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Base units

The SI base units:

Base quantity
Base unit
Name Typical symbol Name Symbol
time t second s
length l, x, r, etc. metre m
mass m kilogram kg
electric current I, i ampere A
thermodynamic temperature T kelvin K
amount of substance n mole mol
luminous intensity Iv candela cd

Definitions

Starting from the definition of the SI in terms of fixed numerical values of the defining constants, definitions of each of the seven base units are deduced by using, as appropriate, one or more of these defining constants to give the following set of definitions:

The second

    The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency DeltanuCs, 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 definition implies the exact relation DeltanuCs = 9 192 631 770 Hz. Inverting this relation gives an expression for the unit second in terms of the defining constant DeltanuCs:

    or

    The effect of this definition is that the second is equal 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 133Cs atom.

The metre

    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–1, where the second is defined in terms of the caesium frequency DeltanuCs.

    This definition implies the exact relation c = 299 792 458 m s–1. Inverting this relation gives an exact expression for the metre in terms of the defining constants c and DeltanuCs:

    The effect of this definition is that one metre is the length of the path travelled by light in vacuum during a time interval with duration of 1/299 792 458 of a second.

The kilogram

    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 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 DeltanuCs.

    This definition implies the exact relation h = 6.626 070 15 x 10–34 kg m2 s–1. Inverting this relation gives an exact expression for the kilogram in terms of the three defining constants h, DeltanuCs and c:

    which is equal to

    The effect of this definition is to define the unit kg m2 s–1 (the unit of both the physical quantities action and angular momentum). Together with the definitions of the second and the metre this leads to a definition of the unit of mass expressed in terms of the Planck constant h.

The ampere

    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 x 10–19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of DeltanuCs.

    This definition implies the exact relation e = 1.602 176 634 x 10–19 A s. Inverting this relation gives an exact expression for the unit ampere in terms of the defining constants e and DeltanuCs:

    which is equal to

    The effect of this definition is that one ampere is the electric current corresponding to the flow of 1/(1.602 176 634 x 10–19) elementary charges per second.

The kelvin

    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 x 10–23 when expressed in the unit J K–1, which is equal to kg m2 s–2 K–1, where the kilogram, metre and second are defined in terms of h, c and DeltanuCs.

    This definition implies the exact relation k = 1.380 649 x 10–23 kg m2 s–2 K–1. Inverting this relation gives an exact expression for the kelvin in terms of the defining constants k, h and DeltanuCs:

    which is equal to

    The effect of this definition is that one kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy k T by 1.380 649 x 10–23 J.

The mole

    The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 x 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, 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.

    This definition implies the exact relation NA = 6.022 140 76 x 1023 mol–1. Inverting this relation gives an exact expression for the mole in terms of the defining constant NA:

    The effect of this definition is that the mole is the amount of substance of a system that contains 6.022 140 76 x 1023 specified elementary entities.

The candela

    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 x 1012 Hz, Kcd, 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 kilogram, metre and second are defined in terms of h, c and DeltanuCs.

    This definition implies the exact relation Kcd = 683 cd sr kg–1 m–2 s3 for monochromatic radiation of frequency nu = 540 x 1012 Hz. Inverting this relation gives an exact expression for the candela in terms of the defining constants Kcd, h and DeltanuCs:

    which is equal to

    The effect of this definition is that one candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 Hz and has a radiant intensity in that direction of (1/683) W/sr.

All other SI units can be derived from these, by multiplying together different powers of the base units.