International System of Units (SI)

I Base Units

II Derived Units

III Prefixes

IV Revision of the International System of Units

IV.1 The base units of the SI

I Base Units

• metre (symbol m) unit of length (L)
• kilogramme (symbol kg) unit of mass (M)
• second (symbol s) unit of time (T)
• ampere (symbol A) unit of electric current (I)
• kelvin (symbol K) unit of thermodynamic temperature (Θ)
• mole (symbol mol) unit of amount of substance (N)
• candela (symbol cd) unit of luminous intensity (J)

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II Derived Units

• hertz (symbol Hz) unit of frequency, equivalent to 1/s ; s^-1
• radian (symbol rad) unit of angle, equivalent to m/m ; dimensionless unit
• steradian (symbol sr) unit of solid angle, equivalent to m²/m² ; dimensionless unit
• newton (symbol N) unit of force (weight), equivalent to kg⋅m/s² ; kg⋅m⋅s^-2
• pascal (symbol Pa) unit of pressure, equivalent to N/m² ; kg⋅m^-1⋅s^-2
• joule (symbol J) unit of energy (work, heat), equivalent to N⋅m or C⋅V or W⋅s ; kg⋅m²⋅s^-2
• watt (symbol W) unit of power (radiant flux), equivalent to J/s or V⋅A ; kg⋅m²⋅s^-3
• coulomb (symbol C) unit of electric charge, equivalent to s⋅A or F⋅V ; s⋅A
• volt (symbol V) unit of voltage (elecrical potential difference, electromotive force), equivalent to W/A or J/C ; kg⋅m²⋅s^-3⋅A^-1
• farad (symbol F) unit of electric capacitance, equivalent to C/V or s/Ω ; kg^-1⋅m^-2⋅s⁴⋅A²
• ohm (symbol Ω) unit of electric resistance (impedance), equivalent to 1/S or V/A ; kg⋅m²⋅s^-3⋅A^-2
• siemens (symbol S) unit of electric conductance, equivalent to 1/Ω or A/V ; kg^-1⋅m^-2⋅s³⋅A²
• weber (symbol Wb) unit of magnetic flux, equivalent to J/A or T⋅m² ; kg⋅m²⋅s^-2⋅A^-1
• tesla (symbol T) unit of magnetic field strength (magnetic flux density), equivalent to V⋅s/m² or Wb/m² or N/(A⋅m) ; kg⋅s^-2⋅A^-1
• henry (symbol Wb) unit of electrical inductance, equivalent to V⋅s/A or Ω⋅s or Wb/A ; kg⋅m²⋅s^-2⋅A^-2
• degree Celsius (symbol °C) unit of temperature (relative to 273.15 K) ; K
• lumen (symbol lm) unit of luminous flux, equivalent to cd⋅sr ; cd
• lux (symbol lx) unit of illuminance, equivalent to lm/m² ; m^-2⋅cd
• becquerel (symbol Bq) unit of radioactivity (decays per unit time), equivalent to 1/s ; s^-1
• gray (symbol Gy) unit of absorbed dose (of ionizing radiation), equivalent to J/kg ; m²⋅s^-2
• sievert (symbol Sv) unit of equivalent dose (of ionizing radiation), equivalent to J/kg ; m²⋅s^-2
• katal (symbol kat) unit of catalytic activity, equivalent to mol/s ; s^-1⋅mol

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III Prefixes

• yotta (symbol Y) 10²⁴
• zetta (symbol Z) 10²¹
• exa (symbol E) 10¹⁸
• peta (symbol P) 10¹⁵
• tera (symbol T) 10¹²
• giga (symbol G) 10⁹
• mega (symbol M) 10⁶
• kilo (symbol k) 10³
• hecto (symbol h) 10²
• deca (symbol da) 10¹
• deci (symbol d) 10⁻¹
• centi (symbol c) 10⁻²
• milli (symbol m) 10⁻³
• micro (symbol µ) 10⁻⁶
• nano (symbol n) 10⁻⁹
• pico (symbol p) 10⁻¹²
• femto (symbol f) 10⁻¹⁵
• atto (symbol a) 10⁻¹⁸
• zepto (symbol z) 10⁻²¹
• yocto (symbol y) 10⁻²⁴

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IV Revision of the International System of Units (SI)

Effective from 20 May 2019, the International System of Units, the SI, is the system of units in which

• the unperturbed ground state hyperfine transition frequency of the caesium 133 atom ∆ν_Cs is 9.192 631 77 GHz
• the speed of light in vacuum c is 2.997 924 58 × 10² Mm/s
• the Planck constant h is 6.626 070 15 × 10⁻¹⁰ yJ s
• the elementary charge e is 1.602 176 634 × 10⁻¹ aC
• the Boltzmann constant k is 1.380 649 × 10⁻² zJ/K
• the Avogadro constant N_A is 6.022 140 76 × 10² Zmol⁻¹
• the luminous efficacy of monochromatic radiation of frequency 540 THz, K_cd, is 683 lm/W

The derived units hertz (Hz), joule (J), coulomb (C), lumen (lm), and watt (W) are related to the units second (s), metre (m), kilogramme (kg), ampere (A), kelvin (K), mole (mol), and candela (cd), respectively.

• Hz = s^–1
• J = m² kg s^–2
• C = A s
• lm = cd m² m^-2 = cd sr
• W = m² kg s^–3

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IV.1 The base units of the SI

• The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆ν_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.
• 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 when expressed in the unit m/s, where the second is defined in terms of ∆ν_Cs.
• The kilogramme, 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 × 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 ∆ν_Cs.
• The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10^–19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ∆ν_Cs.
• 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^–23 when expressed in the unit J K^–1, which is equal to kg m^–2 s^–2 K^–1, where the kilogramme, metre and second are defined in terms of h, c and ∆ν_Cs.
• The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 10^–23 elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol^–1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
• The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, K_cd, to be 683 when expressed in the unit lm W^–1, which is equal to cd sr W^–1, or cd sr kg^–1 m^–2 s³, where the kilogramme, metre and second are defined in terms of h, c and ∆ν_Cs.

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