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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. In other words, measurement is a process of determining how large or small a
physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For exam ...
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 repeatab ...
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: chemistry ...
. 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, indust ...
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 naturalisti ...
, 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 and services from one person or entity to another, often in exchange for money. Economists refer to a system or network that allows trade as a market. An early form of trade, barter, saw the direct exc ...
,
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 ...
,
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, scien ...
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 philoso ...
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 pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(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. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
. 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'' (a ...
, 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 ...
. 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. Est ...
. * 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 ot ...
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 pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(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 pre ...
,
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 t ...
,
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 ea ...
,
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 188 ...
; 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 interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizat ...
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 of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth ...
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 United States customary unit of distance; both are based on the older English unit of length equal to 5,280 Engli ...
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 International System of Units (SI), equal to one thousand metres (kilo- being the SI prefix for ). It is now the measurement unit used for ...
. 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 multi ...
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, Braz ...
, 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 equivale ...
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 The United States Department of Commerce is an executive department of the U.S. federal government concerned with creating the conditions for economic growth and opportunity. Among its tasks are gathering economic and demographic data for bus ...
, 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's central and premier scientific research and development organisation. It was established by an act of parliament in 1945 and is situated on its own campus in the c ...
and in India the National Physical Laboratory of India.


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 and the world's most widely used system of measurement. ...
s were widely adopted around the world, the British systems of English units 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 first defined in the British Weights and Measures Act 1824 and continued to be developed thr ...
s 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 the ...
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, 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 ...
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 compound, chemical composition, and the way in which it is formed. Rocks ...
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 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 Intern ...
is a decimal system 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

The
International System of Units 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. ...
(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 N ...
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 Intern ...
. It is the world's most widely used
system of units A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement i ...
, 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, natio ...
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 ...
. The SI was developed in 1960 from the
metre–kilogram–second The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second (MKS) as base units. It forms the base of the International System of Units (SI), though SI has since been redefined by different fundament ...
(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 the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...
, 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, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines. Variants Rulers have long ...
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 c ...
,
technical drawing Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed. Technical drawing is essential for communicating ideas in industry and engineering ...
, 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 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 State ...
; * 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 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 Intern ...
in 1966 and the units used for measurement of length are
metres The metre (British 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 orthography, the two most notable va ...
(m) and
millimetres 330px, Different lengths as in respect to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 meter to 1 millimeter. The millimetre (American and British English spelling differences#-re, -er, ...
(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 by Edmund Gunter 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. It was designed and introduced in 1620 by English clergyman and mathematician Edmund Gunter (1581–1626). It enabled plots of land to be a ...
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
contract A contract is a legally enforceable agreement between two or more parties that creates, defines, and governs mutual rights and obligations between them. A contract typically involves the transfer of goods, services, money, or a promise to tr ...
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: 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,
day A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours, 1440 minutes, or 86,400 seconds. In everyday life, the word "day" often refers to a solar day, which is the length between two ...
s,
week A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are of ...
s, 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 h ...
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 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 ...
, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the ounce, pound, and
ton Ton is the name of any one of several units of measure. It has a long history and has acquired several meanings and uses. Mainly it describes units of weight. Confusion can arise because ''ton'' can mean * the long ton, which is 2,240 pounds ...
. 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 th ...
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 value measures and
real 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 ...
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 that consists of a set of questions (or other types of prompts) for the purpose of gathering information from respondents through survey or statistical study. A research questionnaire is typically a mix ...
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, an error is not necessarily a "mistake ...
, 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 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 choi ...
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. 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 . ...
, a
mathematical operation In mathematics, an operation is a Function (mathematics), function which takes zero or more input values (also called "''operands''" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most c ...
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 " mista ...
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 to
John 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, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
, 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, postu ...
.


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 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. The ...
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 1940s. ...
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 '' ar ...
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, indust ...
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 Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is de ...
and measurement.


Quantum mechanics

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, ...
, 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 In quantum mechanics, the measurement problem is the problem of how, or whether, wave function collapse occurs. The inability to observe such a collapse directly has given rise to different interpretations of quantum mechanics and poses a key s ...
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 Airy points (after George Biddell Airy) are used for precision measurement ( metrology) to support a length standard in such a way as to minimise bending or drop of a horizontally supported beam. Choice of support points A kinematic support ...
*
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 The limit of detection (LOD or LoD) is the lowest signal, or the lowest corresponding quantity to be determined (or extracted) from the signal, that can be observed with a sufficient degree of confidence or statistical significance. However, the ...
* 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 mi ...
* Dimensionless number *
Econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. ...
* 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 * ISO 10012, Measurement management systems * Key relevance in locksmithing * Least count *
Levels of measurement Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scal ...
*
List of humorous units of measurement Many people have made use of, or invented, units of measurement intended primarily for their humor Humour (Commonwealth English) or humor (American English) is the tendency of experiences to provoke laughter and provide amusement. The ...
*
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 bas ...
*
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. Est ...
* 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 Sta ...
* 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 dis ...
* Primary instrument *
Psychometrics Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and ...
*
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 Ear ...
* Standard (metrology) *
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 test m ...
* Timeline of temperature and pressure measurement technology * Timeline of time measurement technology *
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 physic ...
* Virtual instrumentation *
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 and ...
*
Weights and measures 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 multip ...
*
Metric fixation Metric fixation refers to a tendency for decision-makers to place excessively large emphases on selected metrics. In management (and many other social science fields), decision makers typically use metrics to measure how well a person or an organiz ...


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