Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a

^{2}·kg·s^{−3}. Other physical properties may be measured in compound units, such as material density, measured in kg/m^{3}.

.

A Dictionary of Units of Measurement

'Metrology – in short' 3rd edition, July 2008

{{Authority control Accuracy and precision Metrology

physical quantity
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...

is as compared to a basic reference quantity of the same kind.
The scope and application of measurement are dependent on the context and discipline. In natural science
Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatabil ...

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 speciali ...

, 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, through which its 59 member-states act together on measurement standards in four areas: chemistr ...

. However, in other fields such as statistics
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...

as well as the social
Social organisms, including human(s), live collectively in interacting populations. This interaction is considered social whether they are aware of it or not, and whether the exchange is voluntary or not.
Etymology
The word "social" derives from ...

and behavioural sciences
Behavioral sciences explore the cognitive processes within organisms and the behavioral interactions between organisms in the natural world. It involves the systematic analysis and investigation of human and animal behavior through naturalistic o ...

, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.
Measurement is a cornerstone of trade, science
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence f ...

, technology
Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, scienc ...

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 approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosop ...

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 wid ...

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

The measurement of a property may be categorized by the following criteria: type, magnitude,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 a theatrical presentation
Music
* ''Unit'' (al ...

, and uncertainty
Uncertainty refers to 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 observable or ...

. 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. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Estab ...

.
* 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
Accuracy and precision are two measures of ''observational error''.
''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each other ...

of the measuring instrument.
Standardization of measurement units

Measurements most commonly use theInternational System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...

(SI) as a comparison framework. The system defines seven fundamental units: kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...

, metre
The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pr ...

, candela
The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...

, second
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...

, 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 unit of electric current in the International System of Units (SI). One ampere is equal to elect ...

, kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...

, and mole. All of these units are defined without reference to a particular physical object which serves as a standard. 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 that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, ...

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, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for ...

(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 on the wave, such as two adjacent crests, tr ...

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 in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...

. This directly influenced the Michelson–Morley experiment
The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 ...

; Michelson and Morley cite Peirce, and improve on his method.
Standards

With the exception of a few fundamental quantum constants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that an inch has to be a certain length, nor that amile
The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of distance; both are based on the older English unit of length equal to 5,280 Englis ...

is a better measure of distance than a kilometre. 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 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 mul ...

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 (BIPM), the intergovernmental organization established i ...

(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 that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...

, 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 of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equiva ...

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 an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

), a division of the United States Department of Commerce, 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 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 ...

.
Units and systems

unit is known or standard quantity in terms of which other physical quantities are measured.Imperial and US customary systems

BeforeSI 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 and the world's most widely used system of measurement. E ...

s were widely adopted around the world, the British systems of English unit
English units are the units of measurement used in England up to 1826 (when they were replaced by Imperial units), which evolved as a combination of the Anglo-Saxon and Roman systems of units. Various standards have applied to English units at d ...

s and later imperial units were used in Britain, the Commonwealth
A commonwealth is a traditional English term for a political community founded for the common good. Historically, it has been synonymous with " republic". The noun "commonwealth", meaning "public welfare, general good or advantage", dates from th ...

and the United States. The system came to be known as U.S. customary units
United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English units ...

in the United States and is still in use there and in a few Caribbean
The Caribbean (, ) ( es, El Caribe; french: la Caraïbe; ht, Karayib; nl, De Caraïben) is a region of the Americas that consists of the Caribbean Sea, its islands (some surrounded by the Caribbean Sea and some bordering both the Caribbean S ...

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
In geology, rock (or stone) 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 o ...

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

Themetric system
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Interna ...

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 ...

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

TheInternational System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...

(abbreviated as SI from the French language
French ( or ) is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the Latin spoken in Gaul, and more specifically in ...

name ''Système International d'Unités'') is the modern revision of the metric system
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Interna ...

. It is the world's most widely used system of units, both in everyday commerce
Commerce is the large-scale organized system of activities, functions, procedures and institutions directly and indirectly related to the exchange (buying and selling) of goods and services among two or more parties within local, regional, nation ...

and in science
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence f ...

. 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, i.e. the unit for power, is defined from the base units as m=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 or rule is a tool used in, for example,geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...

, 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 = 1tonne
The tonne ( or ; symbol: t) is a unit of mass equal to 1000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton to distinguish it from the non-metric units of the short ton (United States c ...

;
* 10 years = 1 decade; 100 years = 1 century; 1000 years = 1 millennium
Building trades

The Australian building trades adopted themetric system
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Interna ...

in 1966 and the units used for measurement of length are metres
The metre (British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...

(m) and millimetres (mm). Centimetres (cm) are avoided as they cause confusion when reading 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 byEdmund 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 ...

in 1620. The base unit is Gunter's chain 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 global professional body for surveyors, founded in London in 1868. It works at a cross-governmental level, and aims to promote and enforce the highest international standards in the va ...

(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 contractual 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 ashour
An hour ( symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ...

s, days, weeks, months and year
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in 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 hou ...

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. Infree fall
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it ...

, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the ounce
The ounce () is any of several different units of mass, weight or volume and is derived almost unchanged from the , an Ancient Roman unit of measurement.
The avoirdupois ounce (exactly ) is avoirdupois pound; this is the United States cust ...

, pound, and ton. The metric units gram
The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to t ...

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, nominal value is measured in terms of money, whereas real value is measured against goods or services. A real value is one which has been adjusted for inflation, enabling comparison of quantities as if the prices of goods had not ...

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 questionnaires as a measurement instrument. As all other measurements, measurement in survey research is also vulnerable to measurement error, 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 adecimal separator
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The ch ...

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 oferror
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. The etymology derives from the Latin term 'errare', meaning 'to stray'.
In statistics ...

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, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
E ...

, a mathematical operation 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 necessarily a " mistak ...

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 flu ...

.
* 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 toJohn Wallis
John Wallis (; la, Wallisius; ) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal ...

and Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the great ...

, and was foreshadowed in Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postul ...

.
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 ofStanley Smith Stevens
Stanley Smith Stevens (November 4, 1906 – January 18, 1973) was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory, studying psychoacoustics, and he is credited with the introduction of Stevens's power law. Stevens auth ...

, 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
Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. Th ...

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
Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 194 ...

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
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set.
For a data set, the ''arithm ...

and statistics
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...

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 estimation and measurement.
Quantum mechanics

Inquantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, 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
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...

of the system. When a measurement is performed, the wavefunction of the quantum system " collapses" to a single, definite value. The unambiguous meaning of the measurement problem is an unresolved fundamental problem in quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

.
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
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects.
Overview
The process ...

* Detection limit
* Differential linearity
* Dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as ...

* Dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

* Econometrics
* Electrical measurements
* Environmental error
* History of measurement
The earliest recorded systems of weights and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction and trade. Early standard units might only have ap ...

* History of science and technology
The history of science and technology (HST) is a field of history that examines the understanding of the natural world (science) and the ability to manipulate it ( technology) at different points in time. This academic discipline also studies the ...

* Instrumentation
Instrumentation a collective term for measuring instruments that are used for indicating, measuring and recording physical quantities. The term has its origins in the art and science of scientific instrument-making.
Instrumentation can refer to ...

* Integral linearity
A measurement system consists of a sensor, to input the physical parameter that is of interest, and an output to a medium that is suitable for reading by the system that needs to know the value of the parameter. (This could be a device to convert ...

* ISO 10012, Measurement management systems
* Key relevance in locksmithing
* Least count {{Short description, Smallest value a measuring instrument can measure
In the science of measurement, the least count of a measuring instrument is the smallest value in the measured quantity that can be resolved on the instrument's scale. William ...

* Levels of measurement
* List of humorous units of measurement
Many people have made use of, or invented, units of measurement intended primarily for their humor value. This is a list of such units invented by sources that are notable for reasons other than having made the unit itself, and that are widely ...

* List of unusual units of measurement
An unusual unit of measurement is a unit of measurement that does not form part of a coherent system of measurement, especially because its exact quantity may not be well known or because it may be an inconvenient multiple or fraction of a base ...

* Measurement in quantum mechanics
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what m ...

* Measuring instrument
A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Estab ...

* Measurement (journal)
* Measurement uncertainty
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by ...

* NCSL International
* Number sense
In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by St ...

* Observable quantity
* Orders of magnitude
An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic di ...

* Primary instrument
* Psychometrics
* Quantification (science)
In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantities. Quantification in this sense is fundamental to the scientific method ...

* Remote sensing
Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Earth ...

* Standard (metrology)
In metrology (the science of measurement), a standard (or etalon) is an object, system, or experiment that bears a defined relationship to a unit of measurement of a physical quantity. Standards are the fundamental reference for a system of weig ...

* Test method
A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a definitive procedure that produces a test result. In order to ensure accurate and relevant test results, a tes ...

* Timeline of temperature and pressure measurement technology
Timeline of temperature and pressure measurement technology. A history of temperature measurement and pressure measurement technology.
Timeline
1500s
* 1592–1593 — Galileo Galilei builds a device showing variation of hotness known as the ...

* Timeline of time measurement technology
The history of timekeeping devices dates back to when ancient civilizations first observed astronomical bodies as they moved across the sky. Devices and methods for keeping time have since then improved through a long series of new inventions ...

* Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physi ...

* Virtual instrumentation
Virtual instrumentation is the use of customizable software and modular measurement hardware to create user-defined measurement systems, ''called virtual instruments''.
Traditional hardware instrumentation systems are made up of fixed hardware co ...

* Web analytics
Web analytics is the measurement, collection, analysis, and reporting of web data to understand and optimize web usage. Web analytics is not just a process for measuring web traffic but can be used as a tool for business and market research a ...

* Weights and measures
* Metric fixation
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 Accuracy and precision Metrology