI are actually not the smallest set possible. Smaller sets have been defined. For example, there are unit sets in which the

electricIn physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

and

magnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

have the same unit. This is based on physical laws that show that electric and magnetic field are actually different manifestations of the same phenomenon.

### Units as dimensions

Any value of a

physical quantityA physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

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, "2 candlesticks" Z = 2 [candlestick].

The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. The conventions used to express quantities is referred to as

quantity calculusQuantity calculus is the formal method for describing the mathematical relations between abstract physical quantities. Despite the name, it is more analogous to a system of algebra than calculus in the mathematical sense of the term. Measurements are expressed as products of a numeric value with a...

. In formulas the unit [Z] can be treated as if it were a specific magnitude of a kind of physical

dimensionIn physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

: see

dimensional analysisIn physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

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 GamowGeorge Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...

used to explain:

- "2 candlesticks" times "3 cabdrivers" = 6 [candlestick][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, the 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 one metre long only at a certain temperature.

### Guidelines

- 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, 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 physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m^{2}/s^{2}). Put simply, units obey the laws of indices. (See ExponentiationExponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...

.)
- Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to one kg·m/s
^{2}. Thus a quantity may have several unit designations, for example: the unit for surface tensionSurface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...

can be referred to as either N/m (newtons per metre) or kg/s^{2} (kilograms per second squared). Whether these designations are equivalent is disputed amongst metrologists.

### Expressing a physical value in terms of another unit

Conversion of unitsConversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

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:

just replace the original unit

with its meaning in terms of the desired unit

, e.g. if

, then:

Now

and

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* (

):

- Find facts relating the original unit to the desired unit:

- 1 mile = 5280 feet and 1 hour = 3600 seconds

- Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:

- Last,multiply the original expression of the physical value by the fraction, called a
*conversion factor*A conversion factor changes something to a different version or form. A factor is something that brings results or a cause, while conversion is an action of changing the "version" of a thing....

, to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are dimensionless and have a numerical value of one, multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.

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*:

## Real-world implications

One example of the importance of agreed units is the failure of the

NASAThe National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

Mars Climate OrbiterThe Mars Climate Orbiter was a 338 kilogram robotic space probe launched by NASA on December 11, 1998 to study the Martian climate, atmosphere, surface changes and to act as the communications relay in the Mars Surveyor '98 program, for Mars Polar Lander...

, which was accidentally destroyed on a mission to the

planetA planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

MarsMars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

in September 1999 instead of entering

orbitIn physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

, due to miscommunications about the value of forces: different computer programs used different units of measurement (newton versus pound force). Enormous amounts of effort, time, and money were wasted.

On April 15, 1999

Korean AirKorean Air Lines Co., Ltd. , operating as Korean Air, is both the flag carrier and the largest airline of South Korea, with global headquarters located in Seoul, South Korea. Korean Air's international passenger division and related subsidiary cargo division together serve 130 cities in 45...

cargo flight 6316 from

ShanghaiShanghai is the largest city by population in China and the largest city proper in the world. It is one of the four province-level municipalities in the People's Republic of China, with a total population of over 23 million as of 2010...

to

SeoulSeoul , officially the Seoul Special City, is the capital and largest metropolis of South Korea. A megacity with a population of over 10 million, it is the largest city proper in the OECD developed world...

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 came to be known as the

Gimli GliderThe Gimli Glider is the nickname of the Air Canada aircraft that was involved in a notable aviation incident. On 23 July 1983, Air Canada Flight 143, a Boeing 767-200 jet, ran out of fuel at an altitude of ASL, about halfway through its flight from Montreal to Edmonton via Ottawa...

) ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of

Air CanadaAir Canada is the flag carrier and largest airline of Canada. The airline, founded in 1936, provides scheduled and charter air transport for passengers and cargo to 178 destinations worldwide. It is the world's tenth largest passenger airline by number of destinations, and the airline is a...

's first aircraft to use metric measurements. This accident is apparently the result of confusion both due to the simultaneous use of metric & Imperial measures as well as mass & volume measures.

## See also

- Chinese units of measurement
Chinese units of measurement are the customary and traditional units of measure used in China. In the People's Republic of China, the units were re-standardised during the late 20th century to make them approximate SI units. Many of the units were formerly based on the number 16 instead of 10...

- Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

- Indian weights and measures
India officially uses the metric system of weights and measures. Other prominent systems that have been used historically include British Imperial units, the Akbar system, and many regional traditional systems, some of which have been used for thousands of years....

- International System of Units
The International System of Units 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...

- Japanese units of measurement
' is the traditional Japanese system of measurement. The name shakkanhō originates from the name of two of the units, the shaku, a unit of length, and the kan, a mass measurement.The system is Chinese in origin...

- List of humorous units of measurement

- List of unusual units of measurement
- Spanish customary units
- Taiwanese units of measurement
Taiwanese units of measurement are the customary and traditional units of measure used in Taiwan. Many of the units derive from Japanese units of measurement and have similar names as Chinese units of measurement but different conversions than in China or Hong Kong...

- Unified Code for Units of Measure
The Unified Code for Units of Measure is a system of codes for unambiguously representing measurement units to both humans and machines....

- Units conversion by factor-label
Many, if not most, parameters and measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m³, 100 kPa/bar, 50 miles per hour, 1000 Btu/lb. Converting from one dimensional unit to another is often...

### General

### Legal

US - Authorized tables
### Metric information and associations

### Imperial/U.S. measure information and associations