Kilogram

The kilogram (also kilogramme) is the base unit of mass in the metric system, formally 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 in everyday speech.

Kilogram
General information
Unit systemSI base unit
Unit ofmass
Symbolkg 
Conversions
1 kg in ...... is equal to ...
   Avoirdupois   ≈ 2.205 pounds[Note 1] 
   British Gravitational   ≈ 0.0685 slugs 

The kilogram was originally defined in 1795 as the mass of one litre of water. This was a simple definition, but difficult to use in practice. By the latest definitions of the unit, however, this relationship still has an accuracy of 30 ppm. 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.[1] 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.[2] This allows a properly-equipped metrology laboratory to calibrate a mass measurement instrument such as a Kibble balance directly by measuring natural phenomena, with no need to use an artefact.

Definition of kilogram

The kilogram is defined in terms of three fundamental physical constants: The speed of light c, a specific atomic transition frequency ΔνCs, and the Planck constant h. The formal definition 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.[3][4]

This definition makes the kilogram consistent with the older definitions: the mass remains within 30 ppm of the mass of one litre of water.[5]

Timeline of previous definitions
A replica of the International Prototype of the Kilogram on display at Cité des Sciences et de l'Industrie, featuring the protective double glass bell. The IPK served as primary standard for the kilogram until 2019.
  • 1793: The grave (the precursor of the kilogram) is defined as the mass of 1 litre (dm3) of water, which was determined to be 18841 grains.[6]
  • 1795: the gram (1/1000 of a kilogram) was provisionally defined as the mass of one cubic centimetre of water at the melting point of ice.[7]
  • 1799: The Kilogramme des Archives was manufactured as a prototype
  • 1875-1889: The Metre Convention is signed in 1875, leading to production of The International Prototype of the Kilogram (IPK) in 1879 and its adoption in 1889. It had a mass equal to the mass of 1 dm3 of water under atmospheric pressure and at the temperature of its maximum density, which is approximately 4 °C. The IPK was rarely used or handled. Copies of the IPK kept by national metrology laboratories around the world were compared with the IPK in 1889, 1948, and 1989 to provide traceability of measurements of mass anywhere in the world back to the IPK.
  • 2019: as of 20 May, the kilogram is redefined in terms of the Planck constant as approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018.

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,[8] which itself was a learned coinage, prefixing the Greek stem of χίλιοι khilioi "a thousand" to gramma, a Late Latin term for "a small weight", itself from Greek γράμμα.[9] The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal,[10] 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.[11] 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,[12][8] 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.[13][Note 2] 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]

During the 19th century, the standard system of metric units was the centimetre–gram–second system of units, treating the gram as the fundamental unit of mass and the kilogram as a derived unit. In 1901, however, following the discovery by James Clerk Maxwell that electric measurements could not be explained solely in terms of the three fundamental units of length, mass and time, Giovanni Giorgi proposed a new standard system that would include a fourth fundamental unit to measure quantities in electromagnetism.[22] In 1935 this was adopted by the IEC as the Giorgi system, now also known as MKS system,[23] and in 1946 the CIPM approved a proposal to adopt the ampere as the electromagnetic unit of the "MKSA system".[24]:109,110 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".[25] This led to the launch of SI in 1960 and the subsequent publication of the "SI Brochure", which stated that "It is not permissible to use abbreviations for unit symbols or unit names ...".[26][Note 3] 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 from that of the kilogram.

Redefinition based on fundamental constants
The SI system after the 2019 redefinition: the kilogram is now fixed in terms of the second, the speed of light and the Planck constant; and the ampere no longer depends on the kilogram
A Kibble balance, which was originally used to measure the Planck constant in terms of the IPK, can now be used to calibrate secondary standard weights for practical use.
Main articles: 2019 redefinition of the SI base units and CODATA 2018

The replacement of the International Prototype of the Kilogram as 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.[1] 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 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 20 May 2019.[1][3][27]

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 onward.[1]

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,[28] 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.[29]

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) together with other physical constants.[30][31] This resolution was accepted by the 24th conference of the CGPM[32] in October 2011 and further discussed at the 25th conference in 2014.[33][34] 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.[33] 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.

SI multiples

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.[35] For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 μkg (one microkilogram).

SI multiples of gram (g)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
10−1 g dg decigram 101 g dag decagram
10−2 g cg centigram 102 g hg hectogram
10−3 g mg milligram 103 g kg kilogram
10−6 g µg microgram 106 g Mg megagram (tonne)
10−9 g ng nanogram 109 g Gg gigagram
10−12 g pg picogram 1012 g Tg teragram
10−15 g fg femtogram 1015 g Pg petagram
10−18 g ag attogram 1018 g Eg exagram
10−21 g zg zeptogram 1021 g Zg zettagram
10−24 g yg yoctogram 1024 g Yg yottagram
Common prefixed units are in bold face.[Note 4]
  • The microgram is typically abbreviated "mcg" in pharmaceutical and nutritional supplement labelling, to avoid confusion, since the "μ" prefix is not always well recognised outside of technical disciplines.[Note 5] (The expression "mcg" is also the symbol for an obsolete CGS unit of measure known as the "millicentigram", which is equal to 10 μg.)
  • In the United Kingdom, because serious medication errors have been made from the confusion between milligrams and micrograms when micrograms has been abbreviated, the recommendation given in the Scottish Palliative Care Guidelines is that doses of less than one milligram must be expressed in micrograms and that the word microgram must be written in full, and that it is never acceptable to use "mcg" or "μg".[36]
  • The hectogram (100 g) is a very commonly used unit in the retail food trade in Italy, usually called an etto, short for ettogrammo, the Italian for hectogram.[37][38][39]
  • The former standard spelling and abbreviation "deka-" and "dk" produced abbreviations such as "dkm" (dekametre) and "dkg" (dekagram).[40] The abbreviation "dkg" (10 g) is still used in parts of central Europe in retail for some foods such as cheese and meat.
  • 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."[41] The unit name megatonne or megaton (Mt) is often used in general-interest literature on greenhouse gas emissions, whereas the equivalent unit in scientific papers on the subject is often the teragram (Tg).

See also

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 spelling kilogram is the modern spelling used by the International Bureau of Weights and Measures (BIPM), the US National Institute of Standards and Technology (NIST), the UK's National Measurement Office, National Research Council of Canada, and the National Measurement Institute, Australia.
  3. 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 ..."
  4. 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.
  5. The practice of using the abbreviation "mcg" rather than the SI symbol "μg" was formally mandated in the US for medical practitioners in 2004 by the Joint Commission on Accreditation of Healthcare Organizations (JCAHO) in their "Do Not Use" List: Abbreviations, Acronyms, and Symbols because "μg" and "mg" when handwritten can be confused with one another, resulting in a thousand-fold overdosing (or underdosing). The mandate was also adopted by the Institute for Safe Medication Practices.

References
  1. Resnick, Brian (May 20, 2019). "The new kilogram just debuted. It's a massive achievement". vox.com. Retrieved May 23, 2019.
  2. "The Latest: Landmark Change to Kilogram Approved". AP News. Associated Press. November 16, 2018. Retrieved March 4, 2020.
  3. Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018) (PDF)
  4. Decision CIPM/105-13 (October 2016). The day is the 144th anniversary of the Metre Convention.
  5. The density of water is 0.999972 g/cm3 at 3.984 °C. See Franks, Felix (2012). The Physics and Physical Chemistry of Water. Springer. ISBN 978-1-4684-8334-5.
  6. Guyton; Lavoisier; Monge; Berthollet; et al. (1792). Annales de chimie ou Recueil de mémoires concernant la chimie et les arts qui en dépendent. 15-16. Paris: Chez Joseph de Boffe. p. 277.
  7. Gramme, le poids absolu d'un volume d'eau pure égal au cube de la centième partie du mètre, et à la température de la glace fondante
  8. "Kilogram". Oxford English Dictionary. Oxford University Press. Retrieved November 3, 2011.
  9. Fowlers, HW; Fowler, FG (1964). The Concise Oxford Dictionary. Oxford: The Clarendon Press. Greek γράμμα (as it were γράφ-μα, Doric γράθμα) means "something written, a letter", but it came to be used as a unit of weight, apparently equal to 1/24 of an ounce (1/288 of a libra, which would correspond to about 1.14 grams in modern units), at some time during Late Antiquity. French gramme was adopted from Latin gramma, itself quite obscure, but found in the Carmen de ponderibus et mensuris (8.25) attributed by Remmius Palaemon (fl. 1st century), where it is the weight of two oboli (Charlton T. Lewis, Charles Short, A Latin Dictionary s.v. "gramma", 1879). Henry George Liddell. Robert Scott. A Greek-English Lexicon (revised and augmented edition, Oxford, 1940) s.v. γράμμα, citing the 10th-century work Geoponica and a 4th-century papyrus edited in L. Mitteis, Griechische Urkunden der Papyrussammlung zu Leipzig, vol. i (1906), 62 ii 27.
  10. "Décret relatif aux poids et aux mesures du 18 germinal an 3 (7 avril 1795)" [Decree of 18 Germinal, year III (April 7, 1795) regarding weights and measures]. Grandes lois de la République (in French). Digithèque de matériaux juridiques et politiques, Université de Perpignan. Retrieved November 3, 2011.
  11. Convention nationale, décret du 1er août 1793, ed. Duvergier, Collection complète des lois, décrets, ordonnances, règlemens avis du Conseil d'état, publiée sur les éditions officielles du Louvre, vol. 6 (2nd ed. 1834), p. 70. The metre (mètre) on which this definition depends was itself defined as the ten-millionth part of a quarter of Earth's meridian, given in traditional units as 3 pieds, 11.44 lignes (a ligne being the 12th part of a pouce (inch), or the 144th part of a pied.
  12. Peltier, Jean-Gabriel (1795). "Paris, during the year 1795". Monthly Review. 17: 556. Retrieved August 2, 2018. Contemporaneous English translation of the French decree of 1795
  13. "Kilogram". Oxford Dictionaries. Archived from the original on January 31, 2013. Retrieved November 3, 2011.
  14. "Spelling of "gram", etc". Weights and Measures Act 1985. Her Majesty's Stationery Office. October 30, 1985. Retrieved November 6, 2011.
  15. "kilo (n1)". Oxford English Dictionary (2nd ed.). Oxford: Oxford University Press. 1989. Retrieved November 8, 2011.
  16. "kilo (n2)". Oxford English Dictionary (2nd ed.). Oxford: Oxford University Press. 1989. Retrieved November 8, 2011.
  17. "Style Guide" (PDF). The Economist. January 7, 2002. Archived from the original (PDF) on July 1, 2017. Retrieved November 8, 2011.
  18. "kilogram, kg, kilo". Termium Plus. Government of Canada. October 8, 2009. Retrieved May 29, 2019.
  19. "kilo". How Many?. Archived from the original on November 16, 2011. Retrieved November 6, 2011.
  20. 29th Congress of the United States, Session 1 (May 13, 1866). "H.R. 596, An Act to authorize the use of the metric system of weights and measures". Archived from the original on July 5, 2015.
  21. "Metric System of Measurement:Interpretation of the International System of Units for the United States; Notice" (PDF). Federal Register. 63 (144): 40340. July 28, 1998. Archived from the original (PDF) on October 15, 2011. Retrieved November 10, 2011. Obsolete Units As stated in the 1990 Federal Register notice, ...
  22. Giovanni Giorgi (1901), "Unità Razionali di Elettromagnetismo", Atti della Associazione Elettrotecnica Italiana (in Italian), Torino, OL 18571144M Giovanni Giorgi (1902), Rational Units of Electromagnetism Original manuscript with handwritten notes by Oliver Heaviside
  23. Arthur E. Kennelly (1935), "Adoption of the Meter–Kilogram–Mass–Second (M.K.S.) Absolute System of Practical Units by the International Electrotechnical Commission (I.E.C.), Bruxelles, June, 1935", Proceedings of the National Academy of Sciences of the United States of America, 21 (10): 579–583, Bibcode:1935PNAS...21..579K, doi:10.1073/pnas.21.10.579, PMC 1076662, PMID 16577693
  24. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on August 14, 2017
  25. Resolution 6 – Proposal for establishing a practical system of units of measurement. 9th Conférence Générale des Poids et Mesures (CGPM). October 12–21, 1948. Retrieved May 8, 2011.
  26. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 130, ISBN 92-822-2213-6, archived (PDF) from the original on August 14, 2017
  27. Pallab Ghosh (November 16, 2018). "Kilogram gets a new definition". BBC News. Retrieved November 16, 2018.
  28. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 112, ISBN 92-822-2213-6, archived (PDF) from the original on August 14, 2017
  29. Recommendation 1: Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants (PDF). 94th meeting of the International Committee for Weights and Measures. October 2005. p. 233. Archived (PDF) from the original on June 30, 2007. Retrieved February 7, 2018.
  30. "NIST Backs Proposal for a Revamped System of Measurement Units". Nist.gov. October 26, 2010. Retrieved April 3, 2011.
  31. Ian Mills (September 29, 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (PDF). CCU. Retrieved January 1, 2011.
  32. Resolution 1 – On the possible future revision of the International System of Units, the SI (PDF). 24th meeting of the General Conference on Weights and Measures. Sèvres, France. October 17–21, 2011. Retrieved October 25, 2011.
  33. "BIPM - Resolution 1 of the 25th CGPM". www.bipm.org. Retrieved March 27, 2017.
  34. "General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram" (PDF) (Press release). Sèvres, France: General Conference on Weights and Measures. October 23, 2011. Retrieved October 25, 2011.
  35. BIPM: SI Brochure: Section 3.2, The kilogram
  36. "Prescribing Information for Liquid Medicines". Scottish Palliative Care Guidelines. Archived from the original on July 10, 2018. Retrieved June 15, 2015.
  37. Tom Stobart, The Cook's Encyclopedia, 1981, p. 525
  38. J.J. Kinder, V.M. Savini, Using Italian: A Guide to Contemporary Usage, 2004, ISBN 0521485568, p. 231
  39. Giacomo Devoto, Gian Carlo Oli, Nuovo vocabolario illustrato della lingua italiana, 1987, s.v. 'ètto': "frequentissima nell'uso comune: un e. di caffè, un e. di mortadella; formaggio a 2000 lire l'etto"
  40. U.S. National Bureau of Standards, The International Metric System of Weights and Measures, "Official Abbreviations of International Metric Units", 1932, p. 13
  41. Non-SI units that are accepted for use with the SI, SI Brochure: Section 4 (Table 8), BIPM
External images
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 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

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