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Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependent on the context and discipline. In
natural science Natural science is a Branches of science, branch of science concerned with the description, understanding and prediction of Phenomenon, natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer r ...

natural science
s 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 ...

engineering
, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the ''International vocabulary of metrology'' published by the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
. However, in other fields such as
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
as well as the
social Social organisms, including humans, live collectively in interacting populations. This interaction is considered social whether they are aware of it or not, and whether the exchange is voluntary/involuntary. Etymology The word "Social" derives fr ...

social
and
behavioural sciences Behavioral sciences explore the cognitive processes within organism In biology, an organism (from Ancient Greek, Greek: ὀργανισμός, ''organismos'') is any individual contiguous system that embodies the Life#Biology, properties o ...
, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales. Measurement is a cornerstone of
trade Trade involves the transfer of goods from one person or entity to another, often in exchange for money. Economists refer to a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of r ...

trade
,
science Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe."... modern science is a discovery as well as an invention. ...

science
,
technology Technology ("science of craft", from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. I ...

technology
and
quantitative research Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. It is formed from a Deductive reasoning, deductive approach where emphasis is placed on the testing of theory, shaped by Empiricism, e ...

quantitative research
in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern
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 wi ...
(SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of
metrology Metrology is the scientific study of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with oth ...

metrology
. Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity.


Importance of measurement

# it is needed for buying, selling and exchanging of goods # It is needed for performing scientific experiments. # it is needed for preparing medicines and treating patients. # it is needed for preparing food. # it is needed for the global understanding of the quantity of a substance.


Methodology

The measurement of a property may be categorized by the following criteria:
type Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Type ...
,
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
,
unit Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in ...
, and
uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially ...

uncertainty
. They enable unambiguous comparisons between measurements. * The ''level'' of measurement is a taxonomy for the methodological character of a comparison. For example, two states of a property may be compared by ratio, difference, or ordinal preference. The type is commonly not explicitly expressed, but implicit in the definition of a measurement procedure. * The ''magnitude'' is the numerical value of the characterization, usually obtained with a suitably chosen
measuring instrument A measuring instrument is a device to measure a physical quantity A physical quantity is a physical property of a material or system that can be Quantification (science), quantified by measurement. A physical quantity can be expressed as a ''va ...

measuring instrument
. * A ''unit'' assigns a mathematical weighting factor to the magnitude that is derived as a ratio to the property of an artifact used as standard or a natural physical quantity. * An ''uncertainty'' represents the random and systemic errors of the measurement procedure; it indicates a confidence level in the measurement. Errors are evaluated by methodically repeating measurements and considering the
accuracy and precision In a set of measurements, accuracy is closeness of the measurements to a specific value, while precision is the closeness of the measurements to each other. ''Accuracy'' has two definitions: # More commonly, it is a description of ''systematic er ...

accuracy and precision
of the measuring instrument.


Standardization of measurement units

Measurements most commonly use 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 wi ...
(SI) as a comparison framework. The system defines seven :
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
,
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English o ...
,
candela The candela ( or ; symbol: cd) is the of in the (SI); that is, luminous power per unit emitted by a point light source in a particular direction. Luminous intensity is analogous to , but instead of simply adding up the contributions of ever ...

candela
,
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, th ...
,
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
,
kelvin The kelvin is the base unit of temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, ...

kelvin
, and
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
. Six of these units are defined without reference to a particular physical object which serves as a standard (artifact-free), while the kilogram is still embodied in an artifact which rests at the headquarters of the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
in
Sèvres Sèvres (, ) is a in the southwestern suburbs of , . It is located from the , in the , . The commune, which had a population of 23,251 as of 2018, is known for its famous production at the ', which was also where the (1920) was signed. G ...
near Paris. Artifact-free definitions fix measurements at an exact value related to a
physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity A physical quantity is a physical property of a material or system that can be Quantification (science), quantified by measurement. A physi ...
or other invariable phenomena in nature, in contrast to standard artifacts which are subject to deterioration or destruction. Instead, the measurement unit can only ever change through increased accuracy in determining the value of the constant it is tied to. The first proposal to tie an SI base unit to an experimental standard independent of fiat was by
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, ian, mathematician and scientist who is sometimes known as "the father of ". He was known as a somewhat unusual character. Educated as a chemist an ...

Charles Sanders Peirce
(1839–1914), who proposed to define the metre in terms of the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adja ...

wavelength
of a
spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spect ...
. This directly influenced the
Michelson–Morley experiment The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether upright=1.25, The luminiferous aether: it was hypothesised that the Earth moves through a "medium" of aether that carries light Luminiferous aet ...
; Michelson and Morley cite Peirce, and improve on his method.


Standards

With the exception of a few fundamental
quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an fundamental interaction, interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the ...

quantum
constants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that an
inch Measuring tape with inches The inch (symbol: in or ″) is a unit Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television s ...
has to be a certain length, nor that a
mile The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and US customary unit United States customary units (U.S. customary units) are a system of measurements commonly u ...
is a better measure of distance than a
kilometre The kilometre (SI symbol: km; or ), spelt kilometer in American English, is a unit of length in the metric system, equal to one thousand metres (kilo- being the SI prefix for ). It is now the measurement unit used for expressing distances betw ...
. Over the course of human history, however, first for convenience and then for necessity, standards of measurement evolved so that communities would have certain common benchmarks. Laws regulating measurement were originally developed to prevent fraud in commerce.
Units of measurement A unit of measurement is a definite magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematic ...
are generally defined on a scientific basis, overseen by governmental or independent agencies, and established in international treaties, pre-eminent of which is the
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
(CGPM), established in 1875 by the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally binding written agreement between actors in international law International ...

Metre Convention
, overseeing the International System of Units (SI). For example, the metre was redefined in 1983 by the CGPM in terms of the speed of light, the kilogram was redefined in 2019 in terms of the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
and the international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia and South Africa as being ''exactly'' 0.9144 metres. In the United States, the National Institute of Standards and Technology (
NIST The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, e ...

NIST
), a division of the
United States Department of Commerce The United States Department of Commerce is an executive department The United States federal executive departments are the principal units of the Federal government of the United States, executive branch of the federal government of the U ...
, regulates commercial measurements. In the United Kingdom, the role is performed by the National Physical Laboratory (NPL), in Australia by the National Measurement Institute, in South Africa by the
Council for Scientific and Industrial Research The Council for Scientific and Industrial Research (CSIR) is South Africa South Africa, officially the Republic of South Africa (RSA), is the southernmost country in Africa. With over Demographics of South Africa, 59 million peopl ...
and in India the
National Physical Laboratory of India The CSIR- National Physical Laboratory of India, situated in New Delhi, is the measurement standards laboratory of India. It maintains standards of SI units in India and calibrates the national standards of weights and measures. History of mea ...
.


Units and systems

unit is known or standard quantity in terms of which other physical quantities are measured.


Imperial and US customary systems

Before
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system The metric system is a that succeeded the decimal ...
s were widely adopted around the world, the British systems of
English unit English units are the 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 measurement of the same kind of ...
s and later
imperial unit 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 A system of measurement is a collection of units of measurement A unit of measuremen ...
s were used in Britain, the
Commonwealth A commonwealth is a traditional English term for a political community founded for the common good In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existenc ...

Commonwealth
and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few
Caribbean The Caribbean (, ; es, Caribe; french: Caraïbes; ht, Karayib; also gcf, label=Antillean Creole Antillean Creole (Antillean French Creole, Kreyol, Kwéyòl, Patois) is a French-based creole, which is primarily spoken in the Lesser Antilles ...
countries. These various systems of measurement have at times been called ''foot-pound-second'' systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for the U.S. units. Many Imperial units remain in use in Britain, which has officially switched to the SI system—with a few exceptions such as road signs, which are still in miles. Draught beer and cider must be sold by the imperial pint, and milk in returnable bottles can be sold by the imperial pint. Many people measure their height in feet and inches and their weight in
stone A rock is any naturally occurring solid mass or aggregate of minerals or mineraloid matter. It is categorized by the minerals included, its chemical composition and the way in which it is formed. Rocks form the Earth's outer solid layer, th ...
and pounds, to give just a few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many countries that are considered metricated.


Metric system

The
metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical development of these systems culminated in the definition of the (SI), under the oversight of an international stan ...

metric system
is a decimal
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 in ...
based on its units for length, the metre and for mass, the kilogram. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognised metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.


International System of Units

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 wi ...
(abbreviated as SI from the
French language French ( or ) is a Romance language The Romance languages, less commonly Latin or Neo-Latin languages, are the modern languages that evolved from Vulgar Latin Vulgar Latin, also known as Popular or Colloquial Latin is a range of inf ...

French language
name ''Système International d'Unités'') is the modern revision of the
metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical development of these systems culminated in the definition of the (SI), under the oversight of an international stan ...

metric system
. It is the world's most widely used
system of units A system of measurement is a collection of units of measurement A unit of measurement is a definite magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude ...
, both in everyday
commerce Commerce is the exchange of goods and services, especially on a large scale. Etymology The English-language word ''commerce'' has been derived from the Latin word ''commercium'', from ''com'' ("together") and ''merx'' ("merchandise"). History ...

commerce
and in
science Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe."... modern science is a discovery as well as an invention. ...

science
. The SI was developed in 1960 from the metre–kilogram–second (MKS) system, rather than the centimetre–gram–second (CGS) system, which, in turn, had many variants. The SI units for the seven base physical quantities are: In the SI, base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are constructed from the base units, for example, the
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
, i.e. the unit for power, is defined from the base units as m2·kg·s−3. Other physical properties may be measured in compound units, such as material density, measured in kg/m3.


=Converting prefixes

= The SI allows easy multiplication when switching among units having the same base but different prefixes. To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divides the number of centimetres by 100.


Length

A
ruler A ruler, sometimes called a rule or line gauge, is a device used in geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of spac ...

ruler
or rule is a tool used in, for example,
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
,
technical drawing Technical drawing, drafting or drawing, is the act and discipline Discipline is action ACTION is a bus operator in Canberra Canberra ( ) is the capital city of Australia. Founded following the Federation of Australia, federat ...

technical drawing
, engineering, and carpentry, to measure lengths or distances or to draw straight lines. Strictly speaking, the ''ruler'' is the instrument used to rule straight lines and the calibrated instrument used for determining length is called a ''measure'', however common usage calls both instruments ''rulers'' and the special name ''straightedge'' is used for an unmarked rule. The use of the word ''measure'', in the sense of a measuring instrument, only survives in the phrase ''tape measure'', an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in the photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a pocket, and a five-metre-long tape measure easily retracts to fit within a small housing.


Some special names

Some non-systematic names are applied for some multiples of some units. * 100 kilograms = 1 quintal; 1000 kilogram = 1
tonne The tonne ( or ; symbol: t) is a metric unit of mass equal to 1,000 kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a meas ...
; * 10 years = 1 decade; 100 years = 1 century; 1000 years = 1 millennium


Building trades

The Australian building trades adopted the
metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical development of these systems culminated in the definition of the (SI), under the oversight of an international stan ...

metric system
in 1966 and the units used for measurement of length are
metres The metre ( Commonwealth spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure", and cognate with Sanskrit Sanskrit (, attributively , ''saṃskṛta-'', nominalization, no ...
(m) and
millimetres The millimetre ( international spelling; SI unit symbol mm) or millimeter ( American spelling) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' ...
(mm).
Centimetres A centimetre (international spelling) or centimeter (American spelling) (SI symbol cm) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit ...
(cm) are avoided as they cause confusion when reading
plans A plan is typically any diagram A diagram is a symbolic Depiction, representation of information using Visualization (graphics), visualization techniques. Diagrams have been used since prehistoric times on Cave painting, walls of caves, but bec ...

plans
. For example, the length two and a half metres is usually recorded as 2500 mm or 2.5 m; it would be considered non-standard to record this length as 250 cm.


Surveyor's trade

American surveyors use a decimal-based system of measurement devised by
Edmund Gunter Edmund Gunter (158110 December 1626), was an English clergyman, mathematician, geometer and astronomer of Welsh descent. He is best remembered for his mathematical contributions which include the invention of the Gunter's chain, the #Gunter's qua ...
in 1620. The base unit is
Gunter's chain Gunter's chain (also known as Gunter’s measurement) is a distance measuring device used for surveying Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial or three-dimensional positions ...
of which is subdivided into 4 rods, each of 16.5 ft or 100 links of 0.66 feet. A link is abbreviated "lk", and links "lks", in old deeds and land surveys done for the government. The ''Standard Method of Measurement'' (SMM) published by the
Royal Institution of Chartered Surveyors The Royal Institution of Chartered Surveyors (RICS) is a UK-based professional bodyRegulatory colleges are legal entities in Canada charged with serving the public interest by regulating the practice of a profession. Most regulatory colleges are ...
(RICS) consisted of classification tables and rules of measurement, allowing use of a uniform basis for measuring building works. It was first published in 1922, superseding a Scottish Standard Method of Measurement which had been published in 1915. Its seventh edition (SMM7) was first published in 1988 and revised in 1998. SMM7 was replaced by the ''New Rules of Measurement'', volume 2 (NRM2), which were published in April 2012 by the RICS Quantity Surveying and Construction Professional Group and became operational on 1 January 2013. NRM2 has been in general use since July 2013. SMM7 was accompanied by the Code of Procedure for the Measurement of Building Works (the SMM7 Measurement Code). Whilst SMM7 could have a
contract A contract is a legally binding agreement that defines and governs the rights and duties between or among its parties Image:'Hip, Hip, Hurrah! Artist Festival at Skagen', by Peder Severin Krøyer (1888) Demisted with DXO PhotoLab Clearview ...

contract
ual status within a project, for example in the JCT Standard form of Building Contract), the Measurement Code was not mandatory. NRM2 Is the second of three component parts within the NRM suite: *NRM1 - Order of cost estimating and cost planning for capital building works *NRM2 - Detailed measurement for building works *NRM3 - Order of cost estimating and cost planning for building maintenance works.


Time

Time is an abstract measurement of elemental changes over a non spatial continuum. It is denoted by numbers and/or named periods such as
hour An hour (symbol A symbol is a mark, sign, or that indicates, signifies, or is understood as representing an , , or . Symbols allow people to go beyond what is n or seen by creating linkages between otherwise very different s and s. All ...
s,
day The word day has a number of meanings, depending on the context it is used such as of astronomy, physics, and various calendar systems. As a term in physics and astronomy it is approximately the period during which the Earth completes one ro ...

day
s,
week A week is a time unit equal to seven days. It is the standard time period used for cycles of rest days in most parts of the world, mostly alongside—although not strictly part of—the Gregorian calendar. In many languages, the days of the we ...

week
s,
month A month is a unit of time, used with calendars, that is approximately as long as a natural orbital period of the Moon; the words ''month'' and ''Moon'' are cognates. The traditional concept arose with the cycle of Moon phases; such lunar months ("l ...
s and
year A year is the orbital period of a planetary body, for example, the Earth, moving in Earth's orbit, its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the ...
s. It is an apparently irreversible series of occurrences within this non spatial continuum. It is also used to denote an interval between two relative points on this continuum.


Mass

''Mass'' refers to the intrinsic property of all material objects to resist changes in their momentum. ''Weight'', on the other hand, refers to the downward force produced when a mass is in a gravitational field. In
free fall #REDIRECT Free fall In Newtonian physics, free fall is any motion of a body where gravity Gravity (), or gravitation, is a list of natural phenomena, natural phenomenon by which all things with mass or energy—including planets, star ...

free fall
, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the
ounce The ounce is the name of several different units of mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of " ...
,
pound Pound or Pounds may refer to: Units * Pound (currency) A pound is any of various units of currency A currency, "in circulation", from la, currens, -entis, literally meaning "running" or "traversing" in the most specific sense is money Im ...
, and
ton The ton is a unit of measure A unit of measurement is a definite magnitude of a quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared ...
. The metric units
gram The gram (alternative spelling: gramme; SI unit symbol: g) is a metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical development of these systems culm ...
and kilogram are units of mass. One device for measuring weight or mass is called a weighing scale or, often, simply a ''scale''. A spring scale measures force but not mass, a balance compares weight, both require a gravitational field to operate. Some of the most accurate instruments for measuring weight or mass are based on load cells with a digital read-out, but require a gravitational field to function and would not work in free fall.


Economics

The measures used in economics are physical measures,
nominal price In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods ...
value measures and real price measures. These measures differ from one another by the variables they measure and by the variables excluded from measurements.


Survey research

In the field of survey research, measures are taken from individual attitudes, values, and behavior using
questionnaire A questionnaire is a research instrument consisting of a series of questions (or other types of prompts) for the purpose of gathering information from respondents through survey or statistical study. The questionnaire was invented by the Statistic ...

questionnaire
s as a measurement instrument. As all other measurements, measurement in survey research is also vulnerable to
measurement error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics Statistics is the discipline that co ...
, i.e. the departure from the true value of the measurement and the value provided using the measurement instrument. In substantive survey research, measurement error can lead to biased conclusions and wrongly estimated effects. In order to get accurate results, when measurement errors appear, the results need to be corrected for measurement errors.


Exactness designation

The following rules generally apply for displaying the exactness of measurements: *All non-0 digits and any 0s appearing between them are significant for the exactness of any number. For example, the number 12000 has two significant digits, and has implied limits of 11500 and 12500. *Additional 0s may be added after a
decimal separator A decimal separator is a symbol used to separate the integer An integer (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spok ...

decimal separator
to denote a greater exactness, increasing the number of decimals. For example, 1 has implied limits of 0.5 and 1.5 whereas 1.0 has implied limits 0.95 and 1.05.


Difficulties

Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time it takes an object to fall a distance of one metre (about 39  in). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of
error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. In statistics Statistics is the discipline that concerns the collection, o ...
that arise: * This computation used for the acceleration of gravity . But this measurement is not exact, but only precise to two significant digits. * The Earth's gravitational field varies slightly depending on height above sea level and other factors. * The computation of 0.45 seconds involved extracting a
square root In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

square root
, a
mathematical operation In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gen ...
that required rounding off to some number of significant digits, in this case two significant digits. Additionally, other sources of
experimental error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not a "mistake". Variability ...
include: * carelessness, * determining of the exact time at which the object is released and the exact time it hits the ground, * measurement of the height and the measurement of the time both involve some error, *
Air resistance In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding f ...
. * posture of human participants Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic.


Definitions and theories


Classical definition

In the classical definition, which is standard throughout the physical sciences, ''measurement'' is the determination or estimation of ratios of quantities.Michell, J. (1999). Measurement in psychology: a critical history of a methodological concept. New York: Cambridge University Press. Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to
John Wallis John Wallis (; la, Wallisius; ) was an English clergyman and mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), f ...

John Wallis
and
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

Isaac Newton
, and was foreshadowed in
Euclid's Elements The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, ...
.


Representational theory

In the representational theory, ''measurement'' is defined as "the correlation of numbers with entities that are not numbers". The most technically elaborated form of representational theory is also known as additive conjoint measurement. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens, numbers need only be assigned according to a rule. The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of the requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria. Three type of Representational theory 1) Empirical relation In science, an empirical relationship is a relationship or correlation based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis 2) The rule of mapping The real world is the Domain of mapping, and the mathematical world is the range. when we map the attribute to mathematical system, we have many choice for mapping and the range 3) The representation condition of measurement


Information theory

Information theory recognises that all data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." This definition is implied in what scientists actually do when they measure something and report both the mean and
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
of the measurements. In practical terms, one begins with an initial guess as to the expected value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. Note that in this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is not a clear or neat distinction between Approximation, estimation and measurement.


Quantum mechanics

In quantum mechanics, a measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Before a measurement is made, a quantum system is simultaneously described by all values in a range of possible values, where the probability of measuring each value is determined by the wavefunction of the system. When a measurement is performed, the wavefunction of the quantum system "wavefunction collapse, collapses" to a single, definite value. The unambiguous meaning of the measurement problem is an unresolved fundamental problem in quantum mechanics.


Biology

In biology, there is generally no well established theory of measurement. However, the importance of the theoretical context is emphasized. Moreover, the theoretical context stemming from the theory of evolution leads to articulate the theory of measurement and historicity as a fundamental notion. Among the most developed fields of measurement in biology are the measurement of genetic diversity and species diversity.Magurran, A.E. & McGill, B.J. (Hg.) 2011: Biological Diversity: Frontiers in Measurement and Assessment Oxford University Press.


See also

* Airy points * Conversion of units * Detection limit * Differential linearity * Dimensional analysis * Dimensionless number * Econometrics * Electrical measurements * History of measurement * History of science and technology * Instrumentation * Integral linearity * ISO 10012, Measurement management systems * Key relevance in locksmithing * Least count * Levels of measurement * List of humorous units of measurement * List of unusual units of measurement * Measurement in quantum mechanics * Measuring instrument * Measurement (journal) * Measurement uncertainty * NCSL International * Number sense * Observable quantity * Orders of magnitude * Primary instrument * Psychometrics * Quantification (science) * Remote sensing * Standard (metrology) * Test method * Timeline of temperature and pressure measurement technology * Timeline of time measurement technology * Uncertainty principle * Virtual instrumentation * Web analytics * Weights and measures


References


External links

* *Schlaudt, Oliver 2020: "measurement". In: Kirchhoff, Thomas (ed.): Online Encyclopedia Philosophy of Nature. Heidelberg: Universitätsbibliothek Heidelberg, https://doi.org/10.11588/oepn.2020.0.76654. *Tal, Era 2020: "Measurement in Science". In: Zalta, Edward N. (ed.): The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), URL = .
A Dictionary of Units of Measurement

'Metrology – in short' 3rd edition, July 2008
{{Authority control Measurement, Accuracy and precision Metrology