Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of measurement are dependent on the context and discipline.

In the natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures.

However, in other fields such as statistics as well as the social and behavioral sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.

Measurement is a cornerstone of trade, science, technology, and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (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.


Maya (Sanskrit) is a word with unclear etymology, probably comes from the root ma which means "to measure".

Maya (Devanagari), literally "illusion" or "magic", has multiple meanings in Indian philosophies depending on the context. In ancient Vedic literature, Maya literally implies extraordinary power and wisdom. In later Vedic texts and modern literature dedicated to Indian traditions, Maya connotes a "magic show, an illusion where things appear to be present but are not what they seem". Maya is also a spiritual concept connoting "that which exists, but is constantly changing and thus is spiritually unreal", and the "power or the principle that conceals the true character of spiritual reality".

In Buddhism, Maya is the name of Gautama Buddha's mother. In Hinduism, Maya is also an epithet for goddess, and the name of a manifestation of Lakshmi, the goddess of "wealth, prosperity and love". Maya is also a name for girls.


Maya (Sanskrit) is a word with unclear etymology, probably comes from the root ma which means "to measure".

According to Monier Williams, maya meant "wisdom and extraordinary power" in an earlier older language, but from the Vedic period onwards, the word came to mean "illusion, unreality, deception, fraud, trick, sorcery, witchcraft and magic". However, P. D. Shastri states that the Monier Williams' list is a "loose definition, misleading generalization", and not accurate in interpreting ancient Vedic and medieval era Sanskrit texts; instead, he suggests a more accurate meaning of maya is "appearance, not mere illusion".

According to William Mahony, the root of the word may be man- or "to think", implying the role of imagination in the creation of the world. In early Vedic usage, the term implies, states Mahony, "the wondrous and mysterious power to turn an idea into a physical reality".

Franklin Southworth states the word's origin is uncertain, and other possible roots of maya include may- meaning mystify, confuse, intoxicate, delude, as well as may- which means "disappear, be lost".

Jan Gonda considers the word related to ma, which means "mother", as do Tracy Pintchman and Adrian Snodgrass, serving as an epithet for goddesses such as Lakshmi. Maya here implies art, is the maker’s power, writes Zimmer, "a mother in all three worlds", a creatrix, her magic is the activity in the Will-spirit.

A similar word is also found in the Avestan maya with the meaning of "magic power".


A ruler, sometimes called a rule or line gauge, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure or draw straight lines.[1]


Rulers have long been made from different materials and in a multiple sizes. Some are wooden. Plastics have also been used since they were invented; they can be molded with length markings instead of being scribed. Metal is used for more durable rulers for use in the workshop; sometimes a metal edge is embedded into a wooden desk ruler to preserve the edge when used for straight-line cutting. 12 in or 30 cm in length is useful for a ruler to be kept on a desk to help in drawing. Shorter rulers are convenient for keeping in a pocket.[2] Longer rulers, e.g., 18 in (46 cm) are necessary in some cases. Rigid wooden or plastic yardsticks, 1 yard long, and meter sticks, 1 meter long, are also used. Classically, long measuring rods were used for larger projects, now superseded by tape measure, surveyor's wheel or laser rangefinders.

Desk rulers are used for three main purposes: to measure, to aid in drawing straight lines and as a straight guide for cutting and scoring with a blade. Practical rulers have distance markings along their edges.

A line gauge is a type of ruler used in the printing industry. These may be made from a variety of materials, typically metal or clear plastic. Units of measurement on a basic line gauge usually include inches, agate, picas, and points. More detailed line gauges may contain sample widths of lines, samples of common type in several point sizes, etc.

Measuring instruments similar in function to rulers are made portable by folding (carpenter's folding rule) or retracting into a coil (metal tape measure) when not in use. When extended for use, they are straight, like a ruler. The illustrations on this page show a 2 m (6 ft 7 in) carpenter's rule, which folds down to a length of 25 cm (10 in) to easily fit in a pocket, and a 5 m (16 ft) tape, which retracts into a small housing.

A flexible length measuring instrument which is not necessarily straight in use is the tailor's fabric tape measure, a length of tape calibrated in inches and centimeters. It is used to measure around a solid body, e.g., a person's waist measurement, as well as linear measurement, e.g., inside leg. It is rolled up when not in use, taking up little space.

A contraction rule is made having larger divisions than standard measures to allow for shrinkage of a metal casting. They may also be known as a shrinkage or shrink rule.[3]

A ruler software program can be used to measure pixels on a computer screen or mobile phone. These programs are also known as screen rulers.


Metrology is the science of measurement.[1] It establishes a common understanding of units, crucial in linking human activities.[2] Modern metrology has its roots in the French Revolution's political motivation to standardise units in France, when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention.[3][4] This has evolved into the International System of Units (SI) as a result of a resolution at the 11th Conference Generale des Poids et Mesures (CGPM) in 1960.

Metrology is divided into three basic overlapping activities. The first being the definition of units of measurement, second the realisation of these units of measurement in practice, and last traceability, which is linking measurements made in practice to the reference standards. These overlapping activities are used in varying degrees by the three basic sub-fields of Metrology. The sub-fields are scientific or fundamental metrology, which is concerned with the establishment of units of measurement, Applied, technical or industrial metrology, the application of measurement to manufacturing and other processes in society, and Legal metrology, which covers the regulation and statutory requirements for measuring instruments and the methods of measurement.

In each country, a national measurement system (NMS) exists as a network of laboratories, calibration facilities and accreditation bodies which implement and maintain its metrology infrastructure. The NMS affects how measurements are made in a country and their recognition by the international community, which has a wide-ranging impact in its society (including economics, energy, environment, health, manufacturing, industry and consumer confidence).[10][11] The effects of metrology on trade and economy are some of the easiest-observed societal impacts. To facilitate fair trade, there must be an agreed-upon system of measurement.


The ability to measure alone is insufficient; standardisation is crucial for measurements to be meaningful. The first record of a permanent standard was in 2900 BC, when the royal Egyptian cubit was carved from black granite. The cubit was decreed to be the length of the Pharaoh's forearm plus the width of his hand, and replica standards were given to builders. The success of a standardised length for the building of the pyramids is indicated by the lengths of their bases differing by no more than 0.05 percent.

International system of units

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, and one physical artefact. The artefact is the international prototype kilogram, certified in 1889, and consisting of a cylinder of platinum-iridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units entirely in terms of constants of nature, scheduled to be put into effect on 20 May 2019.[1]

Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the katal, was defined in 1999.

The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.

The motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units (MKS) rather than any variant of the CGS. Since then, the SI has been adopted by all countries except the United States, Liberia and Myanmar.[2]

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 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 of metrology. The discovery and application of electricity was one factor motivating the development of standardized internationally applicable units.

Contents 1 Sources of information 2 Earliest known systems 3 History of units 3.1 Units of length 3.2 Units of mass 3.3 Units of time and angle 4 Forerunners of the metric system 5 Metric conversion 6 References 7 Further reading

Units of length

The Egyptian cubit, the Indus Valley units of length referred to above and the Mesopotamian cubit were used in the 3rd millennium BC and are the earliest known units used by ancient peoples to measure length. The units of length used in ancient India included the dhanus, or dhanush (bow), the krosa (cry, or cow-call) and the yojana (stage).

The common cubit was the length of the forearm from the elbow to the tip of the middle finger. It was divided into the span of the hand or the length between the tip of little finger to the tip of the thumb (one-half cubit), the palm or width of the hand (one sixth), and the digit or width of the middle finger (one twenty-fourth). The Royal Cubit, which was a standard cubit enhanced by an extra palm—thus 7 palms or 28 digits long—was used in constructing buildings and monuments and in surveying in ancient Egypt. The inch, foot, and yard evolved from these units through a complicated transformation not yet fully understood. Some believe they evolved from cubic measures; others believe they were simple proportions or multiples of the cubit. In whichever case, the Greeks and Romans inherited the foot from the Egyptians. The Roman foot (~296 mm) was divided into both 12 unciae (inches) (~24.7 mm) and 16 digits (~18.5 mm). The Romans also introduced the mille passus (1000 paces) or double steps, the pace being equal to five Roman feet (~1480 mm). The Roman mile of 5000 feet (1480 m) was introduced into England during the occupation. Queen Elizabeth I (reigned from 1558 to 1603) changed, by statute, the mile to 5280 feet (~1609 m) or 8 furlongs, a furlong being 40 rod (unit)s (~201 m) of 5.5 yards (~5.03 m) each.

The introduction of the yard (0.9144 m) as a unit of length came later, but its origin is not definitely known. Some believe the origin was the double cubit, others believe that it originated from cubic measure. Whatever its origin, the early yard was divided by the binary method into 2, 4, 8, and 16 parts called the half-yard, span, finger, and nail. The association of the yard with the "gird" or circumference of a person's waist or with the distance from the tip of the nose to the end of the thumb of King Henry I (reigned 1100–1135) are probably standardizing actions, since several yards were in use in Britain. There were also Rods, Poles and Perches for measurements of length. The following table lists the equivalents.


In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.[1][2]

Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere.

The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. Ten dimensions are used to describe superstring theory, eleven dimensions can describe supergravity and M-theory, and the state-space of quantum mechanics is an infinite-dimensional function space.

The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.

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 charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra.

The concept of physical dimension was introduced by Joseph Fourier in 1822. Physical quantities that are of the same kind (also called commensurable) have the same dimension (length, time, mass) and can be directly compared to each other, even if they are originally expressed in differing units of measure (such as yards and meters). If physical quantities have different dimensions (such as length vs. mass), they cannot be expressed in terms of similar units and cannot be compared in quantity (also called incommensurable). For example, asking whether a kilogram is larger than an hour is meaningless.

Any physically meaningful equation (and any inequality) will have the same dimensions on its left and right sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It also serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation.

Unit 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.[1] Any other quantity of that kind can be expressed as a multiple of the unit of measurement.

For example, a length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre". Measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.

The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present. A multitude of systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system.

In trade, weights and measures is often a subject of governmental regulation, to ensure fairness and transparency. The International Bureau of Weights and Measures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI).

Metrology is the science of developing nationally and internationally accepted units of measurement.

In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures historically developed for commercial purposes.

Science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life. The judicious selection of the units of measurement can aid researchers in problem solving (see, for example, dimensional analysis).

In the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement.

Base units

A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a base quantity. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others.

A base unit is one that has been explicitly so designated; a secondary unit for the same quantity is a derived unit. For example, when used with the International System of Units, the gram is a derived unit, not a base unit.

In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, temperature, energy, and weight, and units are used to describe their magnitude or quantity. Many of these quantities are related to each other by various physical laws, and as a result the units of a quantities can be generally be expressed as a product of powers of other units; for example, momentum is mass multiplied by velocity, while velocity is measured in distance divided by time. These relationships are discussed in dimensional analysis. Those that can be expressed in this fashion in terms of the base units are called derived units [fr].

In the International System of Units, there are seven base units: kilogram, metre, candela, second, ampere, kelvin, and mole.

Natural units Main article: Natural units There are other relationships between physical quantities that can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions or simply to define it as unity or a fixed dimensionless number, and reduce the number of explicit fundamental constants by one.

For instance, time and distance are related to each other by the speed of light, c, which is a fundamental constant. It is possible to use this relationship to eliminate either the unit of time or that of distance. Similar considerations apply to the Planck constant, h, which relates energy (with dimension expressible in terms of mass, length and time) to frequency (with dimension expressible in terms of time). In theoretical physics it is customary to use such units (natural units) in which c = 1 and h = 1. A similar choice can be applied to the vacuum permittivity or permittivity of free space, e0.

One could eliminate any of the metre and second by setting c to unity (or to any other fixed dimensionless number). One could then eliminate the kilogram by setting h to a dimensionless number. One could then further eliminate the ampere by setting either the permittivity of free space e0 (alternatively, the Coulomb constant ke = 1/(4pe0)) or the elementary charge e to a dimensionless number. One could similarly eliminate the mole as a base unit by reference to Avogadro's number. One could eliminate the kelvin as it can be argued that temperature simply expresses the energy per particle per degree of freedom, which can be expressed in terms of energy (or mass, length, and time). Another way of saying this is that Boltzmann's constant kB could be expressed as a fixed dimensionless number. Similarly, one could eliminate the candela, as that is defined in terms of other physical quantities. That leaves one base dimension and an associated base unit, but we still have plenty of fundamental constants left to eliminate that too – for instance one could use G, the gravitational constant, me, the electron rest mass, or ?, the cosmological constant. A widely used choice, in particular for theoretical physics, is given by the system of Planck units, which are defined by setting h = c = G = kB = ke = 1.

That leaves every physical quantity expressed as a dimensionless number, so it is not surprising that there are also physicists who have cast doubt on the very existence of incompatible fundamental quantities.[1][2][3]

Natural units

In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly 1. These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as e and c, unless it is known which units (in dimensionful units) the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined.[1][2]

Color measurement

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Closed Loop

Closed loop may refer to:

A feedback loop, often found in:

Closed-loop transfer function, where a closed-loop controller may be used

Electronic feedback loops in electronic circuits

PID controller, a commonly used closed-loop controller

Closed ecological system not relying on matter exchange outside of the system, as opposed to open loop

Ecological sanitation systems or ecosan, intended to close the nutrient and water cycle

Pulling water from one area of a reef aquarium and pumping it immediately elsewhere in the tank to create higher flow and minimize dead spots

Closed-loop communication, a communication technique used to avoid misunderstandings

Circular economy, one in which materials are consistently reused rather than discharged as waste

Closed time loop, or predestination paradox, a paradox of time travel that is often used as a convention in science fiction

Closed curve, a mathematical curve described as a set of continuous parametric equations over a closed interval of real numbers for which the start point equals the end point

Knot loop