Hubbry Logo
KilogramKilogramMain
Open search
Kilogram
Community hub
Kilogram
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Contribute something
Kilogram
Kilogram
Kilogram
View on Wikipedia
from Wikipedia

kilogram
A series of 5, 2, 1, 0.5 and 0.2 kilogram weights, made of cast iron
General information
Unit systemSI
Unit ofmass
Symbolkg
Conversions
1 kg in ...... is equal to ...
   Avoirdupois   
   British Gravitational   ≈ 0.0685 slugs
   Unified atomic mass units   6.02214076×1026 Da

The kilogram (also spelled kilogramme[1]) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg.[1] The word "kilogram" is formed from the combination of the metric prefix kilo- (meaning one thousand) and gram;[2] it is commonly shortened to "kilo" (plural "kilos").[3]

The kilogram is an SI base unit, defined ultimately in terms of three defining constants of the SI, namely a specific transition frequency of the caesium-133 atom, the speed of light, and the Planck constant.[4]: 131  A properly equipped metrology laboratory can calibrate a mass measurement instrument such as a Kibble balance as a primary standard for the kilogram mass.[5]

The kilogram was originally defined in 1795 during the French Revolution as the mass of one litre of water (originally at 0 °C, later changed to the temperature of its maximum density, approximately 4 °C). The current definition of a kilogram agrees with this original definition to within 30 parts per million (0.003%). In 1799, the platinum Kilogramme des Archives replaced it as the standard of mass. In 1889, a cylinder composed 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.[6]

Definition

[edit]

The kilogram is defined in terms of three defining constants:[4]

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

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
≈ (1.4755214×1040)⁠hΔνCs/c2⁠.

This definition is generally consistent with previous definitions: the kilogram remains within 30 parts per million (0.003%) of the mass of one litre of water at the temperature of its maximum density (approximately 4 °C), with the density of water at that temperature very close to 1 kg/L.[10]

Timeline of previous definitions

[edit]
The International Prototype of the Kilogram, whose mass was defined to be one kilogram from 1889 to 2019.

Name and terminology

[edit]

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 χίλιοι khilioi "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.[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]

For use with east Asian character sets, the SI symbol is encoded as a single Unicode character, U+338F ㎏ SQUARE KG in the CJK Compatibility block.

Redefinition based on fundamental constants

[edit]
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; furthermore 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 article: 2019 revision of the SI

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.[6]

The International Committee for Weights and Measures (CIPM) approved a revision 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.[6][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.[6]

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 that 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

[edit]
Main article: Orders of magnitude (mass)
"Milligram" redirects here. For the American band, see Milligram (band). For the Serbian band, see Miligram (band). For the horse, see Milligram (horse).

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)
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
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
10−27 g rg rontogram 1027 g Rg ronnagram
10−30 g qg quectogram 1030 g Qg quettagram
Common prefixed units are in bold face.[Note 3]

Usage and practical issues with SI mass units

[edit]
  • 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", "μg" or "ng" respectively.[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]

See also

[edit]

Notes

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Kilogram

View on Grokipedia
from Grokipedia
The kilogram (symbol: kg) is the SI unit of mass in the International System of Units (SI), one of seven base units that form the foundation of the modern metric system used worldwide for scientific, technical, and everyday measurements. It is defined by taking the fixed numerical value of the Planck constant h to be exactly 6.626 070 15 × 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 the speed of light c and the caesium hyperfine transition frequency ∆νCs. This definition ensures the kilogram's stability and universality, linking mass directly to fundamental physical constants rather than a physical artifact, and it took effect on 20 May 2019 following adoption by the 26th General Conference on Weights and Measures (CGPM). Historically, the kilogram was first defined in 1795 during the as the mass of one cubic of at the of , but this was refined in by the 1st CGPM to the mass of the (IPK), a of platinum-iridium stored at the International Bureau of Weights and Measures (BIPM) in , . This artifact-based definition served for over 130 years but faced challenges due to potential drifts in the IPK's mass from surface contamination or material instability, with measurements showing a loss of about 50 micrograms since . The 2019 redefinition, part of a broader revision of the SI that also updated the , , and mole, eliminated reliance on the IPK by tying the kilogram to invariant constants, enabling precise realizations through methods like the (which equates mechanical and electrical power) or the X-ray crystal density method using silicon-28 spheres. The choice of h's value maintains continuity, with the former IPK's mass equaling 1 kg to within a relative standard uncertainty of 1 × 10−8. The kilogram's role extends beyond pure science, underpinning global trade, manufacturing, healthcare, and environmental monitoring by providing a traceable standard for mass measurements from micrograms to tonnes. For instance, it forms the basis for derived units like the newton (force) and joule (), and its redefinition has enhanced measurement precision in fields such as and , where accuracies better than 10 are now achievable. Maintained by national institutes under the BIPM's coordination, the kilogram ensures international equivalence, supporting the mutual recognition arrangement that facilitates frictionless commerce valued at trillions of euros annually.

History and Evolution of the Definition

Early Concepts and Prototype Development

During the , efforts to standardize measurements culminated in the development of the , with the kilogram originating as a key unit of mass. In 1790, the French National Assembly tasked the with creating an invariable system of weights and measures, leading to the formation of the Commission des Poids et Mesures. Prominent chemist served on this commission, contributing to the foundational concepts for mass units by advocating for definitions tied to natural phenomena. The commission's work aimed to replace the disparate regional standards that hindered trade and science, proposing a decimal-based system rooted in universal properties. In 1795, the French Academy of Sciences formalized the initial definition of the kilogram—originally termed the "grave"—as the mass of one cubic decimeter (1 liter) of pure water at its temperature of maximum density, approximately . This water-based standard was intended to provide a reproducible reference grounded in a common substance, with the provisional kilogram established in as a practical embodiment of this mass. The name was later adjusted to "kilogram" to denote a thousand grams, aligning with the decimal progression of the . However, the water-based definition proved challenging due to variations in 's density influenced by fluctuations and impurities in even distilled samples, making precise replication difficult without controlled conditions. These issues, including the impracticality of maintaining exact environmental parameters for commercial and scientific use, prompted a shift toward a stable physical prototype. In , the Kilogramme des Archives—a cylindrical artifact crafted from and intended to match the mass of one cubic decimeter of at maximum —was deposited in the French National Archives as the first official standard. This prototype provided a more durable reference, though it marked a transition from intrinsic to artifact-based .

Artifact-Based Standards and the IPK

In 1889, at the first General Conference on Weights and Measures (CGPM), the kilogram was officially defined as the mass of the (IPK), a physical artifact sanctioned as the global standard of mass. This marked the transition from earlier water-based prototypes to an international artifact-based system, with the IPK serving as the definitive reference until its replacement in 2019. The IPK, crafted by the company in , was selected from several candidates after rigorous testing for stability and purity. The IPK is a cylindrical artifact measuring approximately 39 mm in both diameter and height, constructed from a 90% –10% alloy to enhance and resistance to . It is housed in a triple-locked vault at the International Bureau of Weights and Measures (BIPM) in , , under controlled atmospheric conditions—maintained at a of 18–23 °C and 40–60% relative humidity—to limit exposure to air and potential contaminants. Access requires approval from the International Committee for Weights and Measures (CIPM) and is restricted to periodic calibrations. To disseminate the kilogram standard globally, 40 national prototypes, identical in material and design to the IPK, were produced and calibrated against it at the BIPM in before distribution to member states and the BIPM itself. These served as primary references for national metrology institutes, with secondary working standards calibrated against them locally. Every 40 years or so, the BIPM conducted periodic verifications, during which national prototypes were compared to the IPK and its official copies using precision comparators; notable verifications occurred in 1946 and from . These comparisons revealed gradual divergences, with a difference of about 25 micrograms between the IPK and national prototypes by the late . Despite its design for permanence, the IPK demonstrated over time, with an estimated mass loss of around 50 relative to its official copies since 1889. This drift, observed through long-term comparisons, is attributed primarily to surface , including adsorption of atmospheric hydrocarbons and mercury vapors, as well as potential self-contamination from volatile impurities within the . Short-term fluctuations of up to 30 could occur monthly due to handling or environmental exposure, while longer-term changes averaged 1 per between major verifications. Calibration against the IPK required a standardized protocol to ensure consistent readings, as surface films could alter apparent by tens of micrograms. The BIPM procedure, established in the early and refined over time, involves initial immersion in organic solvents like and to dissolve organic residues, followed by with deionized at 100 °C to remove inorganic contaminants, and final drying in a controlled environment. This " and " , taking about 50 minutes, was performed immediately before measurements, with reproducibility verified to within 2–5 micrograms across operations. National prototypes underwent similar protocols during verifications. Early indications of emerged in the 1920s through informal comparisons at national laboratories, but systematic evidence surfaced during the 1946 verification, which showed drifts of up to 50 micrograms in some prototypes since 1889. By the , recalibrations prompted adjustments to national standards; for instance, the U.S. national prototype K20 was found to have lost about 100 micrograms relative to its 1939 calibration, leading to updated correction values for dissemination of the unit. These events highlighted the challenges of artifact-based standards, influencing ongoing refinements in storage and handling practices at the BIPM.

Transition to Fundamental Constants

Throughout the 20th century, metrologists recognized the instability of the artifact-based kilogram definition, as periodic verifications revealed gradual mass changes in the (IPK) and national prototypes, with a divergence of approximately 25 micrograms observed during the 1989–1991 comparisons. This drift, amounting to about 50 micrograms since 1889, underscored the limitations of relying on a physical object susceptible to environmental factors like and surface oxidation, prompting proposals for invariant definitions based on fundamental physical constants to ensure long-term stability and universality. A key advancement came in the 1970s with the development of the , originally known as the watt balance, invented by Bryan Kibble at the UK's National Physical Laboratory (NPL). Conceptualized in 1975, the device equates the weight of a to an electromagnetic force generated by a current-carrying coil in a , allowing precise measurement of in terms of electrical quantities such as voltage and resistance, which are traceable to the hh. This innovation provided an experimental pathway to link the kilogram directly to quantum electrical standards, reducing dependence on mechanical artifacts and enabling measurements with uncertainties below 10 parts per billion. Parallel efforts focused on the atom-counting approach through the International Avogadro Project, coordinated by institutions like Germany's (PTB), which aimed to define the kilogram using highly pure, nearly perfect silicon-28 spheres. By measuring the spheres' volume via and their lattice spacing with , researchers determined the number of silicon atoms, thereby linking mass to the NAN_A and, indirectly, to hh through the molar mass constant. This method, pursued since the early 2000s, achieved uncertainties comparable to the , around 2 parts per 10^8, and complemented electrical approaches by providing an independent verification route. International collaboration, facilitated by the International Committee for Weights and Measures (CIPM) and the Consultative Committee for Mass and Related Quantities (CCM), drove progress, with the Committee on Data for Science and Technology (CODATA) playing a crucial role in adjusting values of fundamental constants through least-squares analyses of global measurements. CODATA's 2017 special adjustment refined hh to 6.626 070 15×10−346.626\,070\,15 \times 10^{-34} J s with a relative of 1.5 \times 10^{-9}, ensuring consistency across experiments and paving the way for the redefinition. The 24th General Conference on Weights and Measures (CGPM) in 2011 adopted Resolution 1, endorsing the revision of the SI by fixing numerical values for hh, the elementary charge ee, the Boltzmann constant kk, and NAN_A, contingent on achieving requisite measurement precision. This diplomatic milestone built on decades of research, inviting further international efforts to meet the criteria outlined in the 2007 CGPM Resolution 12. Culminating at the 26th CGPM in 2018, Resolution 1 formally redefined the SI, with the kilogram specified as: "The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant hh to be 6.626 070 15 × 10^{-34} when expressed in the unit J s, which is equal to kg m² s^{-2}, where the metre and the second are defined in terms of c and Δν_{Cs}." The redefinition took effect on 20 May 2019 (World Metrology Day), marking the complete transition of all SI base units to fundamental constants through unanimous global consensus.

Current Definition and Realization

Definition via Planck's Constant

The kilogram, symbol kg, is the SI unit of . It is defined by taking the fixed numerical value of the hh to be exactly 6.62607015×10−346.62607015 \times 10^{-34} when expressed in the unit J s, which is equal to kg m² s⁻¹, where the and are defined in terms of the cc and the cesium hyperfine transition frequency ΔνCs\Delta \nu_{\text{Cs}}. This definition, adopted at the 26th General Conference on Weights and Measures in 2018 and effective from 20 May 2019, anchors the kilogram directly to a fundamental physical constant rather than a physical artifact. By fixing the value of hh, the definition links the kilogram to universal constants that are invariant across time and space, ensuring the unit's reproducibility without reliance on material standards that could degrade or vary. Planck's constant, discovered by in 1900 through his analysis of , serves as a cornerstone of by quantifying the discrete nature of energy, as expressed in the relation E=hνE = h \nu between a photon's energy EE and its frequency ν\nu. This theoretical foundation ties mass to quantum phenomena, where the energy equivalent of mass via Einstein's E=mc2E = m c^2 allows derivation of a relation such as m=h/(Δν⋅λ2)m = h / (\Delta \nu \cdot \lambda^2), with λ\lambda as the (λ=c/Δν\lambda = c / \Delta \nu), connecting mass to frequency and length in the SI framework through and relations. This approach extends to the broader SI system, where the kilogram joins the other six base units—all now defined via exact values of the seven defining constants: the cc, the hyperfine transition frequency ΔνCs\Delta \nu_{\text{Cs}}, the hh, the ee, the kBk_{\text{B}}, the NAN_{\text{A}}, and the KcdK_{\text{cd}}—creating an interdependent structure that enhances precision and universality across .

Methods for Practical Realization

Since the 2019 redefinition of the SI units, the kilogram is realized in laboratories through primary methods that link mass directly to the fixed value of Planck's constant, enabling precise experimental determinations without reference to physical artifacts. The two principal techniques are the and the X-ray crystal density (XRCD) method, also known as the Avogadro approach, both of which achieve relative standard uncertainties on the order of a few parts in 10810^8. These methods allow national institutes (NMIs) such as the National Institute of Standards and Technology (NIST) in the United States and the National Physical Laboratory (NPL) in the to generate kilogram standards traceable to fundamental constants. The operates on the principle of equating the gravitational force on a test to an electromagnetic force generated by a current-carrying coil in a , combined with a velocity mode to calibrate the system. In the weighing mode, the equation is mxg=I1Bℓm_x g = I_1 B \ell, where mxm_x is the test , gg is the local acceleration due to gravity, I1I_1 is the current, BB is the magnetic flux density, and ℓ\ell is the effective length of the coil in the field. In the moving (velocity) mode, the induced voltage satisfies U2=vBℓU_2 = v B \ell, where U2U_2 is the voltage and vv is the coil . Combining these yields the mass realization equation: mx=I1U2gvm_x = \frac{I_1 U_2}{g v} The current I1I_1 and voltage U2U_2 are measured using the (voltage standard KJ=2e/hK_J = 2e/h) and (resistance standard RK=h/e2R_K = h/e^2), directly tying the measurement to Planck's constant hh. This method has demonstrated relative uncertainties below 50 (ppb) in operational systems, with ongoing refinements targeting sub-10 ppb precision. The Avogadro method realizes the kilogram by determining the mass of a near-perfect sphere of isotopically pure 28^{28}Si, where the number of atoms NN is calculated from the sphere's volume VsV_s and the lattice parameter aa of the crystal: N=8Vs/a3N = 8 V_s / a^3 for the face-centered cubic structure of silicon. The mass of the sphere is then ms=N×m(28Si)m_s = N \times m(^{28}\mathrm{Si}), where m(28Si)m(^{28}\mathrm{Si}) is the atomic mass of 28^{28}Si, given by m(28Si)=M(28Si)×um(^{28}\mathrm{Si}) = M(^{28}\mathrm{Si}) \times u with M(28Si)M(^{28}\mathrm{Si}) the molar mass (approximately 0.027977 kg/mol) and uu the atomic mass constant (u=10−3/NAu = 10^{-3}/N_A kg, with NAN_A fixed at 6.02214076×10236.02214076 \times 10^{23} mol−1^{-1}). The volume and lattice parameter are measured using interferometry and X-ray diffraction, achieving relative uncertainties around 20 ppb in practice, comparable to the Kibble balance. International key comparisons, such as CCM.M-K8 coordinated by the International Bureau of Weights and Measures (BIPM), have verified the equivalence of realizations from both methods. The CCM.M-K8.2024 comparison, completed in 2024, showed deviations typically below a few ppb, with a key comparison reference value uncertainty of approximately 7.4 ppb, confirming consistency at the sub-10 ppb level or better for select implementations. As of 2025, NMIs disseminate the kilogram using a consensus value derived from multiple realizations, with an uncertainty of about 20 µg and ongoing adjustments (e.g., a potential -5 µg shift by late 2025). NMIs like NIST, NPL, (PTB) in , and National Metrology Institute of Japan (NMIJ) employ these techniques to calibrate working standards, disseminating the kilogram through mass comparisons and ensuring global via periodic verifications. Future enhancements focus on cryogenic Kibble balances, which operate at low temperatures to minimize thermal noise and mechanical losses in the coil and magnetic system, potentially reducing uncertainties to below 1 ppb and enabling more compact, routine realizations of the kilogram.

Name, Symbol, and Terminology

Etymology and Historical Naming

The term "kilogram" originates from the Greek "khilioi," meaning "thousand," prefixed to the French "gramme," a unit denoting a small mass derived from the "gramma" and Greek "gramma." This nomenclature was formally introduced in 1795 by the during the establishment of the in the wake of the . The kilogram was initially defined as the mass of one liter (or one cubic decimeter) of pure water at the temperature of melting ice (0 °C), while the gram—its foundational subunit—was set as the mass of one cubic centimeter of the same water. Thus, the kilogram equaled exactly 1,000 grams, providing a decimal progression suited to scientific and commercial needs. This relation underscored the metric system's emphasis on coherence, with the kilogram serving as the practical base unit for mass rather than the smaller gram. In French, the original spelling was "kilogramme," featuring a double "m" to align with words like "gramme," but English adopted "kilogram" as early as , shortening it for consistency with linguistic conventions; by the , this single-"m" form had become the in . The term gained global traction through the 1875 , a treaty signed by 17 nations in that not only endorsed the kilogram prototype but also harmonized its nomenclature across borders, establishing it as the universal unit of mass under the emerging . In other languages, adaptations reflect local phonetics, such as "kilogramo" in Spanish, while the kilogram's adoption marked a shift from pre-metric terms like the French "millier" (thousandweight), a traditional measure for bulk goods, to a unified framework.

Symbols, Abbreviations, and Usage Conventions

The official symbol for the kilogram in the (SI) is "kg", consisting of a lowercase "k" for the prefix kilo- followed immediately by a lowercase "g" for gram, with no space between them. This symbol is printed in upright and is never pluralized, such that quantities are expressed as, for example, 2 kg rather than 2 kgs. Abbreviations such as "kgs" or capitalized forms like "Kg" are prohibited, as are historical notations involving a subscript on the "k", such as ₖg, which have been avoided in modern usage to maintain consistency. According to conventions established by the International Bureau of Weights and Measures (BIPM) and detailed in ISO 80000-1, a space must separate the numerical value from the unit symbol, as in 5 kg, rather than 5kg; no period follows the symbol unless it ends a sentence. Capitalization of the symbol is restricted to the start of a sentence or in titles, where "Kg" may appear, but lowercase "kg" is standard otherwise. These rules ensure clarity in and prevent ambiguity with other symbols. The symbol "kg" must be distinguished from similar non-SI notations, such as "kn" for the (a unit of speed equal to one per hour, accepted for use with the SI in maritime and contexts) and "kgf" for (a non-SI unit of force equivalent to the weight of one kilogram under , approximately 9.80665 N, still used in some fields but not part of the SI base units). In compound units, "kg" is treated as a single entity, with multiplication indicated by a space or middle dot, as in N m for , avoiding direct juxtaposition. Internationally, these conventions are widely adopted, including in non-metric countries like the , where the kilogram and its symbol "kg" are legally recognized for trade, scientific, and medical applications under , despite the prevalence of customary units in everyday consumer contexts. In the , adherence to SI symbol rules is mandatory for federal agencies and international to facilitate global standardization.

Integration in the SI System

Relation to Other Base Units

The (SI) comprises seven base units, each representing a fundamental : the kilogram (kg) for mass, the (m) for , the second (s) for time, the (A) for , the (K) for thermodynamic temperature, the mole (mol) for amount of substance, and the (cd) for . These units form the foundation for all SI measurements, with derived units constructed as products or quotients of powers of these base units. Prior to the 2019 revision of the SI, the kilogram was defined independently as the mass of the international prototype kilogram, a platinum-iridium artifact maintained at the International Bureau of Weights and Measures (BIPM), while the other base units were already linked to fundamental physical constants. Following the redefinition, the kilogram is now defined by fixing the numerical value of the h=6.626 070 15×10−34h = 6.626\,070\,15 \times 10^{-34} J s, where the joule is expressed as kg m² s⁻², thereby interconnecting mass directly with length (via the , defined through the cc) and time (via the second, defined through the hyperfine transition frequency). This shift links the kilogram to the (via the ee), (via the kk, which incorporates mass, length, and time), mole (via the NAN_A, relating to ), and indirectly to the (via , which involves energy units with mass). The post-2019 framework establishes full interdependence among the base units, as all are now derived from a set of seven fixed defining constants, eliminating previous hierarchies where the kilogram served as an independent reference. This structure ensures universal consistency, allowing any SI unit to be expressed through products or quotients of these constants, and permits the redefinition of individual units without disrupting the system as a whole, provided the defining constants remain fixed. For instance, derived units involving highlight these connections: the newton (N) for is given by N=kg⋅m⋅s−2\mathrm{N} = \mathrm{kg \cdot m \cdot s^{-2}}, linking to length and time; the joule (J) for by J=kg⋅m2⋅s−2\mathrm{J} = \mathrm{kg \cdot m^2 \cdot s^{-2}}; and the (Pa) for by Pa=kg⋅m−1⋅s−2\mathrm{Pa} = \mathrm{kg \cdot m^{-1} \cdot s^{-2}}.

Prefixes and Derived Units

The kilogram, as the of , forms multiples and submultiples using standard SI prefixes, though with specific conventions to avoid cumbersome names like "millikilogram." Submultiples smaller than the kilogram are typically expressed using the gram (1 g = 10^{-3} kg) combined with prefixes, such as the milligram (mg = 10^{-3} g = 10^{-6} kg) for pharmaceutical dosages or the (µg = 10^{-6} g = 10^{-9} kg) in trace analysis. Larger multiples avoid the prefix "kilo-" directly on kilogram; instead, the (t = 10^3 kg) is the accepted non-SI unit for 1000 kilograms, commonly used in and , while the megagram (Mg = 10^6 g = 10^3 kg) serves for even larger scales like bulk materials. The following table lists common SI prefixes applied to the gram for mass units, illustrating their factors relative to the kilogram:
PrefixSymbolFactor (relative to 1 g)Equivalent in kg
micro-µ10^{-6}10^{-9} kg
nano-n10^{-9}10^{-12} kg
milli-m10^{-3}10^{-6} kg
kilo-k10^31 kg
mega-M10^610^3 kg
These prefixes ensure scalability across scientific and practical contexts, with the providing a practical alternative for the 10^3 kg multiple to maintain simplicity. Derived SI units incorporating the kilogram express physical quantities involving , often combined with other base units. For instance, is given by the (kg m^{-3}), quantifying per unit volume in fields like . The uses kg m^2, representing a body's resistance to rotational acceleration about an axis. is expressed as joules per kilogram (J kg^{-1} K^{-1}), equivalent to m^2 s^{-2} K^{-1}, measuring the energy required to raise the temperature of one kilogram by one . Although the SI promotes exclusive use of its units, non-SI units like the pound (lb) remain common in certain regions, particularly , where 1 lb = 0.45359237 kg exactly for pounds in contexts. This conversion facilitates interoperability in and .

Practical Usage and Challenges

Everyday Applications and Standards

The kilogram serves as a fundamental unit for measuring in numerous everyday contexts, including grocery labeling, pharmaceutical dosing, and industrial . In grocery settings, must declare the net in kilograms or grams to ensure accurate information and compliance with labeling regulations, such as those requiring metric units for of contents on principal display panels. In pharmaceuticals, drug dosages are commonly expressed in milligrams (one-thousandth of a kilogram), with calculations often based on milligrams per kilogram of body weight to tailor treatments precisely and safely. Similarly, in , the kilogram quantifies material usage, such as the approximately 900 kilograms of incorporated into the average automobile for components like the and body panels, enabling efficient production and . Legal metrology enforces the kilogram's role in commerce through standardized weighing instruments calibrated to kilogram-based units, promoting and . The (OIML) provides recommendations, such as OIML R 76-1, which outline metrological and technical requirements for non-automatic weighing instruments used in , ensuring scales maintain accuracy within specified tolerances for kilogram measurements. These verified scales are essential for transactions involving bulk goods, where discrepancies could lead to economic losses, and are subject to periodic against national kilogram prototypes. The kilogram's global adoption stems from the 1875 , signed by 17 nations including the , establishing the International Bureau of Weights and Measures to maintain SI units like the kilogram for uniform international standards. While mandatory in most signatory countries for official and commercial use, adoption remains voluntary in the and , though widespread in practice across industries and retail. Practical examples include , where jet fuel density is standardized between 0.775 and 0.840 kg/L at 15°C to calculate load and performance accurately. In education, the kilogram facilitates teaching the distinction between mass—an invariant measure of matter in kilograms—and weight, the gravitational force measured in newtons, using relatable benchmarks like a 1 kg bag of to illustrate concepts in school curricula. This approach, as recommended by experts, builds intuitive understanding of SI units through everyday objects, such as grouping U.S. nickels (5 g each) to approximate 1 kg.

Issues in Measurement and Maintenance

Prior to the 2019 redefinition of the (SI), the kilogram was maintained through the (IPK), a platinum-iridium cylinder stored at the International Bureau of Weights and Measures (BIPM). Over more than a century of use, the IPK exhibited long-term instability, with measurements indicating a mass loss of approximately 50 micrograms relative to its official value since 1889. This drift, attributed to surface contamination, adsorption of atmospheric gases, or mercury amalgamation, necessitated periodic recalibrations against working copies, but the copies themselves showed inconsistencies, with some gaining up to 20 micrograms over decades. Such variability undermined the stability of the unit, as the IPK's uncertainty was conventionally set to zero, masking potential errors in global standards. Following the redefinition of the kilogram in terms of the hh on 20 May 2019, the IPK was retired as the and assigned a conventional of 10 μg10 \, \mu \mathrm{g} to account for its historical drift, facilitating during a transitional period. Practical realization now relies on two primary methods: the Kibble (or watt) balance, which equates mechanical power to electrical power using quantum standards for voltage and resistance, and the X-ray crystal density (XRCD) method, which determines the of a -28 sphere via its atomic lattice parameters. Both methods achieve relative uncertainties of a few parts in 10810^8, but challenges persist in their implementation, including precise alignment of mechanical components in the and correction for surface oxide layers and binding energy effects in XRCD measurements using near-perfect spheres. A key issue in post-redefinition maintenance is the observed discrepancy between realizations from Kibble balances and XRCD experiments, which has prevented full equivalence of individual national institutes' (NMIs) standards. This inconsistency, on the order of tens of micrograms, arises from systematic differences in the experimental techniques and has been quantified through BIPM-coordinated key comparisons, such as CCM.M-K8, where results from multiple Kibble and XRCD setups are intercompared. To address this, dissemination of the kilogram occurs in phased transitions: Phase 1 (2019–2021) linked to the IPK with added uncertainty; Phase 2 (ongoing as of 2025) uses a consensus value of 1 kg − 7 μg with a standard uncertainty of 20 μg, derived from weighted averages of NMI realizations; and Phase 3, targeted for future implementation, will enable direct to individual experiments once at least five consistent results (including both methods) achieve uncertainties below 20 parts in 10910^9. Ongoing maintenance involves regular key comparisons every two to three years to monitor agreement and update the consensus value, with changes limited to ±5 parts in 10910^9 for stability. The CCM.M-K8. comparison, completed in 2024, showed significant improvement in agreement between methods compared to prior rounds, though investigations into remaining discrepancies continue through a dedicated roadmap, including enhanced modeling of systematic effects and additional experiments. These efforts ensure the kilogram's long-term invariance, though they highlight the complexity of quantum-based compared to the artifact era, requiring sustained international collaboration to reduce uncertainties below 10 μg for high-precision applications like fundamental physics and industrial .

References

  1. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf
  2. https://www.bipm.org/en/history-si/kilogram
  3. https://www.nist.gov/si-redefinition/kilogram-introduction
  4. https://www.ptb.de/cms/en/ptb/fachabteilungen/abt1/fb-11/ag-111/national-prototype-of-the-kilogram.html
  5. https://www.bipm.org/en/about-us
  6. https://www.nist.gov/si-redefinition/kilogram-past
  7. https://www.sciencedirect.com/science/article/pii/S0022316622085546
  8. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf/2d2b50bf-f2b4-9661-f402-5f9d66e4b507
  9. https://physicstoday.aip.org/features/an-atomic-physics-perspective-on-the-kilograms-new-definition
  10. https://www.bipm.org/en/mass-metrology/ipk
  11. https://iopscience.iop.org/article/10.1088/0026-1394/52/2/310
  12. https://www.bipm.org/documents/20126/28428218/working-document-ID-6763/23933265-3f75-42d7-f1d5-fa20b90a4052
  13. https://pmc.ncbi.nlm.nih.gov/articles/PMC6664201/
  14. https://www.nist.gov/si-redefinition/kilogram-kibble-balance
  15. https://www.ptb.de/cms/en/research-development/research-on-the-new-si/ptb-experiment.html
  16. https://iopscience.iop.org/article/10.1088/1681-7575/aa950a
  17. https://www.bipm.org/en/committees/cg/cgpm/24-2011/resolution-1
  18. https://www.bipm.org/en/committees/cg/cgpm/26-2018/resolution-1
  19. https://www.bipm.org/en/si-base-units/kilogram
  20. https://www.nist.gov/si-redefinition/kilogram-mass-and-plancks-constant
  21. https://www.bipm.org/documents/20126/41489673/SI-App2-kilogram.pdf/5881b6b5-668d-5d2b-f12a-0ef8ca437176
  22. https://www.nist.gov/programs-projects/nist-mise-en-pratique-redefinition-kilogram
  23. https://www.bipm.org/documents/20126/48150799/CCM.M-K8.2021.pdf/9a71fc63-fb10-614e-27df-727d3722ff52
  24. https://www.bipm.org/documents/20126/275177277/CCM-25_06-7_WGM_TGPfD-Kg-Report/44896737-0dae-2711-fe32-3493e211c763
  25. https://www.etymonline.com/word/kilogram
  26. https://www.rug.nl/education/courses/other-education/radiation-protection/a-z/a-z-data/kilogram?lang=en
  27. https://www.britannica.com/science/metric-system-measurement
  28. https://www.merriam-webster.com/dictionary/kilogram
  29. https://www.nist.gov/si-redefinition/kilogram/kilogram-focus-history
  30. https://www.spanish.academy/blog/measurements-and-dimensions-in-spanish/
  31. https://www.bbc.com/travel/article/20180923-how-france-created-the-metric-system
  32. https://www.nist.gov/pml/owm/si-units-mass
  33. https://www.nist.gov/pml/owm/metric-si-prefixes
  34. https://www.nist.gov/pml/owm/writing-si-metric-system-units
  35. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors
  36. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/cpg-sec140500-metric-declarations-quantity-contents-product-labels
  37. https://www.ncbi.nlm.nih.gov/books/NBK560924/
  38. https://www.investopedia.com/ask/answers/062315/what-types-raw-materials-would-be-used-auto-manufacturer.asp
  39. https://www.oiml.org/en/files/pdf_r/r076-1-e06.pdf
  40. https://www.nist.gov/blogs/taking-measure/busting-myths-about-metric-system
  41. https://ukma.org.uk/what-is-metric/uk-progress/uk-metric-timeline/
  42. https://www.exxonmobil.com/en/aviation/products-and-services/products/exxonmobil-jet-a-1
  43. https://www.nist.gov/blogs/taking-measure/top-10-tips-teaching-metric-system
  44. https://www.bipm.org/en/-/2021-kg-consensus
  45. https://www.bipm.org/documents/20126/276927654/Annual_Review_2024/93e00d95-24c1-4689-f7fc-98d437eb2371
Add your contribution
Related Hubs
Contribute something
User Avatar
No comments yet.