A unit of measurement is a definite 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. Any other quantity of
that kind can be expressed as a multiple of the unit of measurement.
For example, a length is a physical quantity. The metre 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".
Measurement is a process of
determining how large or small a physical quantity is as compared to a
basic reference quantity of the same kind.
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
(SI), the modern form of the metric system.
In trade, weights and measures is 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).
Metrology is the science of developing nationally and internationally
accepted units of measurement.
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.
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).
In the social sciences, there are no standard units of measurement and
the theory and practice of measurement is studied in psychometrics and
the theory of conjoint measurement.
2 Systems of units
2.1 Traditional systems
2.2 Metric systems
2.3 Natural systems
2.4 Legal control of weights and measures
3 Base and derived units
4 Calculations with units of measurement
4.1 Units as dimensions
4.2 Expressing a physical value in terms of another unit
5 Real-world implications
6 See also
8 External links
Main article: History of measurement
A unit of measurement is a standardised quantity of a physical
property, used as a factor to express occurring quantities of that
Units of measurement
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, Egypt and the Indus Valley, and
Elam in Persia as well.
Weights and measures are mentioned in the
19:35–36). It is a commandment to be honest and have fair measures.
Magna Carta 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 completely
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
Systems of units
Main article: System of measurement
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.
A number of metric systems of units have evolved since the adoption of
the original metric system in
France in 1791. The current
international standard metric system is the International System of
Units (abbreviated to SI). An important feature of modern systems is
standardization. Each unit has a universally recognized size.
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
US customary units derive from earlier
Imperial units were mostly used in the British
Commonwealth and the former British Empire.
US customary units
US customary units are
still the main system of measurement used in the
United States despite
Congress having legally authorised metric measure on 28 July 1866.
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
6998254000000000000♠0.0254 m, and the US and imperial
avoirdupois pound is now defined as exactly
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. Similar to
natural units, atomic units (au) are a convenient system of units of
measurement used in atomic physics.
Also a great number of unusual and non-standard units may be
encountered. These may include the solar mass
(7030200000000000000♠2×1030 kg), the megaton (the energy
released by detonating one million tons of trinitrotoluene, TNT) and
Legal control of weights and measures
Weights and Measures Act and Trading standards
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
base units. The most widely used system of units is the International
System of Units, or SI. There are seven SI base units. All other SI
units can be derived from these base 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
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 electric and magnetic field have the same unit.[citation
needed] This is based on physical laws that show that electric and
magnetic field are actually different manifestations of the same
Calculations with units of measurement
Units as dimensions
Any value of a physical quantity 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:
displaystyle Z=ntimes [Z]=n[Z].
For example, let
be "2 candlesticks", then
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 calculus. In
formulas the unit [Z] can be treated as if it were a specific
magnitude of a kind of physical dimension: see dimensional analysis
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
displaystyle Z_ 1
be "2 candlesticks" and
displaystyle Z_ 2
"3 cabdrivers", then
"2 candlesticks" times "3 cabdrivers"
displaystyle =6[Z_ 1 ][Z_ 2 ]=6
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
One metre is the same length regardless of temperature, but
a metal bar will be exactly one metre long only at a certain
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. 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
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 (newtons per metre) or kg/s2 (kilograms per second squared).
Whether these designations are equivalent is disputed amongst
Expressing a physical value in terms of another unit
Conversion of units
Conversion of units 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.
displaystyle Z=n_ i times [Z]_ i
just replace the original unit
displaystyle [Z]_ i
with its meaning in terms of the desired unit
displaystyle [Z]_ j
, e.g. if
displaystyle [Z]_ i =c_ ij times [Z]_ j
displaystyle Z=n_ i times (c_ ij times [Z]_ j )=(n_ i times c_ ij
)times [Z]_ j
displaystyle n_ i
displaystyle c_ ij
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:
displaystyle Z=n_ i times [Z]_ i times (c_ ij times [Z]_ j /[Z]_
For example, you have an expression for a physical value Z involving
the unit feet per second (
displaystyle [Z]_ i
) and you want it in terms of the unit miles per hour (
displaystyle [Z]_ j
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:
displaystyle 1= frac 1,mathrm mi 5280,mathrm ft quad
mathrm and quad 1= frac 3600,mathrm s 1,mathrm h
Last, multiply the original expression of the physical value by the
fraction, called a conversion factor, 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.
displaystyle 52.8, frac mathrm ft mathrm s =52.8, frac
mathrm ft mathrm s frac 1,mathrm mi 5280,mathrm ft
frac 3600,mathrm s 1,mathrm h = frac 52.8times 3600 5280
,mathrm mi/h =36,mathrm mi/h
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:
displaystyle mathrm frac 9, rm L 100, rm km =mathrm
frac 9, rm L 100, rm km mathrm frac 1000000, rm mu L
1, rm L mathrm frac 1, rm km 1000, rm m = frac 9times
1000000 100times 1000 ,mathrm mu L/m =90,mathrm mu L/m
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 versus pound
force). Considerable amounts of effort, time, and money were
On 15 April 1999,
Korean Air cargo 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.
In 1983, a Boeing 767 (which came to be 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.
This accident was the result of both confusion due to the simultaneous
use of metric and Imperial measures and confusion of mass and volume
List of humorous units of measurement
List of unusual units of measurement
Unified Code for Units of Measure
United States customary units
System of measurement
Unit of account
Units of information
Systems of measurement
International System of Units
International System of Units (SI)
UK imperial system
US customary units
French (Trad. • Mesures usuelles)
Biblical and Talmudic
Humorous (FFF system)
^ "measurement unit", in International Vocabulary of Metrology
– Basic and General Concepts and Associated Terms (VIM) (PDF) (3rd
ed.), Joint Committee for Guides in Metrology, 2008,
pp. 6–7 .
^ Yunus A. Çengel & Michael A. Boles (2002). Thermodynamics: An
Engineering Approach (Eighth ed.). TN: McGraw Hill. p. 996.
ISBN 9780073398174. CS1 maint: Uses authors parameter (link)
^ "US Metric Act of 1866". Archived from the original on 10 October
2014. as amended by Public Law 110–69 dated 9 August 2007
^ "NIST Handbook 44 Appendix B". National Institute of Standards and
Technology. 2002. Archived from the original on 13 February
^ Emerson, W.H. (2008). "On quantity calculus and units of
measurement". Metrologia. 45 (2): 134–138.
^ "Unit Mixups". US Metric Association. Archived from the original on
23 September 2010.
Mars Climate Orbiter
Mars Climate Orbiter Mishap Investigation Board Phase I Report"
(PDF). NASA. 10 November 1999.
Korean Air Flight 6316" (Press release). NTSB. Archived from the
original on 6 October 2006.
Korean Air incident". Aviation Safety Net. Archived from the
original on 31 July 2013.
^ Witkin, Richard (30 July 1983). "Jet's Fuel Ran Out After Metric
Conversion Errors". New York Times. Retrieved 21 August 2007. 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
Rowlett, Russ (2005) A Dictionary of Units of
Measurement – Russ
Rowlett and the University of North Carolina at Chapel Hill
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
List of units with selected conversion factors
"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.
Metrology Act 1996
Text of the Units of
Measurement Regulations 1995 as in force today
(including any amendments) within the United Kingdom, from
Metric information and associations
BIPM (official site)
UK Metric Association
US Metric Association
Unified Code for Units of Measure (UCUM)
Imperial measure information
British Weights and Me