Measurement

For the scientific journal, seeMeasurement(journal).

Measurementis thequantificationofattributesof 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 aphysical quantityis as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. Innatural sciencesandengineering,measurements do not apply tonominal propertiesof objects or events, which is consistent with the guidelines of theInternational vocabulary of metrologypublished by theInternational Bureau of Weights and Measures.However, in other fields such asstatisticsas well as thesocialandbehavioural sciences,measurements can havemultiple levels,which would include nominal, ordinal, interval and ratio scales.

Four measuring devices having metric calibrations

Measurement is a cornerstone oftrade,science,technologyandquantitative researchin many disciplines. Historically, manymeasurement systemsexisted 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 modernInternational System of Units(SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field ofmetrology.

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

History

This section is an excerpt fromHistory of measurement.[edit]

Detail of acubitrod in theMuseo EgizioofTurin

The earliest recorded systems ofweights and measuresoriginate 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 applied to a single community or small region, with every area developing its own standards for lengths, areas, volumes and masses. Often such systems were closely tied to one field of use, so that volume measures used, for example, for dry grains were unrelated to those for liquids, with neither bearing any particular relationship to units of length used for measuring cloth or land. With development of manufacturing technologies, and the growing importance of trade between communities and ultimately across the Earth, standardized weights and measures became critical. Starting in the 18th century, modernized, simplified and uniform systems of weights and measures were developed, with the fundamental units defined by ever more precise methods in the science ofmetrology.The discovery and application ofelectricitywas one factor motivating the development of standardized internationally applicable units.

Methodology

The measurement of a property may be categorized by the following criteria:type,magnitude,unit,anduncertainty.They enable unambiguous comparisons between measurements.

• Thelevelof 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.
• Themagnitudeis the numerical value of the characterization, usually obtained with a suitably chosenmeasuring instrument.
• Aunitassigns 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.
• Anuncertaintyrepresents therandom and systemic errorsof the measurement procedure; it indicates a confidence level in the measurement. Errors are evaluated by methodically repeating measurements and considering theaccuracy and precisionof the measuring instrument.

Standardization of measurement units

Measurements most commonly use theInternational System of Units(SI) as a comparison framework. The system defines sevenfundamental units:kilogram,metre,candela,second,ampere,kelvin,andmole.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 aphysical constantor 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 seven base units in the SI system. Arrows point from units to those that depend on them.

The first proposal to tie an SI base unit to an experimental standard independent of fiat was byCharles Sanders Peirce(1839–1914),who proposed to define the metre in terms of thewavelengthof aspectral line.This directly influenced theMichelson–Morley experiment;Michelson and Morley cite Peirce, and improve on his method.

Standards

With the exception of a few fundamentalquantumconstants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that aninchhas to be a certain length, nor that amileis a better measure of distance than akilometre.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 measurementare generally defined on a scientific basis, overseen by governmental or independent agencies, and established in international treaties, pre-eminent of which is theGeneral Conference on Weights and Measures(CGPM), established in 1875 by theMetre Convention,overseeing the International System of Units (SI). For example, the metre was redefined in 1983 by the CGPM in terms of the speed of light, the kilogram was redefined in 2019 in terms of thePlanck constantand the international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia and South Africa as beingexactly0.9144 metres.

In the United States, the National Institute of Standards and Technology (NIST), a division of theUnited States Department of Commerce,regulates commercial measurements. In the United Kingdom, the role is performed by theNational Physical Laboratory(NPL), in Australia by theNational Measurement Institute,in South Africa by theCouncil for Scientific and Industrial Researchand in India theNational Physical Laboratory of India.

Units and systems

Main articles:Unit of measurementandSystem of measurement

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

Ababy bottlethat measures in threemeasurement systems—metric,imperial (UK),andUS customary.

Imperial and US customary systems

Main article:Imperial and US customary measurement systems

BeforeSI unitswere widely adopted around the world, the British systems ofEnglish unitsand laterimperial unitswere used in Britain, theCommonwealthand the United States. The system came to be known asU.S. customary unitsin the United States and is still in use there and in a fewCaribbeancountries. These various systems of measurement have at times been calledfoot-pound-secondsystems 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 instoneand 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 systemis a decimalsystem of measurementbased on its units for length, the metre and for mass, the kilogram. It exists in several variations, with different choices ofbase 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(abbreviated as SI from theFrench languagenameSystème International d'Unités) is the modern revision of themetric system.It is the world's most widely usedsystem of units,both in everydaycommerceand inscience.The SI was developed in 1960 from themetre–kilogram–second(MKS) system, rather than thecentimetre–gram–second(CGS) system, which, in turn, had many variants. The SI units for the seven base physical quantities are:

Base quantity	Base unit	Symbol	Defining constant
time	second	s	hyperfine splitting incaesium-133
length	metre	m	speed of light,c
mass	kilogram	kg	Planck constant,h
electric current	ampere	A	elementary charge,e
temperature	kelvin	K	Boltzmann constant,k
amount of substance	mol	mol	Avogadro constant,NA
luminous intensity	candela	cd	luminous efficacyof a 540 THz source,Kcd

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, thewatt,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

Main article:Length measurement

See also:List of length, distance, or range measuring devices

A 2-metre carpenter'sruler

Aruleror rule is a tool used in, for example,geometry,technical drawing,engineering, and carpentry, to measure lengths or distances or to draw straight lines. Strictly speaking, theruleris the instrument used torulestraight lines and the calibrated instrument used for determining length is called ameasure,however common usage calls both instrumentsrulersand the special namestraightedgeis used for an unmarked rule. The use of the wordmeasure,in the sense of a measuring instrument, only survives in the phrasetape 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.

Time

Main article:Time

Time is an abstract measurement ofelementalchanges over a non-spatial continuum. It is denoted by numbers and/or named periods such ashours,days,weeks,monthsandyears.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

Main article:Weighing scale

Massrefers 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,(no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include theounce,pound,andton.The metric unitsgramand kilogram are units of mass.

One device for measuring weight or mass is called a weighing scale or, often, simply ascale.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

Main article:Measurement in economics

The measures used in economics are physical measures,nominal pricevalue measures andreal pricemeasures. These measures differ from one another by the variables they measure and by the variables excluded from measurements.

Survey research

Main article:Survey methodology

Measurement station C of EMMA experiment situated at the depth of 75 meters in thePyhäsalmi Mine.

In the field of survey research, measures are taken from individual attitudes, values, and behavior usingquestionnairesas a measurement instrument. As all other measurements, measurement in survey research is also vulnerable tomeasurement 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 becorrected 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 separatorto 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 theproblem of measuring the timeit takes an object to fall a distance of one metre (about 39in). 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 oferrorthat arise:

• This computation used for theacceleration of gravity9.8 metres per second squared (32 ft/s²). 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 asquare root,amathematical operationthat required rounding off to some number of significant digits, in this case two significant digits.

Additionally, other sources ofexperimental errorinclude:

• 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,
• 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,measurementis the determination or estimation of ratios of quantities.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 WallisandIsaac Newton,and was foreshadowed inEuclid's Elements.

Representational theory

In the representational theory,measurementis defined as "the correlation of numbers with entities that are not numbers".The most technically elaborated form of representational theory is also known asadditive 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,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, anempirical relationshipis a relationship or correlation based solely onobservationrather 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

Theory

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 themeanandstatisticsof 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. In this view, unlike thepositivistrepresentational 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 betweenestimationand measurement.

Quantum mechanics

Inquantum mechanics,a measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Quantum measurements are always statistical samples from a probability distribution; the distribution for many quantum phenomena is discrete.Quantum measurements alterquantum statesand yet repeated measurements on a quantum state are reproducible. The measurement appears to act as a filter, changing the quantum state into one with the single measured quantum value.The unambiguous meaning of thequantum measurementis an unresolved fundamental problem inquantum mechanics;the most common interpretation is that when a measurement is performed, the wavefunction of the quantum system "collapses"to a single, definite value.

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.

See also

Main article:Outline of metrology and measurement

• Conversion of units
• Electrical measurements
• History of measurement
• ISO 10012,Measurement management systems
• Levels of measurement
• List of humorous units of measurement
• List of unusual units of measurement
• Measurement in quantum mechanics
• Measurement uncertainty
• NCSL International
• Observable quantity
• Orders of magnitude
• Quantification (science)
• Standard (metrology)
• Timeline of temperature and pressure measurement technology
• Timeline of time measurement technology
• Weights and measures

External links

• Media related toMeasurementat Wikimedia Commons
• Schlaudt, Oliver 2020: "measurement". In: Kirchhoff, Thomas (ed.): Online Encyclopedia Philosophy of Nature. Heidelberg: Universitätsbibliothek Heidelberg,measurement.
• Tal, Era 2020: "Measurement in Science". In: Zalta, Edward N. (ed.): The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), URL = <Measurement in Science>.
• Ball, Robert Stawell(1883)."Measurement".Encyclopædia Britannica.Vol. XV (9th ed.). pp. 659–668.
• A Dictionary of Units of MeasurementArchived2018-10-06 at theWayback Machine
• 'Metrology – in short' 3rd edition, July 2008ISBN978-87-988154-5-7