Fact-checked by Grok 2 weeks ago

SI base unit

The SI base units are the seven fundamental units of measurement in the (SI), which provide the basis for defining all other units in this globally standardized coherent system adopted in 1960. These units correspond to the basic physical quantities of time (second, s), length (, m), mass (, kg), electric current (, A), thermodynamic temperature (, K), amount of substance (, mol), and luminous intensity (, cd), selected for their historical importance and dimensional independence. Since the 2019 revision of the SI, effective from 20 May 2019, all base units are defined by assigning exact numerical values to seven key physical constants—the frequency ΔνCs, c, h, e, k, NA, and Kcd—ensuring the system's definitions are invariant and linked directly to universal phenomena rather than artifacts or specific experimental realizations. This revision, approved by the 26th General Conference on Weights and Measures in 2018, updated the definitions of the , , , and to align with this constant-based framework, while the second, , and had already been so defined. The definitions of the SI base units are as follows: This structure allows derived SI units, such as the for or the joule for , to be expressed as products of powers of these base units without additional constants, promoting in scientific, , and everyday measurements worldwide.

Overview

Definition

SI base units are the foundational components of the (SI), serving as the primary standards for measuring seven mutually independent base quantities; all other SI units, known as derived units, are formed by combining these base units through multiplication and division without introducing any numerical factors other than unity. This structure ensures a coherent system where derived quantities, such as or , can be expressed precisely in terms of the base quantities without or loss of dimensional . The key criterion for designating a unit as an SI base unit is its association with a base quantity that cannot be derived from combinations of other quantities using the laws of physics, thereby maintaining dimensional independence and avoiding the introduction of arbitrary constants that could compromise measurement precision. For instance, length and mass represent such base quantities, as they form irreducible dimensions essential for describing physical phenomena; in contrast, derived quantities like area or force are constructed from products or powers of these base quantities. At the 11th General Conference on Weights and Measures (CGPM) in 1960, the seven base quantities were selected to encompass the core aspects of physical reality relevant to science, technology, and everyday applications, providing a minimal yet comprehensive set for deriving all necessary measurements. This choice reflects a balance between historical conventions and the need for practical universality, ensuring that the SI system supports advancements across diverse fields without requiring additional independent units.

Role in measurement

SI base units serve as the foundational elements of the International System of Units (SI), enabling the coherent derivation of all other SI units through simple and without the need for factors other than unity. This arises because derived units are expressed as products of powers of the base units, ensuring that equations involving physical quantities maintain dimensional consistency and numerical simplicity. For instance, units such as area or are formed directly from combinations like squared or per time, respectively, promoting a unified framework for measurements across various scales and applications. The adoption of SI base units facilitates unambiguous communication of measurements in , science, and technology, where precision and are paramount to avoid errors and ensure . By providing a common language for quantifying physical quantities, these units support global commerce—such as in manufacturing specifications and —and advance scientific collaboration by allowing researchers worldwide to replicate experiments and compare results reliably. This is essential for industries ranging from to pharmaceuticals, where inconsistent units could lead to costly misunderstandings or safety risks. In , SI base units form the basis for expressing any as a product of powers of these fundamental units, enabling the verification of equation validity and the of relationships between variables. This approach underscores the of the base quantities—such as , , and time—allowing complex derived quantities to be broken down into their dimensional components for analytical purposes. By rooting all measurements in this set of base units, dimensional analysis becomes a powerful tool for ensuring theoretical consistency in fields like and physics. The use of a single, carefully selected set of SI base units minimizes redundancy in the measurement system, eliminating the need for multiple arbitrary scales and fostering universality across disciplines including physics, , and engineering. This streamlined structure enhances efficiency in calculations and data interpretation, as professionals can rely on a shared set of references without discipline-specific adjustments. Ultimately, it promotes a cohesive global ecosystem that supports innovation and equitable access to standardized knowledge.

The Seven Base Units

Physical quantities

The International System of Units (SI) is founded on seven base physical quantities that are regarded as dimensionally independent, serving as the foundation for defining all other physical quantities through derived units. These quantities were selected to encompass the essential aspects of measurement in physics, chemistry, and related sciences without redundancy or interdependence. The seven base quantities are: , , time, , , , and . Length is a fundamental quantity describing the extent of space between points, essential for , , and positioning. quantifies the amount of in a body, providing the basis for concepts like and gravitational interaction. Time measures the duration of events and intervals between occurrences, underpinning dynamics and periodicity. represents the flow of , forming the core for electromagnetic phenomena and . Thermodynamic temperature indicates the degree of hotness or coldness of a , critical for and . counts the number of specified elementary entities, such as atoms or molecules, vital for and chemical reactions. assesses the brightness of a source in a given direction, accounting for human visual sensitivity in photometry. These quantities are chosen because they are mutually independent—none can be derived from the others—and collectively allow the coherent expression of virtually all measurable physical properties across disciplines, from mechanical motion to quantum interactions, through products and quotients. This minimal set ensures universality and simplicity in scientific communication and experimentation. The selection of these seven base quantities has remained unchanged since their complete establishment at the 14th General Conference on Weights and Measures (CGPM) in , providing long-term stability for global despite ongoing refinements in unit definitions.

Symbols and units

The seven SI base units, each corresponding to a fundamental as outlined in the previous section on physical quantities, are standardized with specific names and symbols to ensure consistency in scientific communication. These are presented in the following table: (Table 2, p. 115) The symbols for SI units are written in roman (upright) typeface, regardless of the typeface used in the surrounding text, to distinguish them from mathematical variables or quantities, which are typically italicized. Unit symbols are not followed by a period except in the case of the abbreviation for "number" (no), and they are not pluralized; for example, 5 m (five metres) rather than 5 ms. Prefixes such as kilo- or milli- are not directly applied to the symbols of base units except in the case of the kilogram (kg), where the 'k' denotes kilo; all other base units use decimal prefixes only when forming multiples or submultiples, such as km for kilometre. (Section 5.3.1, pp. 130-131) Pronunciation guidelines for the unit names follow conventions to promote uniformity, with variations allowed for local languages but symbols remaining unchanged. For instance, is pronounced "SEK-und," as "AM-peer," as "KEL-vin," the mole as "mole," and the candela as "can-DEE-la" or "can-DELL-a." In equations and , unit symbols are commonly used without alteration, such as in expressions like v = 3 × 108 m/s, where the symbols maintain their standard form. (Appendix 2, pp. 163-164) The symbols and names of the SI base units are invariant internationally, fixed by the General Conference on Weights and Measures (CGPM) and unaffected by national languages or regional spelling differences, ensuring global interoperability in measurement standards. For example, while the unit name may be spelled "" in or "meter" in , the symbol 'm' remains identical worldwide. (Section 1.2, p. 111)

Historical Development

Establishment and early revisions

The International System of Units (SI) was formally established in 1960 by the 11th General Conference on Weights and Measures (CGPM), which adopted six base units derived from the metre-kilogram-second (MKS) system to create a coherent, practical framework for international measurements. This decision replaced the patchwork of disparate national and regional systems that had previously hindered global scientific and trade consistency, building directly on the metric system's foundations laid in the through the 1875 . The selection of these initial six base units—metre for length, for mass, second for time, for electric current, degree Kelvin (later ) for thermodynamic temperature, and new candle (later ) for luminous intensity—was driven by the need to address fundamental physical quantities essential for practical applications in science and industry. The was added as the seventh base unit in 1971. This choice ensured dimensional independence among the units while aligning with established conventions in physics and chemistry, extending the MKS system's emphasis on mechanical measurements to include electromagnetic, thermal, and photometric domains. The Bureau International des Poids et Mesures (BIPM), established under the 1875 , played a central role in proposing and coordinating these developments, while the CGPM, as the supreme authority, approved the resolutions to standardize the units worldwide. Early revisions focused on refining names, symbols, and definitions without altering the core set of base units. In , at the 13th CGPM, the name "" and symbol "K" were officially adopted for the unit of , replacing "degree Kelvin" and clarifying its relation to the triple point of . The name "" and symbol "cd" were also adopted at this conference for . The 14th CGPM in 1971 introduced the as the seventh unit, defining it as the containing as many elementary entities as atoms in 0.012 of , with the name "" and symbol "" formalized to support chemical measurements. By the 15th CGPM in 1975, while the units remained unchanged, new names were assigned to derived units for radiation, such as () for activity and () for , enhancing the system's utility in emerging fields like . A significant update came in 1983 at the 17th CGPM, which redefined the in terms of the in , setting it as the distance light travels in 1/299 792 458 of a second to improve precision and universality. These adjustments, overseen by the BIPM and ratified by successive CGPM meetings, refined the SI's foundations through the late without expanding the number of units.

Path to redefinition

The traditional definitions of several base units relied on physical artifacts or specific experimental procedures, which introduced limitations in stability and universality. For instance, the was defined by the mass of a platinum-iridium cylinder maintained at the International Bureau of Weights and Measures (BIPM), but this artifact exhibited gradual mass drift due to surface contamination and environmental factors, amounting to approximately 50 micrograms over more than a century relative to its working copies. Similarly, the ampere's based on the force between parallel current-carrying conductors was practically realized through electrochemical cells, such as the silver voltameter, leading to discrepancies and inconsistencies across national laboratories because these methods were sensitive to chemical impurities and temperature variations. These challenges underscored the philosophical motivation to redefine the base units in terms of invariant physical constants, ensuring a grounded in universal laws of nature rather than mutable human artifacts, thereby enhancing reproducibility, accessibility, and long-term stability for global . Key developments in from the mid-20th century onward provided the technical foundation for this shift. The , discovered in 1962, enabled the realization of voltage standards through superconducting junctions, linking electrical measurements directly to the frequency of cesium atomic transitions and the . Complementing this, the , observed in 1980, established a resistance standard invariant to material properties, quantized in terms of the and . For timekeeping, advancements in atomic clocks progressed from early and technologies in the 1950s to cesium fountain clocks in the 1990s, achieving fractional frequency uncertainties below 10^{-15}, which stabilized the second and facilitated links to other constants. In mass metrology, the Watt balance, invented by Bryan Kibble in 1975, equated mechanical power to electrical power, allowing the to be determined via the without relying on artifacts; prototypes demonstrated uncertainties approaching parts in 10^8 by the 2000s. Consultative committees under the International Committee for Weights and Measures (CIPM) drove the conceptual evolution toward a constant-based . The Consultative Committee for Units (), formed in to advise on unit systems, began exploring constant-linked definitions in the , influenced by quantum breakthroughs, and issued preliminary recommendations in 1975 for aligning electrical units with fundamental constants. The Consultative Committee for Mass and Related Quantities (CCM), established in 1980, addressed mass-specific issues, highlighting artifact instability in reports from the 1980s and proposing experimental paths like the Watt balance. By the 1990s, joint CCU-CCM efforts intensified; in 1999, the CCU endorsed redefining the , , and other units via fixed constants, contingent on measurement precision targets. This culminated in a formal roadmap in 2010, outlining criteria for relative uncertainties below 2 × 10^{-8} and compatibility among constant determinations, paving the way for comprehensive redefinition while ensuring continuity with existing values.

2019 revision

The 26th General Conference on Weights and Measures (CGPM), held in November 2018, unanimously adopted Resolution 1 to revise the (SI), with the changes taking effect on 20 May . This revision redefined four base units—the , , , and —by fixing the numerical values of fundamental physical constants: the h, the e, the k, and the N_A, respectively. It also included refinements to the definitions of , , and to align with these fixed constants, while maintaining the existing definitions based on the caesium hyperfine frequency \Delta \nu_{Cs} and the c. The specific fixed values established in the resolution were h = 6.62607015 \times 10^{-34} J s for the , e = 1.602176634 \times 10^{-19} C for the , k = 1.380649 \times 10^{-23} J/K for the , and N_A = 6.02214076 \times 10^{23} mol^{-1} for the . These assignments ensured that the SI base units are now universally and precisely realizable without reference to physical artifacts, building on prior experimental determinations of these constants with relative uncertainties below $2 \times 10^{-8}. The resolution explicitly abrogated the previous definitions of the affected units and outlined the new structure in terms of seven defining constants. The revision process involved extensive preparation over several years by the International Committee for Weights and Measures (CIPM), its Consultative Committee for Units (CCU), and institutes worldwide, including CODATA's 2017 adjustment of fundamental constants that informed the exact numerical values. Key highlights from the text emphasize the SI's evolution to a system based on invariant constants, promoting stability, accuracy, and accessibility for scientific and technological applications. The CGPM's decision was supported by 55 member states and observers, reflecting broad international consensus. The transition to the revised SI preserved the numerical values of all base units and derived quantities, ensuring continuity in measurements, but enhanced reproducibility by eliminating dependencies on material standards like the international prototype kilogram. This immediate outcome allowed national institutes to implement new realization methods promptly after 20 May , without disrupting existing calibrations.

Current Definitions

Principles of fixed constants

The redefinition of the () in established a framework where all base units are realized through the exact numerical values assigned to a set of seven fundamental physical constants. This core principle ensures that the definitions of the units are invariant over time and space, as they are anchored in universal properties of nature rather than physical artifacts that could degrade or vary. In this explicit-constant approach, the seven defining constants—the c, the h, the e, the k, the N_A, the hyperfine transition frequency of \Delta \nu_{\mathrm{Cs}}, and the K_{cd}—are fixed to exact numerical values in SI units. The base units are then derived from these constants via explicit defining equations, allowing the entire system of units to be constructed coherently without reliance on intermediate standards. This method provides a direct link between the SI and fundamental physical laws, promoting consistency across scientific disciplines. The theoretical advantages of this system include the elimination of uncertainties associated with material artifacts, such as the former , which could drift due to environmental factors. By fixing the s, the aligns more closely with natural invariances, enhancing long-term stability and reliability for worldwide. In practice, this metrological realization reverses the traditional paradigm: instead of a defining the of a through , the 's exact now defines the , enabling precise realizations through advanced experimental techniques.

Definitions of the units

The seven SI base units are defined by assigning exact numerical values to seven defining constants of nature, ensuring their stability and universality independent of artifacts or specific experimental conditions. These definitions, effective since 20 May 2019, link each unit directly to fundamental physical constants, with realization through precise measurements that reproduce the unit in practice. The second (s) is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency \Delta \nu_{\text{Cs}}, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s^{-1}. This corresponds to the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ^{133}Cs atom at rest at 0 K. Realization of the second is achieved using caesium atomic clocks or other frequency standards traceable to \Delta \nu_{\text{Cs}}. The (m) is the . It is defined by taking the fixed numerical value of the in c to be 299 792 458 when expressed in the unit m s^{-1}, where is already defined. Equivalently, the metre is the length of the path travelled by in during a time interval of $1/299\,792\,458 of a second. This definition is realized through or frequency combs, measuring distances in terms of the of with known . The kilogram (kg) is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 \times 10^{-34} when expressed in the unit J s, which is equal to m^2 s^{-2}, where the and the second are defined in terms of c and \Delta \nu_{\text{Cs}}. Practical realization uses the , which equates mechanical power to electrical power via m g v = B l I v, linking to h through measurements of v, magnetic flux density B, coil length l, and current I. Alternatively, the X-ray crystal density method determines via silicon sphere volume and atom count traceable to h. The (A) is the SI unit of . It is defined by taking the fixed numerical value of the e to be 1.602 176 634 \times 10^{-19} when expressed in the unit C, which is equal to A s, where the second is defined in terms of \Delta \nu_{\text{Cs}}. This means 1 A is the corresponding to the flow of exactly $1/(1.602\,176\,634 \times 10^{-19}) s per second. Realization involves single-electron tunneling devices or Josephson voltage standards to count electrons or measure currents traceable to e. The (K) is the unit of . It is defined by taking the fixed numerical value of the k to be 1.380 649 \times 10^{-23} when expressed in the unit J ^{-1}, which is equal to m^2 s^{-2} ^{-1}, where the , , and second are defined in terms of h, c, and \Delta \nu_{\text{Cs}}. Equivalently, a change of 1 K produces a change of k in a . This is realized using acoustic gas thermometry or Johnson noise thermometry, linking to electrical measurements traceable to k. The (mol) is the unit of . It is defined by taking the fixed numerical value of the N_{\text{A}} to be 6.022 140 76 \times 10^{23} when expressed in the unit mol^{-1}. Thus, 1 mol contains exactly 6.022 140 76 \times 10^{23} elementary entities (such as atoms, molecules, ions, or other particles). Realization is achieved through methods like the of or electrochemical counting, ensuring the number of entities matches N_{\text{A}}. The (cd) is the unit of in a given . It is defined by taking the fixed numerical value of the of of exactly 540 \times 10^{12} Hz K_{\text{cd}} to be 683 when expressed in the unit lm W^{-1}, which is equal to cd sr kg^{-1} m^{-2} s^3, where the , , and second are defined in terms of h, c, and \Delta \nu_{\text{Cs}}. Equivalently, the is the luminous intensity of a source that emits of 540 THz with of $1/683 W/sr in that direction. Realization uses tunable lasers at 540 THz with cryogenic to calibrate detectors against the defined .

References

  1. [1]
    The SI - BIPM
    The seven base units were chosen for historical reasons, and were, by convention, regarded as dimensionally independent: the metre, the kilogram, the second, ...SI base units · SI prefixes · Promotion of the SI · Defining constants
  2. [2]
    SI base units - BIPM
    The definitions of four of the SI base units – the kilogram, the ampere, the kelvin and the mole – were changed. Their new definitions are based on fixed ...
  3. [3]
    SI Brochure - BIPM
    SI Brochure: The International System of Units (SI). Note for translators and editors: Details on changes made since May 2019 are available on request to ...
  4. [4]
    Resolution-CGPM-26-1 - BIPM
    The second, symbol s, is the SI unit of time. · The metre, symbol m, is the SI unit of length. · The kilogram, symbol kg, is the SI unit of mass. · The ampere, ...
  5. [5]
    second - BIPM
    SI base unit: second (s). The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ΔνCs, ...
  6. [6]
    SI base unit: metre (m) - BIPM
    The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458.
  7. [7]
    SI base unit: kilogram (kg) - BIPM
    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 6.626 070 15 x 10 –34.
  8. [8]
    - ampere - BIPM
    SI base unit: ampere (A). The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary ...
  9. [9]
    - kelvin - BIPM
    The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 ...
  10. [10]
    - mole - BIPM
    SI base unit: mole (mol). The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 x 1023 elementary entities.
  11. [11]
    - candela - BIPM
    SI base unit: candela (cd). The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical ...
  12. [12]
    NIST Guide to the SI, Chapter 4: The Two Classes of SI Units and ...
    Jan 28, 2016 · Table 1 gives the seven base quantities, assumed to be mutually independent ... SI base units." Definitions of the SI base units are given in ...
  13. [13]
    [VIM3] 1.4 base quantity - BIPM
    NOTE 1 The subset mentioned in the definition is termed the “set of base quantities”. ... 1.10 base unit · 1.11 derived unit · 1.12 coherent derived unit · 1.13 ...
  14. [14]
    Resolution 12 of the 11th CGPM (1960) - BIPM
    The name and symbol for the unit of thermodynamic temperature were modified by the 13th CGPM in 1967 (Resolution 3). A seventh base unit, the mole, was adopted ...Missing: selection | Show results with:selection
  15. [15]
    [PDF] SI Brochure - 9th ed./version 3.02 - BIPM
    May 20, 2019 · Different types of definitions for the base units have been used: specific properties of artefacts such as the mass of the international ...
  16. [16]
    [PDF] The International System of Units (SI)
    The SI base units and SI derived units, including those with special names, have the important advantage of forming a coherent set with the effect that unit ...
  17. [17]
    [PDF] The International System of Units (SI), 2019 Edition
    • The SI was previously defined in terms of seven base units and derived units defined as products of powers of the base units. The seven base units were chosen.
  18. [18]
    SI Units | NIST - National Institute of Standards and Technology
    Apr 12, 2010 · The SI is made up of 7 base units that define the 22 derived units with special names and symbols, which are illustrated in NIST SP 1247, SI ...
  19. [19]
    [PDF] Guide for the Use of the International System of Units (SI)
    Feb 3, 1975 · 4.1 SI base units ... coherent system of SI units.”2. The SI also includes the prefixes to form decimal multiples and submultiples of SI ...
  20. [20]
    Resolution 3 of the 14th CGPM (1971) - BIPM
    The mole is the amount of substance with as many elementary entities as in 0.012 kg of carbon 12, where the entities must be specified.
  21. [21]
    [PDF] The International System of Units (SI) - BIPM
    Prior to the definitions adopted in 2018, the SI was defined through seven base units from which the derived units were constructed as products of powers of the ...
  22. [22]
    Resolution 3 of the 13th CGPM (1967) - BIPM
    Resolution 3 defines the unit of thermodynamic temperature as "kelvin" with symbol "K", and also allows use of degrees Celsius for temperature intervals.<|separator|>
  23. [23]
    Resolution 1 of the 17th CGPM (1983) - BIPM
    Resolution 1 of the 17th CGPM (1983). Definition of the metre. The 17th Conférence Générale des Poids et Mesures (CGPM),. considering.Missing: 1967 1968
  24. [24]
    The revision of the SI—the result of three decades of progress in ...
    On 16 November 2018 a revision of the International System of Units (the SI) was agreed by the General Conference on Weights and Measures.Missing: early | Show results with:early
  25. [25]
    Units Based on Constants: The Redefinition of the International ...
    Mar 10, 2016 · This paper describes the motivation and rationale behind this endeavor, introduces the new definitions, and reviews the requirements for the ...
  26. [26]
    Redefining the SI Base Units | NIST
    Nov 2, 2011 · The international General Conference on Weights and Measures (CGPM) has approved a plan to redefine four of the seven base units of the International System of ...
  27. [27]
    The watt or Kibble balance: a technique for implementing the new SI ...
    The redefinition of the SI unit of mass in terms of a fixed value of the Planck constant has been made possible by the Kibble balance, previously known as ...
  28. [28]
    Metrology in the balance - Physics World
    Mar 22, 2011 · The “watt balance” approach, on the other hand, ties the mass unit to the Planck constant, via a special device that balances mechanical with ...
  29. [29]
    CCU - BIPM
    The CCU was set up in 1964, to replace the Commission for the System of Units, set up by the CIPM in 1954.
  30. [30]
    The International System of Units (SI): Defining constants - BIPM
    The definitions of the base units specify the exact numerical value of each constant when its value is expressed in the corresponding SI unit.
  31. [31]
    [PDF] FAQs - Frequently asked questions about the revision of the SI - BIPM
    May 20, 2019 · A2: Defining the kilogram in terms of fundamental physical constants ensures its long-term stability, and hence its reliability, which was ...
  32. [32]
    Kibble balance - BIPM
    The BIPM Kibble balance uses a magnetic field, coil, and mass standard. It uses a one-mode measurement scheme, and is housed in a vacuum enclosure.
  33. [33]
    2021-01-11-kg-consensus - BIPM
    Jan 11, 2021 · The new definition of the kilogram, based on the fixed numerical value of the Planck constant, came into force on 20 May 2019. In principle ...