kilogram | |
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General information | |
Unit system | SI base unit |
Unit of | mass |
Symbol | kg |
Conversions | |
Avoirdupois | ? pounds^{[Note 1]} |
British Gravitational | ? slugs |
The kilogram (also kilogramme^{[1]}) is the base unit of mass in the International System of Units (SI), the metric system, 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.
The kilogram was originally defined in 1795 as the mass of one litre of water. Modern superseding definitions of a kilogram agree 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 until 2019.^{[2]} The kilogram was the last of the SI units to be defined by a physical artefact.
The kilogram is now defined in terms of the second and the metre, based on fixed fundamental constants of nature.^{[3]} 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, although precision kilogram masses remain in use as secondary standards for ordinary purposes.
The kilogram is defined in terms of three fundamental physical constants: The speed of light c, a specific atomic transition frequency ??_{Cs}, and the Planck constant h.
According to the General Conference on Weights and Measures (CGPM):
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 when expressed in the unit J?s, which is equal to kg?m^{2}?s^{-1}, where the metre and the second are defined in terms of c and ??_{Cs}.
-- CGPM ^{[4]}^{[5]}
This definition is generally consistent with previous definitions: the mass remains within 30 ppm of the mass of one litre of water.^{[6]}
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,^{[9]} which itself was a learned coinage, prefixing the Greek stem of khilioi "a thousand" to gramma, a Late Latin term for "a small weight", itself from Greek .^{[10]} The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal,^{[11]} 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.^{[12]} In the decree of 1795, the term gramme thus replaced gravet, and kilogramme replaced grave.
The French spelling was adopted in Great Britain when the word was used for the first time in English in 1795,^{[13]}^{[9]} 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.^{[14]}
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^{[15]} and kilometre.^{[16]} While kilo as an alternative is acceptable, to The Economist for example,^{[17]} 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.^{[18]}^{[19]} 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,^{[20]} but in 1990 revoked the status of the word kilo.^{[21]}
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 ...".^{[22]}^{[Note 2]}
It is primarily because of units for electromagnetism that the kilogram rather than the gram was eventually adopted as the base unit of mass in the SI. The relevant series of discussions and decisions started roughly in the 1850s and effectively concluded in 1946. By the end of the 19th century, the 'practical units' for electric and magnetic quantities such as the ampere and the volt were well established in practical use (e.g. for telegraphy). Unfortunately, they were not coherent with the then-prevailing base units for length and mass, the centimeter, and the gram. However, the 'practical units' also included some purely mechanical units. In particular, the product of the ampere and the volt gives a purely mechanical unit of power, the watt. It was noticed that the purely mechanical practical units such as the watt would be coherent in a system in which the base unit of length was the meter and the base unit of mass was the kilogram. Because no one wanted to replace the second as the base unit of time, the metre and the kilogram are the only pair of base units of length and mass such that (1) the watt is a coherent unit of power, (2) the base units of length and time are integer-power-of-ten ratios to the metre and the gram (so that the system remains 'metric'), and (3) the sizes of the base units of length and mass are convenient for practical use.^{[Note 3]} This would still leave out the purely electrical and magnetic units: while the purely mechanical practical units such as the watt are coherent in the metre-kilogram-second system, the explicitly electrical and magnetic units such as the volt, the ampere, etc. are not.^{[Note 5]} The only way to also make those units coherent with the metre-kilogram-second system is to modify that system in a different way: the number of fundamental dimensions must be increased from three (length, mass, and time) to four (the previous three, plus one purely electrical one).^{[Note 6]}
During the second half of the 19th century, the centimetre-gram-second system of units was becoming widely accepted for scientific work, treating the gram as the fundamental unit of mass and the kilogram as a decimal multiple of the base unit formed by using a metric prefix. However, as the century drew to a close, there was widespread dissatisfaction with the units for electricity and magnetism in the CGS system. There were two obvious choices for absolute units.^{[Note 7]} of electromagnetism: the 'electrostatic' (CGS-ESU) system and the 'electromagnetic' (CGS-EMU) system. But the sizes of coherent electric and magnetic units were not convenient in either of these systems; for example, the ESU unit of electrical resistance, which was later named the statohm, corresponds to about , while the EMU unit, which was later named the abohm, corresponds to .^{[Note 8]}
To circumvent this difficulty, a third set of units was introduced: the so-called practical units. The practical units were obtained as decimal multiples of coherent CGS-EMU units, chosen so that the resulting magnitudes were convenient for practical use and so that the practical units were, as far as possible, coherent with each other.^{[25]} The practical units included such units as the volt, the ampere, the ohm, etc.,^{[26]}^{[27]} which were later incorporated in the SI system and which are used to this day.^{[Note 9]} The reason the meter and the kilogram were later chosen to be the base units of length and mass was that they are the only combination of reasonably sized decimal multiples or submultiples of the meter and the gram that can be made coherent with the volt, the ampere, etc.
The reason is that electrical quantities cannot be isolated from mechanical and thermal ones: they are connected by relations such as current × electric potential difference = power. For this reason, the practical system also included coherent units for certain mechanical quantities. For example, the previous equation implies that ampere × volt is a coherent derived practical unit of power;^{[Note 10]} this unit was named the watt. The coherent unit of energy is then the watt times the second, which was named the joule. The joule and the watt also have convenient magnitudes and are decimal multiples of CGS coherent units for energy (the erg) and power (the erg per second). The watt is not coherent in the centimeter-gram-second system, but it is coherent in the meter-kilogram-second system--and in no other system whose base units of length and mass are reasonably sized decimal multiples or submultiples of the meter and the gram.
However, unlike the watt and the joule, the explicitly electrical and magnetic units (the volt, the ampere...) are not coherent even in the (absolute three-dimensional) meter-kilogram-second system. Indeed, one can work out what the base units of length and mass have to be in order for all the practical units to be coherent (the watt and the joule as well as the volt, the ampere, etc.). The values are (one half of a meridian of the Earth, called a quadrant) and (called an eleventh-gram^{[Note 11]}).^{[Note 13]}
Therefore, the full absolute system of units in which the practical electrical units are coherent is the quadrant-eleventh-gram-second (QES) system. However, the extremely inconvenient magnitudes of the base units for length and mass made it so that no one seriously considered adopting the QES system. Thus, people working on practical applications of electricity had to use units for electrical quantities and for energy and power that were not coherent with the units they were using for e.g. length, mass, and force.
Meanwhile, scientists developed yet another fully coherent absolute system, which came to be called the Gaussian system, in which the units for purely electrical quantities are taken from CGE-ESU, while the units for magnetic quantities are taken from the CGS-EMU. This system proved very convenient for scientific work and is still widely used. However, the sizes of its units remained either too large or too small--by many orders of magnitude--for practical applications.
Finally, in both CGS-ESU and CGS-EMU as well as in the Gaussian system, Maxwell's equations are 'unrationalized', meaning that they contain various factors of 4? that many workers found awkward. So yet another system was developed to rectify that: the 'rationalized' Gaussian system, usually called the Lorentz-Heaviside system. This system is still used in some subfields of physics. However, the units in that system are related to Gaussian units by factors of ? , which means that their magnitudes remained, like those of the Gaussian units, either far too large or far too small for practical applications.
In 1901, Giovanni Giorgi proposed a new system of units that would remedy this situation.^{[28]} He noted that the mechanical practical units such as the joule and the watt are coherent not only in the QES system, but also in the meter-kilogram-second (MKS) system.^{[29]}^{[Note 14]} It was of course known that adopting the meter and the kilogram as base units--obtaining the three dimensional MKS system--would not solve the problem: while the watt and the joule would be coherent, this would not be so for the volt, the ampere, the ohm, and the rest of the practical units for electric and magnetic quantities (the only three-dimensional absolute system in which all practical units are coherent is the QES system).
But Giorgi pointed out that the volt and the rest could be made coherent if the idea that all physical quantities must be expressible in terms of dimensions of length, mass, and time, is relinquished and a fourth base dimension is added for electric quantities. Any practical electrical unit could be chosen as the new fundamental unit, independent from the meter, kilogram, and second. Likely candidates for the fourth independent unit included the coulomb, the ampere, the volt, and the ohm, but eventually, the ampere proved to be the most convenient for metrology. Moreover, the freedom gained by making an electric unit independent from the mechanical units could be used to rationalize Maxwell's equations.
The idea that one should give up on having a purely 'absolute' system (i.e. one where only length, mass, and time are the base dimensions) was a departure from a viewpoint that seemed to underlie the early breakthroughs by Gauss and Weber (especially their famous 'absolute measurements' of Earth's magnetic field^{[30]}), and it took some time for the scientific community to accept it--not least because many scientists clung to the notion that the dimensions of a quantity in terms of length, mass, and time somehow specify its 'fundamental physical nature'.^{[31]}^{:24, 26}^{[29]}
By the 1920s, dimensional analysis had become much better understood^{[29]} and it was becoming widely accepted that the choice of both the number and of the identities of the "fundamental" dimensions should be dictated by convenience only and that there is nothing really fundamental about the dimensions of a quantity.^{[31]} In 1935, Giorgi's proposal was adopted by the IEC as the Giorgi system. It is this system that has since then been called the MKS system,^{[32]} although 'MKSA' appears in careful usage. In 1946 the CIPM approved a proposal to adopt the ampere as the electromagnetic unit of the "MKSA system".^{[33]} In 1948 the CGPM commissioned the CIPM "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention".^{[34]} This led to the launch of SI in 1960.
To summarize, the ultimate reason that the kilogram was chosen over the gram as the base unit of mass was, in one word, the volt-ampere. Namely, the combination of the meter and the kilogram was the only choice of base units of length and mass such that 1. the volt-ampere--which is also called the watt and which is the unit of power in the practical system of electrical units--is coherent, 2. the base units of length and mass are decimal multiples or submultiples of the meter and the gram, and 3. the base units of length and mass have convenient sizes.
The CGS and MKS systems co-existed during much of the early-to-mid 20th century, but as a result of the decision to adopt the "Giorgi system" as the international system of units in 1960, the kilogram is now the SI base unit for mass, while the definition of the gram is derived.
The replacement of the International Prototype of the Kilogram 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.^{[2]} Physical standard masses such as the IPK and its replicas still serve as secondary standards.
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 , effectively defining the kilogram in terms of the second and the metre. The new definition took effect on 20 May 2019.^{[2]}^{[4]}^{[35]}
Prior to the redefinition, the kilogram and several other SI units based on the kilogram were defined by a man-made metal artefact: the Kilogramme des Archives from 1799 to 1889, and the International Prototype of the Kilogram from 1889 to 2019.^{[2]}
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,^{[36]} 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 International Committee for Weights and Measures (CIPM) in 2005, it was recommended that the same be done with the kilogram.^{[37]}
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 × length^{2} / time) together with other physical constants.^{[38]}^{[39]} This resolution was accepted by the 24th conference of the CGPM^{[40]} in October 2011 and further discussed at the 25th conference in 2014.^{[41]}^{[42]} 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.^{[41]} 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.
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 the precise measurement of the strength of gravity in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.
Because SI prefixes may not be concatenated (serially linked) within the name or symbol for a unit of measure, SI prefixes are used with the unit gram, not kilogram, which already has a prefix as part of its name.^{[43]} For instance, one-millionth of a kilogram is 1mg (one milligram), not 1?kg (one microkilogram).
Submultiples | Multiples | |||||
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Value | SI symbol | Name | Value | SI symbol | Name | |
10^{-1} g | dg | decigram | 10^{1} g | dag | decagram | |
10^{-2} g | cg | centigram | 10^{2} g | hg | hectogram | |
10^{-3} g | mg | milligram | 10^{3} g | kg | kilogram | |
10^{-6} g | µg | microgram | 10^{6} g | Mg | megagram (tonne) | |
10^{-9} g | ng | nanogram | 10^{9} g | Gg | gigagram | |
10^{-12} g | pg | picogram | 10^{12} g | Tg | teragram | |
10^{-15} g | fg | femtogram | 10^{15} g | Pg | petagram | |
10^{-18} g | ag | attogram | 10^{18} g | Eg | exagram | |
10^{-21} g | zg | zeptogram | 10^{21} g | Zg | zettagram | |
10^{-24} g | yg | yoctogram | 10^{24} g | Yg | yottagram | |
Common prefixed units are in bold face.^{[Note 15]} |
Obsolete Units As stated in the 1990 Federal Register notice, ...
[p. 534] The expedient suggests itself of attaching the prefix ab or abs to a practical or Q. E. S. unit, in order to express the absolute or corresponding C. G. S. magnetic unit. ... [p. 535] In a comprehensive system of electromagnetic terminology, the electric C. G. S. units should also be christened. They are sometimes referred to in electrical papers, but always in an apologetic, symbolical fashion, owing to the absence of names to cover their nakedness. They might be denoted by the prefix abstat.
External images | |
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BIPM: The IPK in three nested bell jars | |
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?g) | |
BIPM: Mettler HK1000 balance, featuring 1?g resolution and a 4kg 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?Gal accuracy |