# Kilogram

Last updated

kilogram
A series of 5, 2, 1, 0.5 and 0.2 kilogram weights, made out of rusty cast iron
General information
Unit system SI
Unit of mass
Symbolkg
Conversions
1 kg in ...... is equal to ...
Avoirdupois    2.204623 pounds [Note 1]
British Gravitational   0.0685 slugs
CGS units    1000 grams
Atomic mass units    6.02214076×1026 Da

The kilogram (also kilogramme [1] ) is the base unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. [2] It means 'one thousand grams'.

## Contents

The kilogram is defined in terms of the Planck constant, the second, and the metre, both of which are based on fundamental physical constants. This allows a properly equipped metrology laboratory to calibrate a mass measurement instrument such as a Kibble balance as the primary standard to determine an exact kilogram mass. [3] [4]

The kilogram was originally defined in 1795 during the French Revolution as the mass of one litre of water. The current definition of a kilogram agrees with this original definition to within 30 parts per million. In 1799, the platinum Kilogramme des Archives replaced it as the standard of mass. In 1889, a cylinder of platinum-iridium, the International Prototype of the Kilogram (IPK), became the standard of the unit of mass for the metric system and remained so for 130 years, before the current standard was adopted in 2019. [5]

## Definition

The kilogram is defined in terms of three fundamental physical constants:

• a specific atomic transition frequency , which defines the duration of the second, [6]
• the speed of light c, which when combined with the second, defines the length of the metre, [6]
• and the Planck constant h, which when combined with the metre and second, defines the mass of the kilogram. [6]

The formal definition according to the General Conference on Weights and Measures (CGPM) is:

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.

CGPM [7] [8]

Defined in term of those units, the kg is formulated as: [9]

kg = (299792458)2/(6.62607015×10−34)(9192631770)hΔνCs/c2 = 917097121160018/621541050725904751042hΔνCs/c2(1.475521399735270×1040)hΔνCs/c2 .

This definition is generally consistent with previous definitions: the mass remains within 30 ppm of the mass of one litre of water. [10]

## Name and terminology

The kilogram is the only base SI unit with an SI prefix (kilo) as part of its name. The word kilogramme or kilogram is derived from the French kilogramme, [15] which itself was a learned coinage, prefixing the Greek stem of χίλιοιkhilioi "a thousand" to gramma, a Late Latin term for "a small weight", itself from Greek γράμμα. [16] The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal , [17] which revised the provisional system of units introduced by the French National Convention two years earlier, where the gravet had been defined as weight (poids) of a cubic centimetre of water, equal to 1/1000 of a grave . [18] In the decree of 1795, the term gramme thus replaced gravet, and kilogramme replaced grave. [13]

The French spelling was adopted in Great Britain when the word was used for the first time in English in 1795, [19] [15] with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common. [1] UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. [20]

In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has been used to mean both kilogram [21] and kilometre[ citation needed ]. [22] While kilo as an alternative is acceptable, to The Economist for example, [23] the Canadian government's Termium Plus system states that "SI (International System of Units) usage, followed in scientific and technical writing" does not allow its usage and it is described as "a common informal name" on Russ Rowlett's Dictionary of Units of Measurement. [24] [25] When the United States Congress gave the metric system legal status in 1866, it permitted the use of the word kilo as an alternative to the word kilogram, [26] but in 1990 revoked the status of the word kilo. [27]

The SI system was introduced in 1960 and in 1970 the BIPM started publishing the SI Brochure, which contains all relevant decisions and recommendations by the CGPM concerning units. The SI Brochure states that "It is not permissible to use abbreviations for unit symbols or unit names ...". [28] [Note 2]

## Redefinition based on fundamental constants

The replacement of the International Prototype of the Kilogram (IPK) as the primary standard was motivated by evidence accumulated over a long period of time that the mass of the IPK and its replicas had been changing; the IPK had diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led to several competing efforts to develop measurement technology precise enough to warrant replacing the kilogram artefact with a definition based directly on physical fundamental constants. [5]

The International Committee for Weights and Measures (CIPM) approved a redefinition of the SI base units in November 2018 that defines the kilogram by defining the Planck constant to be exactly 6.62607015×10−34 kg⋅m2⋅s−1, effectively defining the kilogram in terms of the second and the metre. The new definition took effect on May 20, 2019. [5] [7] [29]

Prior to the redefinition, the kilogram and several other SI units based on the kilogram were defined by a man-made metal artifact: the Kilogramme des Archives from 1799 to 1889, and the IPK from 1889 to 2019. [5]

In 1960, the metre, previously similarly having been defined with reference to a single platinum-iridium bar with two marks on it, was redefined in terms of an invariant physical constant (the wavelength of a particular emission of light emitted by krypton, [30] and later the speed of light) so that the standard can be independently reproduced in different laboratories by following a written specification.

At the 94th Meeting of the CIPM in 2005, it was recommended that the same be done with the kilogram. [31]

In October 2010, the CIPM voted to submit a resolution for consideration at the General Conference on Weights and Measures (CGPM), to "take note of an intention" that the kilogram be defined in terms of the Planck constant, h (which has dimensions of energy times time, thus mass × length2 / time) together with other physical constants. [32] [33] This resolution was accepted by the 24th conference of the CGPM [34] in October 2011 and further discussed at the 25th conference in 2014. [35] [36] Although the Committee recognised that significant progress had been made, they concluded that the data did not yet appear sufficiently robust to adopt the revised definition, and that work should continue to enable the adoption at the 26th meeting, scheduled for 2018. [35] Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. The Kibble balance is one way to do this. [37]

As part of this project, a variety of very different technologies and approaches were considered and explored over many years. Some of these approaches were based on equipment and procedures that would enable the reproducible production of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) using measurement techniques and material properties that are ultimately based on, or traceable to, physical constants. Others were based on devices that measured either the acceleration or weight of hand-tuned kilogram test masses and which expressed their magnitudes in electrical terms via special components that permit traceability to physical constants. All approaches depend on converting a weight measurement to a mass and therefore require precise measurement of the strength of gravity in laboratories (gravimetry). All approaches would have precisely fixed one or more constants of nature at a defined value.[ citation needed ]

## SI multiples

Because an SI unit may not have multiple prefixes (see SI prefix), prefixes are added to gram , rather than the base unit kilogram, which already has a prefix as part of its name. [38] For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 μkg (one microkilogram).

SI multiples of gram (g)
SubmultiplesMultiples
ValueSI symbolNameValueSI symbolName
10−1 gdgdecigram101 gdagdecagram
10−2 gcgcentigram102 ghghectogram
10−3 gmgmilligram103 gkgkilogram
10−6 gμgmicrogram106 gMgmegagram (tonne)
10−9 gngnanogram109 gGggigagram
10−12 gpgpicogram1012 gTgteragram
10−15 gfgfemtogram1015 gPgpetagram
10−18 gagattogram1018 gEgexagram
10−21 gzgzeptogram1021 gZgzettagram
10−24 gygyoctogram1024 gYgyottagram
10−27 grgrontogram1027 gRgronnagram
10−30 gqgquectogram1030 gQgquettagram
Common prefixed units are in bold face. [Note 3]

## Practical issues with SI weight names

• Serious medication errors have been made by confusing milligrams and micrograms when micrograms has been abbreviated. [39] The abbreviation "mcg" rather than the SI symbol "μg" is formally mandated for medical practitioners in the US by the Joint Commission on Accreditation of Healthcare Organizations (JCAHO). [40] In the United Kingdom, the National Institute for Health and Care Excellence and Scottish Palliative Care Guidelines state that "micrograms" and "nanograms" must both be written in full, and never abbreviated as "mcg" or "μg". [39] [41]
• The hectogram (100 g) (Italian: ettogrammo or etto) is a very commonly used unit in the retail food trade in Italy. [42] [43] [44]
• The former standard spelling and abbreviation "deka-" and "dk" produced abbreviations such as "dkm" (dekametre) and "dkg" (dekagram). [45] As of 2020, the abbreviation "dkg" (10 g) is still used in parts of central Europe in retail for some foods such as cheese and meat. [46] [47] [48] [49] [50]
• The unit name megagram is rarely used, and even then typically only in technical fields in contexts where especially rigorous consistency with the SI standard is desired. For most purposes, the name tonne is instead used. The tonne and its symbol, "t", were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPM for use with the SI. According to the BIPM, "This unit is sometimes referred to as 'metric ton' in some English-speaking countries." [51]

## Notes

1. The avoirdupois pound is part of both United States customary system of units and the Imperial system of units. It is defined as exactly 0.45359237 kilograms.
2. The French text (which is the authoritative text) states "Il n'est pas autorisé d'utiliser des abréviations pour les symboles et noms d'unités ..."
3. Criterion: A combined total of at least five occurrences on the British National Corpus and the Corpus of Contemporary American English, including both the singular and the plural for both the -gram and the -gramme spelling.

## Related Research Articles

The General Conference on Weights and Measures is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre Convention through which member states act together on matters related to measurement science and measurement standards. The CGPM is made up of delegates of the governments of the member states and observers from the Associates of the CGPM. It elects the International Committee for Weights and Measures as the supervisory board of the BIPM to direct and supervise it.

The litre or liter is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A cubic decimetre occupies a volume of 10 cm × 10 cm × 10 cm and is thus equal to one-thousandth of a cubic metre.

The Metre Convention, also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations: Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, Germany, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States of America, and Venezuela.

The International System of Units, internationally known by the abbreviation SI, 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 it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.

The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

The metric system is a system of measurement that is a decimal system. The current international standard for the metric system is the International System of Units, in which all units can be expressed in terms of seven base units. The units that serve as the SI base units are the metre, kilogram, second, ampere, kelvin, mole, and candela.

Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in 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. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960.

The gram is a unit of mass in the International System of Units (SI) equal to one thousandth of a kilogram.

A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the definition of the kilogram unit of mass based on fundamental constants.

The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by ɡ0 or ɡn, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant defined by standard as 9.80665 m/s2. This value was established by the 3rd General Conference on Weights and Measures and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from the rotation of the Earth ; the total is about 0.5% greater at the poles than at the Equator.

France has a unique history of units of measurement due to its radical decision to invent and adopt the metric system after the French Revolution.

The gravitational metric system is a non-standard system of units, which does not comply with the International System of Units (SI). It is built on the three base quantities length, time and force with base units metre, second and kilopond respectively. Internationally used abbreviations of the system are MKpS, MKfS or MKS . However, the abbreviation MKS is also used for the MKS system of units, which, like the SI, uses mass in kilogram as a base unit.

A conventional electrical unit is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.

The International Prototype of the Kilogram is an object whose mass was used to define the kilogram from 1889, when it replaced the Kilogramme des Archives, until 2019, when it was replaced by a new definition of the kilogram based entirely on physical constants. During that time, the IPK and its duplicates were used to calibrate all other kilogram mass standards on Earth.

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In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

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The scientific community examined several approaches to redefining the kilogram before deciding on a redefinition of the SI base units in November 2018. Each approach had advantages and disadvantages.

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 NIST: K20, the US National Prototype Kilogram resting on an egg crate fluorescent light panel BIPM: Steam cleaning a 1 kg prototype before a mass comparison BIPM: The IPK and its six sister copies in their vault The Age: Silicon sphere for the Avogadro Project NPL: The NPL's Watt Balance project NIST: This particular Rueprecht Balance, an Austrian-made precision balance, was used by the NIST from 1945 until 1960 BIPM: The FB‑2 flexure-strip balance, the BIPM's modern precision balance featuring a standard deviation of one ten-billionth of a kilogram (0.1 μg) BIPM: Mettler HK1000 balance, featuring 1 μg resolution and a 4 kg maximum mass. Also used by NIST and Sandia National Laboratories' Primary Standards Laboratory Micro-g LaCoste: FG‑5 absolute gravimeter, (diagram), used in national laboratories to measure gravity to 2  μGal accuracy