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125-601: Decimal multiplicative prefixes have been a feature of all forms of the metric system , with six of these dating back to the system's introduction in the 1790s. Metric prefixes have also been used with some non-metric units. The SI prefixes are metric prefixes that were standardised for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 2022. Since 2009, they have formed part of

250-407: A " μ " key, so it is necessary to use a key-code; this varies depending on the operating system, physical keyboard layout, and user's language. The LaTeX typesetting system features an SIunitx package in which the units of measurement are spelled out, for example, \qty{3}{\tera\hertz} formats as "3 THz". The use of prefixes can be traced back to the introduction of the metric system in

375-466: A coherent system the units of force , energy , and power are chosen so that the equations hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, Einstein 's mass–energy equation , E = mc , does not require extraneous constants when expressed in coherent units. The CGS system had two units of energy,

500-828: A commission to implement this new standard alone, and in 1799, the new system was launched in France. The units of the metric system, originally taken from observable features of nature, are now defined by seven physical constants being given exact numerical values in terms of the units. In the modern form of the International System of Units (SI), the seven base units are: metre for length, kilogram for mass, second for time, ampere for electric current, kelvin for temperature, candela for luminous intensity and mole for amount of substance. These, together with their derived units, can measure any physical quantity. Derived units may have their own unit name, such as

625-585: A decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it. Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, other metric systems include: the MKS system of units and the MKSA systems, which are the direct forerunners of the SI; the centimetre–gram–second (CGS) system and its subtypes,

750-576: A driver, in order to maintain symmetry. The prefixes from tera- to quetta- are based on the Ancient Greek or Ancient Latin numbers from 4 to 10, referring to the 4th through 10th powers of 10. The initial letter h has been removed from some of these stems and the initial letters z , y , r , and q have been added, ascending in reverse alphabetical order, to avoid confusion with other metric prefixes. When mega and micro were adopted in 1873, there were then three prefixes starting with "m", so it

875-450: A fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre–kilogram–second– coulomb (MKSC) and metre–kilogram–second– ampere (MKSA) systems are examples of such systems. The metre–tonne–second system of units (MTS) was based on the metre, tonne and second – the unit of force was the sthène and the unit of pressure was the pièze . It was invented in France for industrial use and from 1933 to 1955

1000-430: A kilogram is a milligram , not a microkilogram . The BIPM specifies 24 prefixes for the International System of Units (SI): The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a coherent system of units . Every physical quantity has exactly one coherent SI unit. For example, 1 m/s = 1 m / (1 s) is the coherent derived unit for velocity. With

1125-408: A list of non-SI units accepted for use with SI , including the hour, minute, degree of angle, litre, and decibel. Although the term metric system is often used as an informal alternative name for the International System of Units, other metric systems exist, some of which were in widespread use in the past or are even still used in particular areas. There are also individual metric units such as

1250-467: A metre. This is unlike older systems of units in which the ratio between the units for longer and shorter distances varied: there are 12 inches in a foot, but the number of 5,280 feet in a mile is not a power of 12. For many everyday applications, the United States has resisted the adoption of a decimal-based system, continuing to use "a conglomeration of basically incoherent measurement systems ". In

1375-459: A number of definitions for the non-SI unit, the calorie . There are gram calories and kilogram calories. One kilogram calorie, which equals one thousand gram calories, often appears capitalised and without a prefix (i.e. Cal ) when referring to " dietary calories " in food. It is common to apply metric prefixes to the gram calorie, but not to the kilogram calorie: thus, 1 kcal = 1000 cal = 1 Cal. Metric prefixes are widely used outside

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1500-556: A number of different ways over the centuries. The SI system originally derived its terminology from the metre, kilogram, second system of units , though the definitions of the fundamental SI units have been changed to depend only on constants of nature. Other metric system variants include the centimetre–gram–second system of units , the metre–tonne–second system of units , and the gravitational metric system . Each of these has some unique named units (in addition to unaffiliated metric units ) and some are still in use in certain fields. In

1625-410: A positive or negative power. It can also be combined with other unit symbols to form compound unit symbols. For example, g/cm is an SI unit of density , where cm is to be interpreted as ( cm ) . Prefixes are added to unit names to produce multiples and submultiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of

1750-476: A reintroduction of compound prefixes (e.g. kiloquetta- for 10) if a driver for prefixes at such scales ever materialises, with a restriction that the last prefix must always be quetta- or quecto- . This usage has not been approved by the BIPM. In written English, the symbol K is often used informally to indicate a multiple of thousand in many contexts. For example, one may talk of a 40K salary ( 40 000 ), or call

1875-420: A representative quantity is defined as a base unit of measure. The definition of base units has increasingly been realised in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit derived from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which

2000-406: A second greater than 1; the non-SI units of minute , hour and day are used instead. On the other hand, prefixes are used for multiples of the non-SI unit of volume, the litre (l, L) such as millilitres (ml). Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors. For example, in

2125-524: A specification for units of measurement. The International Bureau of Weights and Measures (BIPM) has described SI as "the modern form of metric system". In 1971 the mole became the seventh base unit of the SI. After the metre was redefined in 1960, the International Prototype of the Kilogram (IPK) was the only physical artefact upon which base units (directly the kilogram and indirectly

2250-474: A standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a mutual acceptance arrangement . In 1791 the commission originally defined the metre based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard metre is now defined as exactly 1 ⁄ 299 792 458 of

2375-411: A thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre , not a millimillimetre . Multiples of the kilogram are named as if the gram were the base unit, so a millionth of

2500-594: A version of the CGPM document (NIST SP 330) which clarifies usage for English-language publications that use American English . The concept of a system of units emerged a hundred years before the SI. In the 1860s, James Clerk Maxwell , William Thomson (later Lord Kelvin), and others working under the auspices of the British Association for the Advancement of Science , building on previous work of Carl Gauss , developed

2625-421: A wide range. For example, driving distances are normally given in kilometres (symbol km ) rather than in metres. Here the metric prefix ' kilo- ' (symbol 'k') stands for a factor of 1000; thus, 1 km = 1000 m . The SI provides twenty-four metric prefixes that signify decimal powers ranging from 10 to 10 , the most recent being adopted in 2022. Most prefixes correspond to integer powers of 1000;

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2750-475: Is a decimal and metric system of units established in 1960 and periodically updated since then. The SI has an official status in most countries, including the United States , Canada , and the United Kingdom , although these three countries are among the handful of nations that, to various degrees, also continue to use their customary systems. Nevertheless, with this nearly universal level of acceptance,

2875-409: Is a decimal -based system of measurement . The current international standard for the metric system is the International System of Units (Système international d'unités or SI), in which all units can be expressed in terms of seven base units: the metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd). These can be made into larger or smaller units with

3000-411: Is derived from length. These derived units are coherent , which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the second ; the unit of length should be either the metre or

3125-470: Is expressed in g/cm , force expressed in dynes and mechanical energy in ergs . Thermal energy was defined in calories , one calorie being the energy required to raise the temperature of one gram of water from 15.5 °C to 16.5 °C. The meeting also recognised two sets of units for electrical and magnetic properties – the electrostatic set of units and the electromagnetic set of units. The CGS units of electricity were cumbersome to work with. This

3250-458: Is important not to use the unit alone to specify the quantity. As the SI Brochure states, "this applies not only to technical texts, but also, for example, to measuring instruments (i.e. the instrument read-out needs to indicate both the unit and the quantity measured)". Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example,

3375-545: Is not coherent. The principle of coherence was successfully used to define a number of units of measure based on the CGS, including the erg for energy , the dyne for force , the barye for pressure , the poise for dynamic viscosity and the stokes for kinematic viscosity . A French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention , also called Treaty of

3500-410: Is not fundamental or even unique – it is a matter of convention. The system allows for an unlimited number of additional units, called derived units , which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is called a coherent derived unit. For example, the coherent derived SI unit of velocity

3625-520: Is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit". Various consultative committees of the CIPM decided in 2016 that more than one mise en pratique would be developed for determining the value of each unit. These methods include the following: The International System of Units, or SI,

3750-468: Is otherwise identical to the SI Brochure. For example, since 1979, the litre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or English-style handwriting. The American NIST recommends that within the United States "L" be used rather than "l". Metrologists carefully distinguish between

3875-427: Is the metre per second , with the symbol m/s . The base and coherent derived units of the SI together form a coherent system of units ( the set of coherent SI units ). A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system, then the equations between the numerical values have exactly the same form, including numerical factors, as

Metric prefix - Misplaced Pages Continue

4000-424: Is the inverse of electrical resistance , with the consequence that the siemens is the inverse of the ohm, and similarly, the ohm and siemens can be replaced with a ratio of an ampere and a volt, because those quantities bear a defined relationship to each other. Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI, such as acceleration, which has

4125-584: The Avogadro number number of specified molecules, was added along with several other derived units. The system was promulgated by the General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM) in 1960. At that time, the metre was redefined in terms of the wavelength of a spectral line of the krypton-86 atom (krypton-86 being a stable isotope of an inert gas that occurs in undetectable or trace amounts naturally), and

4250-530: The CGS electrostatic (cgs-esu) system, the CGS electromagnetic (cgs-emu) system, and their still-popular blend, the Gaussian system ; the metre–tonne–second (MTS) system; and the gravitational metric systems , which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force. The SI has been adopted as the official system of weights and measures by nearly all nations in

4375-529: The ISO/IEC 80000 series of standards, which define the International System of Quantities (ISQ), specifies base and derived quantities that necessarily have the corresponding SI units. Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling

4500-592: The ISO/IEC 80000 standard. They are also used in the Unified Code for Units of Measure (UCUM). The BIPM specifies twenty-four prefixes for the International System of Units (SI) . The first uses of prefixes in SI date back to the definition of kilogram after the French Revolution at the end of the 18th century. Several more prefixes came into use, and were recognised by the 1947 IUPAC 14th International Conference of Chemistry before being officially adopted for

4625-522: The International System of Units (SI). The International System of Units is the modern metric system. It is based on the metre–kilogram–second–ampere (MKSA) system of units from early in the 20th century. It also includes numerous coherent derived units for common quantities like power (watt) and irradience (lumen). Electrical units were taken from the International system then in use. Other units like those for energy (joule) were modelled on those from

4750-562: The Mètre des Archives and Kilogramme des Archives (or their descendants) as their base units, but differing in the definitions of the various derived units. In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the Earth, and together with the milligram and millimetre, this became the first system of mechanical units . He showed that the strength of a magnet could also be quantified in terms of these units, by measuring

4875-543: The Practical System of Electric Units , or QES (quad–eleventhgram–second) system, was being used. Here, the base units are the quad, equal to 10  m (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to 10  g , and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude. In 1901, Giovanni Giorgi showed that by adding an electrical unit as

5000-642: The Year 2000 problem the Y2K problem . In these cases, an uppercase K is often used with an implied unit (although it could then be confused with the symbol for the kelvin temperature unit if the context is unclear). This informal postfix is read or spoken as "thousand", "grand", or just "k". The financial and general news media mostly use m or M, b or B, and t or T as abbreviations for million, billion (10) and trillion (10), respectively, for large quantities, typically currency and population. The medical and automotive fields in

5125-399: The centimetre–gram–second system of units or cgs system in 1874. The systems formalised the concept of a collection of related units called a coherent system of units. In a coherent system, base units combine to define derived units without extra factors. For example, using meters per second is coherent in a system that uses meter for length and seconds for time, but kilometre per hour

Metric prefix - Misplaced Pages Continue

5250-486: The erg that was related to mechanics and the calorie that was related to thermal energy ; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the joule . Maxwell's equations of electromagnetism contained a factor of 1 / ( 4 π ) {\displaystyle 1/(4\pi )} relating to steradians , representative of

5375-608: The speed of light in vacuum c , the hyperfine transition frequency of caesium Δ ν Cs , the Planck constant h , the elementary charge e , the Boltzmann constant k , the Avogadro constant N A , and the luminous efficacy K cd . The nature of the defining constants ranges from fundamental constants of nature such as c to the purely technical constant K cd . The values assigned to these constants were fixed to ensure continuity with previous definitions of

5500-419: The sverdrup and the darcy that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI. Sometimes, SI unit name variations are introduced, mixing information about the corresponding physical quantity or the conditions of its measurement; however, this practice is unacceptable with the SI. "Unacceptability of mixing information with units: When one gives

5625-448: The watt (J/s) and lux (cd/m ), or may just be expressed as combinations of base units, such as velocity (m/s) and acceleration (m/s ). The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is a coherent system , derived units were built up from

5750-528: The year , equal to exactly 31 557 600  seconds ( ⁠365 + 1  / 4 ⁠  days). The unit is so named because it was the average length of a year in the Julian calendar . Long time periods are then expressed by using metric prefixes with the annum, such as megaannum (Ma) or gigaannum (Ga). The SI unit of angle is the radian , but degrees , as well as arc-minutes and arc-seconds , see some scientific use. Common practice does not typically use

5875-435: The 11th CGPM conference in 1960. Other metric prefixes used historically include hebdo- (10) and micri- (10). Double prefixes have been used in the past, such as micromillimetres or millimicrons (now nanometres ), micromicrofarads (μμF; now picofarads , pF), kilomegatonnes (now gigatonnes ), hectokilometres (now 100  kilometres ) and the derived adjective hectokilometric (typically used for qualifying

6000-617: The 1790s, long before the 1960 introduction of the SI. The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not (e.g., millidyne and milligauss). Metric prefixes may also be used with some non-metric units, but not, for example, with the non-SI units of time. The units kilogram , gram , milligram , microgram, and smaller are commonly used for measurement of mass . However, megagram, gigagram, and larger are rarely used; tonnes (and kilotonnes, megatonnes, etc.) or scientific notation are used instead. The megagram does not share

6125-449: The BIPM publishes a mises en pratique , ( French for 'putting into practice; implementation', ) describing the current best practical realisations of the unit. The separation of the defining constants from the definitions of units means that improved measurements can be developed leading to changes in the mises en pratique as science and technology develop, without having to revise the definitions. The published mise en pratique

6250-475: The IPK. During extraordinary verifications carried out in 2014 preparatory to redefinition of metric standards, continuing divergence was not confirmed. Nonetheless, the residual and irreducible instability of a physical IPK undermined the reliability of the entire metric system to precision measurement from small (atomic) to large (astrophysical) scales. By avoiding the use of an artefact to define units, all issues with

6375-521: The International Committee for Weights and Measures (CIPM ), and the International Bureau of Weights and Measures (BIPM ). All the decisions and recommendations concerning units are collected in a brochure called The International System of Units (SI) , which is published in French and English by the BIPM and periodically updated. The writing and maintenance of the brochure is carried out by one of

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6500-571: The Latin annus ), is commonly used with metric prefixes: ka , Ma, and Ga. Official policies about the use of SI prefixes with non-SI units vary slightly between the International Bureau of Weights and Measures (BIPM) and the American National Institute of Standards and Technology (NIST). For instance, the NIST advises that "to avoid confusion, prefix symbols (and prefix names) are not used with

6625-475: The Metre Convention". This working document was Practical system of units of measurement . Based on this study, the 10th CGPM in 1954 defined an international system derived six base units: the metre, kilogram, second, ampere, degree Kelvin, and candela. The 9th CGPM also approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known

6750-471: The Metre, by 17 nations. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention, brought together many international organisations to establish the definitions and standards of a new system and to standardise the rules for writing and presenting measurements. Initially the convention only covered standards for

6875-402: The SI "has been used around the world as the preferred system of units, the basic language for science, technology, industry, and trade." The only other types of measurement system that still have widespread use across the world are the imperial and US customary measurement systems . The international yard and pound are defined in terms of the SI. The quantities and equations that provide

7000-509: The SI Brochure notes that the name of the unit with the symbol °C is correctly spelled as 'degree Celsius ': the first letter of the name of the unit, 'd', is in lowercase, while the modifier 'Celsius' is capitalised because it is a proper name. The English spelling and even names for certain SI units and metric prefixes depend on the variety of English used. US English uses the spelling deka- , meter , and liter , and International English uses deca- , metre , and litre . The name of

7125-455: The SI unit m/s . A combination of base and derived units may be used to express a derived unit. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa) – and the pascal can be defined as one newton per square metre (N/m ). Like all metric systems, the SI uses metric prefixes to systematically construct, for the same physical quantity, a set of units that are decimal multiples of each other over

7250-490: The SI units. The ISQ is formalised, in part, in the international standard ISO/IEC 80000 , which was completed in 2009 with the publication of ISO 80000-1 , and has largely been revised in 2019–2020. The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the Metre Convention . They are the General Conference on Weights and Measures (CGPM ),

7375-421: The United States use the abbreviations cc or ccm for cubic centimetres. One  cubic centimetre is equal to one  millilitre . For nearly a century, engineers used the abbreviation MCM to designate a "thousand circular mils " in specifying the cross-sectional area of large electrical cables . Since the mid-1990s, kcmil has been adopted as the official designation of a thousand circular mils, but

7500-403: The abbreviation SI (from French Système international d'unités ), is the modern form of the metric system and the world's most widely used system of measurement . Coordinated by the International Bureau of Weights and Measures (abbreviated BIPM from French : Bureau international des poids et mesures ) it is the only system of measurement with official status in nearly every country in

7625-511: The ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force. According to the SI Brochure, unit names should be treated as common nouns of the context language. This means that they should be typeset in the same character set as other common nouns (e.g. Latin alphabet in English, Cyrillic script in Russian, etc.), following

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7750-428: The ampere, mole and candela) depended for their definition, making these units subject to periodic comparisons of national standard kilograms with the IPK. During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence had occurred between the mass of the IPK and all of its official copies stored around the world: the copies had all noticeably increased in mass with respect to

7875-403: The astronomical unit is mentioned in the SI standards as an accepted non-SI unit. Prefixes for the SI standard unit second are most commonly encountered for quantities less than one second. For larger quantities, the system of minutes (60 seconds), hours (60 minutes) and days (24 hours) is accepted for use with the SI and more commonly used. When speaking of spans of time,

8000-436: The base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal-based and identified by a standard set of prefixes . The metric system is extensible, and new derived units are defined as needed in fields such as radiology and chemistry. For example, the katal , a derived unit for catalytic activity equivalent to one mole per second (1 mol/s),

8125-515: The base units. The SI selects seven units to serve as base units , corresponding to seven base physical quantities. They are the second , with the symbol s , which is the SI unit of the physical quantity of time ; the metre , symbol m , the SI unit of length ; kilogram ( kg , the unit of mass ); ampere ( A , electric current ); kelvin ( K , thermodynamic temperature ); mole ( mol , amount of substance ); and candela ( cd , luminous intensity ). The base units are defined in terms of

8250-445: The base units. After the redefinition, the SI is defined by fixing the numerical values of seven defining constants. This has the effect that the distinction between the base units and derived units is, in principle, not needed, since all units, base as well as derived, may be constructed directly from the defining constants. Nevertheless, the distinction is retained because "it is useful and historically well established", and also because

8375-416: The base units. Twenty-two coherent derived units have been provided with special names and symbols. The seven base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units. Since the sizes of coherent units will be convenient for only some applications and not for others, the SI provides twenty-four prefixes which, when added to

8500-401: The coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes. The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the gram were the base unit. Prefix names and symbols are attached to the unit name gram and

8625-463: The committees of the CIPM. The definitions of the terms "quantity", "unit", "dimension", etc. that are used in the SI Brochure are those given in the international vocabulary of metrology . The brochure leaves some scope for local variations, particularly regarding unit names and terms in different languages. For example, the United States' National Institute of Standards and Technology (NIST) has produced

8750-476: The context in which the SI units are defined are now referred to as the International System of Quantities (ISQ). The ISQ is based on the quantities underlying each of the seven base units of the SI . Other quantities, such as area , pressure , and electrical resistance , are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with

8875-595: The corresponding equations between the physical quantities. Twenty-two coherent derived units have been provided with special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons. The derived units in the SI are formed by powers, products, or quotients of the base units and are unlimited in number. Derived units apply to some derived quantities , which may by definition be expressed in terms of base quantities , and thus are not independent; for example, electrical conductance

9000-497: The defining constants. For example, the kilogram is defined by taking the Planck constant h to be 6.626 070 15 × 10  J⋅s , giving the expression in terms of the defining constants All units in the SI can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The choice of which and even how many quantities to use as base quantities

9125-410: The definition of a unit and its realisation. The SI units are defined by declaring that seven defining constants have certain exact numerical values when expressed in terms of their SI units. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. For each base unit

9250-463: The definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body. Adopting the metric system is known as metrication . The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions,

9375-403: The definitions. A consequence is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the unit. One problem with artefacts is that they can be lost, damaged, or changed; another is that they introduce uncertainties that cannot be reduced by advancements in science and technology. The original motivation for the development of the SI

9500-502: The designation MCM still remains in wide use. A similar system is used in natural gas sales in the United States: m (or M ) for thousands and mm (or MM ) for millions of British thermal units or therms , and in the oil industry, where MMbbl is the symbol for "millions of barrels". This usage of the capital letter M for "thousand" is from Roman numerals , in which M means 1000. Metric system The metric system

9625-517: The development of the CGS system. The International System of Units consists of a set of defining constants with corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes. The seven defining constants are the most fundamental feature of the definition of the system of units. The magnitudes of all SI units are defined by declaring that seven constants have certain exact numerical values when expressed in terms of their SI units. These defining constants are

9750-421: The distance that light travels in a second . The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency. The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which

9875-401: The early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as kilo- and mega- , and those that were negative powers of ten were given Latin-derived prefixes such as centi- and milli- . However, 1935 extensions to the prefix system did not follow this convention: the prefixes nano- and micro- , for example have Greek roots. During the 19th century

10000-534: The electrical units in terms of length, mass, and time using dimensional analysis was beset with difficulties – the dimensions depended on whether one used the ESU or EMU systems. This anomaly was resolved in 1901 when Giovanni Giorgi published a paper in which he advocated using a fourth base unit alongside the existing three base units. The fourth unit could be chosen to be electric current , voltage , or electrical resistance . Electric current with named unit 'ampere'

10125-439: The exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a coherent SI unit. The complete set of SI units consists of both

10250-425: The fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor made equations more awkward than necessary, and so Oliver Heaviside suggested adjusting the system of units to remove it. The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do –

10375-431: The first time in 1960. The most recent prefixes adopted were ronna- , quetta- , ronto- , and quecto- in 2022, after a proposal from British metrologist Richard J. C. Brown. The large prefixes ronna- and quetta- were adopted in anticipation of needs for use in data science, and because unofficial prefixes that did not meet SI requirements were already circulating. The small prefixes were also added, even without such

10500-514: The flexibility allowed by official policy in the case of the degree Celsius (°C). NIST states: "Prefix symbols may be used with the unit symbol °C and prefix names may be used with the unit name degree Celsius . For example, 12 m°C (12 millidegrees Celsius) is acceptable." In practice, it is more common for prefixes to be used with the kelvin when it is desirable to denote extremely large or small absolute temperatures or temperature differences. Thus, temperatures of star interiors may be given with

10625-422: The fuel consumption measures). These are not compatible with the SI. Other obsolete double prefixes included "decimilli-" (10), which was contracted to "dimi-" and standardised in France up to 1961. There are no more letters of the Latin alphabet available for new prefixes (all the unused letters are already used for units). As such, Richard J.C. Brown (who proposed the prefixes adopted for 10 and 10) has proposed

10750-420: The hectolitre (100 litres). Larger volumes are usually denoted in kilolitres, megalitres or gigalitres, or else in cubic metres (1 cubic metre = 1 kilolitre) or cubic kilometres (1 cubic kilometre = 1 teralitre). For scientific purposes, the cubic metre is usually used. The kilometre, metre, centimetre, millimetre, and smaller units are common. The decimetre is rarely used. The micrometre is often referred to by

10875-421: The kilogram in terms of fundamental constants. 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 a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has

11000-417: The length of the day is usually standardised to 86 400  seconds so as not to create issues with the irregular leap second . Larger multiples of the second such as kiloseconds and megaseconds are occasionally encountered in scientific contexts, but are seldom used in common parlance. For long-scale scientific work, particularly in astronomy , the Julian year or annum (a) is a standardised variant of

11125-492: The loss, damage, and change of the artefact are avoided. A proposal was made that: The new definitions were adopted at the 26th CGPM on 16 November 2018, and came into effect on 20 May 2019. The change was adopted by the European Union through Directive (EU) 2019/1258. Prior to its redefinition in 2019, the SI was defined through the seven base units from which the derived units were constructed as products of powers of

11250-574: The metre and the kilogram. This became the foundation of the MKS system of units. At the close of the 19th century three different systems of units of measure existed for electrical measurements: a CGS-based system for electrostatic units , also known as the Gaussian or ESU system, a CGS-based system for electromechanical units (EMU), and an International system based on units defined by the Metre Convention for electrical distribution systems. Attempts to resolve

11375-429: The metric SI system. Common examples include the megabyte and the decibel . Metric prefixes rarely appear with imperial or US units except in some special cases (e.g., microinch, kilofoot, kilopound ). They are also used with other specialised units used in particular fields (e.g., megaelectronvolt , gigaparsec , millibarn , kilodalton ). In astronomy, geology, and palaeontology, the year , with symbol 'a' (from

11500-419: The metric system, multiples and submultiples of units follow a decimal pattern. A common set of decimal-based prefixes that have the effect of multiplication or division by an integer power of ten can be applied to units that are themselves too large or too small for practical use. The prefix kilo , for example, is used to multiply the unit by 1000, and the prefix milli is to indicate a one-thousandth part of

11625-510: The modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice. Basic units: metre , kilogram , second , ampere , kelvin , mole , and candela for derived units, such as Volts and Watts, see International System of Units . A number of different metric system have been developed, all using

11750-431: The name and symbol of a coherent unit produce twenty-four additional (non-coherent) SI units for the same quantity; these non-coherent units are always decimal (i.e. power-of-ten) multiples and sub-multiples of the coherent unit. The current way of defining the SI is a result of a decades-long move towards increasingly abstract and idealised formulation in which the realisations of the units are separated conceptually from

11875-430: The older CGS system, but scaled to be coherent with MKSA units. Two additional base units – the kelvin , which is equivalent to degree Celsius for change in thermodynamic temperature but set so that 0 K is absolute zero , and the candela , which is roughly equivalent to the international candle unit of illumination – were introduced. Later, another base unit, the mole , a unit of amount of substance equivalent to

12000-453: The older non-SI name micron , which is officially deprecated. In some fields, such as chemistry , the ångström (0.1 nm) has been used commonly instead of the nanometre. The femtometre , used mainly in particle physics, is sometimes called a fermi . For large scales, megametre, gigametre, and larger are rarely used. Instead, ad hoc non-metric units are used, such as the solar radius , astronomical units , light years , and parsecs ;

12125-453: The only ones that do not are those for 10, 1/10, 100, and 1/100. The conversion between different SI units for one and the same physical quantity is always through a power of ten. This is why the SI (and metric systems more generally) are called decimal systems of measurement units . The grouping formed by a prefix symbol attached to a unit symbol (e.g. ' km ', ' cm ') constitutes a new inseparable unit symbol. This new symbol can be raised to

12250-503: The original, called the IPK . It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of 5 × 10 . The revision of the SI replaced the IPK with an exact definition of the Planck constant as expressed in SI units, which defines

12375-476: The oscillations of a magnetised needle and finding the quantity of "magnetic fluid" that produces an acceleration of one unit when applied to a unit mass. The centimetre–gram–second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the British Association for the Advancement of Science (BAAS). The system's characteristics are that density

12500-450: The prefix myria- , derived from the Greek word μύριοι ( mýrioi ), was used as a multiplier for 10 000 . When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below. Prefixes are not usually used to indicate multiples of

12625-417: The prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI. The decimal prefix for ten thousand, myria- (sometimes spelt myrio- ), and the early binary prefixes double- (2×) and demi- ( ⁠ 1 / 2 ⁠ ×) were parts of the original metric system adopted by France in 1795, but were not retained when the SI prefixes were internationally adopted by

12750-478: The quantity symbols, formatting of numbers and the decimal marker, expressing measurement uncertainty, multiplication and division of quantity symbols, and the use of pure numbers and various angles. In the United States, the guideline produced by the National Institute of Standards and Technology (NIST) clarifies language-specific details for American English that were left unclear by the SI Brochure, but

12875-475: The risk of confusion that the tonne has with other units with the name "ton". The kilogram is the only coherent unit of the International System of Units that includes a metric prefix. The litre (equal to a cubic decimetre), millilitre (equal to a cubic centimetre), microlitre, and smaller are common. In Europe, the centilitre is often used for liquids, and the decilitre is used less frequently. Bulk agricultural products, such as grain, beer and wine, often use

13000-564: The second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as 1 ⁄ 299,792,458 of the distance light travels in a second. The kilogram was defined by a cylinder of platinum-iridium alloy until a new definition in terms of natural physical constants was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 10 ( quetta– ) and 10 ( quecto– ). International System of Units The International System of Units , internationally known by

13125-460: The standard metre artefact from 1889 was retired. Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the katal for catalytic activity, was added in 1999. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on

13250-438: The time-related unit symbols (names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) ° (degree), ′ (minute), and ″ (second)", whereas the BIPM adds information about the use of prefixes with the symbol as for arcsecond when they state: "However astronomers use milliarcsecond, which they denote mas, and microarcsecond, μas, which they use as units for measuring very small angles." Some of

13375-411: The unit metre and time has the unit second, and speed has the derived unit metre per second. Density, or mass per unit volume, has the unit kilogram per cubic metre. A characteristic feature of metric systems is their reliance upon multiples of 10. For example, the base unit of length is the metre, and distances much longer or much shorter than 1 metre are measured in units that are powers of 10 times

13500-413: The unit of MK (megakelvin), and molecular cooling may be given with the unit mK (millikelvin). In use the joule and kilojoule are common, with larger multiples seen in limited contexts. In addition, the kilowatt-hour , a composite unit formed from the kilowatt and hour, is often used for electrical energy; other multiples can be formed by modifying the prefix of watt (e.g. terawatt-hour). There exist

13625-465: The unit symbol g respectively. For example, 10  kg is written milligram and mg , not microkilogram and μkg . Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbol J/K ) is the coherent SI unit for two distinct quantities: heat capacity and entropy ; another example is the ampere, which is the coherent SI unit for both electric current and magnetomotive force . This illustrates why it

13750-545: The unit whose symbol is t and which is defined according to 1 t = 10  kg is 'metric ton' in US English and 'tonne' in International English. Symbols of SI units are intended to be unique and universal, independent of the context language. The SI Brochure has specific rules for writing them. In addition, the SI Brochure provides style conventions for among other aspects of displaying quantities units:

13875-450: The unit. Thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as: The decimalised system is based on the metre , which had been introduced in France in the 1790s . The historical development of these systems culminated in

14000-627: The use of metric prefixes . SI derived units are named combinations – such as the hertz (cycles per second), newton (kg⋅m/s ), and tesla (1 kg⋅s ⋅A ) – or a shifted scale, in the case of degrees Celsius . Certain units have been officially accepted for use with the SI . Some of these are decimalised, like the litre and electronvolt , and are considered "metric". Others, like the astronomical unit are not. Ancient non-metric but SI-accepted multiples of time ( minute and hour ) and angle ( degree , arcminute , and arcsecond ) are sexagesimal (base 60). The "metric system" has been formulated in

14125-435: The usual grammatical and orthographical rules of the context language. For example, in English and French, even when the unit is named after a person and its symbol begins with a capital letter, the unit name in running text should start with a lowercase letter (e.g., newton, hertz, pascal) and is capitalised only at the beginning of a sentence and in headings and publication titles . As a nontrivial application of this rule,

14250-626: The world, employed in science, technology, industry, and everyday commerce. The SI comprises a coherent system of units of measurement starting with seven base units , which are the second (symbol s, the unit of time ), metre (m, length ), kilogram (kg, mass ), ampere (A, electric current ), kelvin (K, thermodynamic temperature ), mole (mol, amount of substance ), and candela (cd, luminous intensity ). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units , which can always be represented as products of powers of

14375-620: The world. The French Revolution (1789–99) enabled France to reform its many outdated systems of various local weights and measures. In 1790, Charles Maurice de Talleyrand-Périgord proposed a new system based on natural units to the French National Assembly , aiming for global adoption. With the United Kingdom not responding to a request to collaborate in the development of the system, the French Academy of Sciences established

14500-435: Was added in 1999. The base units used in a measurement system must be realisable . Each of the definitions of the base units in the SI is accompanied by a defined mise en pratique [practical realisation] that describes in detail at least one way in which the base unit can be measured. Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise

14625-465: Was chosen as the base unit, and the other electrical quantities derived from it according to the laws of physics. When combined with the MKS the new system, known as MKSA, was approved in 1946. In 1948, the 9th CGPM commissioned a study to assess the measurement needs of the scientific, technical, and educational communities and "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to

14750-545: Was created, it included the " μ " symbol for micro at codepoint 0xB5 ; later, the whole of ISO 8859-1 was incorporated into the initial version of Unicode . Many fonts that support both characters render them identical, but because the micro sign and the Greek lower-case letter have different applications (normally, a Greek letter would be used with other Greek letters, but the micro sign is never used like that), some fonts render them differently, e.g. Linux Libertine and Segoe UI . Most English-language keyboards do not have

14875-402: Was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and to standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948, and is based on the metre–kilogram–second system of units (MKS) combined with ideas from

15000-464: Was laid down. These rules were subsequently extended and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used, and how the values of quantities should be expressed. The 10th CGPM in 1954 resolved to create an international system of units and in 1960, the 11th CGPM adopted the International System of Units , abbreviated SI from the French name Le Système international d'unités , which included

15125-519: Was necessary to use some other symbol besides upper and lowercase 'm'. Eventually the Greek letter "μ" was adopted. However, with the lack of a "μ" key on most typewriters, as well as computer keyboards, various other abbreviations remained common, including "mc", "mic", and "u". From about 1960 onwards, "u" prevailed in type-written documents. Because ASCII , EBCDIC , and other common encodings lacked code-points for " μ ", this tradition remained even as computers replaced typewriters. When ISO 8859-1

15250-489: Was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the metre , kilogram and second , in the International System of Electrical and Magnetic Units . During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including

15375-399: 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

15500-473: Was used both in France and in the Soviet Union . Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl , Technische Masseneinheit (TME), mug or metric slug . Although the CGPM passed a resolution in 1901 defining the standard value of acceleration due to gravity to be 980.665 cm/s , gravitational units are not part of

15625-452: Was used until a new definition was introduced in May 2019 . Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the Metre Convention serve as de facto standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas were subject to periodic validation by comparison to

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