ConstantID

The seven constants that define the SI

On 20 May 2019 the International System of Units stopped resting on artefacts and material properties. Since then, every unit follows from seven constants whose values are fixed exactly. The decision was taken by the 26th General Conference on Weights and Measures in November 2018, using values from the CODATA 2017 special adjustment.

Which defining constants each SI base unit depends on The second depends on the caesium frequency; the metre on c and the caesium frequency; the kilogram on h, c and the caesium frequency; the ampere on e and the caesium frequency; the kelvin on k, h and the caesium frequency; the mole on the Avogadro constant only; the candela on the luminous efficacy, h and the caesium frequency. ΔνCsCaesium frequency cSpeed of light hPlanck constant eElementary charge kBoltzmann constant NAAvogadro constant KcdLuminous efficacy ssecond mmetre kgkilogram Aampere Kkelvin molmole cdcandela Defining constantSI base unit
Each SI base unit (right) and the defining constants it is built from (left). Every unit except the mole depends on the caesium frequency, because each needs the second.

The values

ConstantExact valueDefinesBefore 2019
ΔνCs Caesium frequency9 192 631 770 Hzsecond (s)Defined by the caesium frequency since 1967; only reworded in 2019.
c Speed of light299 792 458 m s−1metre (m)Defined by the speed of light since 1983; only reworded in 2019.
h Planck constant6.626 070 15 × 10−34 J Hz−1kilogram (kg)The mass of the International Prototype of the Kilogram, a platinum–iridium cylinder kept near Paris since 1889.
e Elementary charge1.602 176 634 × 10−19 Campere (A)The current that makes two infinitely long parallel wires 1 m apart attract with 2 × 10⁻⁷ newton per metre (1948).
k Boltzmann constant1.380 649 × 10−23 J K−1kelvin (K)1/273.16 of the thermodynamic temperature of the triple point of water.
NA Avogadro constant6.022 140 76 × 1023 mol−1mole (mol)The amount of substance in 0.012 kilogram of carbon-12 (1971).
Kcd Luminous efficacy683 lm W−1candela (cd)Defined by the 683 lm/W luminous efficacy since 1979; only reworded in 2019.

Why change

The kilogram was the last unit defined by an object. Comparisons with its official copies drifted by about 50 micrograms over a century, and nobody could say whether the copies or the prototype had changed. Any unit that depended on the kilogram, such as the ampere, the mole and the candela, inherited the problem. Fixing the Planck constant makes the kilogram reproducible anywhere with a Kibble balance or by counting atoms in a silicon sphere.

The electrical units had a second problem: since 1990 practical metrology had used conventional values of the Josephson and von Klitzing constants that were slightly inconsistent with the SI. Fixing e and h made the quantum standards exact SI realisations and ended the split. See volt-90 and ohm-90 for the size of the old offsets.

What became exact

34 CODATA values were measured in 2014 or earlier and are exact now, because they are built only from the fixed constants:

Units exact ℏ Atomic unit of action 1.054 571 817… × 10−34 J s Units exact e Atomic unit of charge 1.602 176 634 × 10−19 C Physico-chemical exact NA Avogadro constant 6.022 140 76 × 1023 mol−1 Physico-chemical exact k Boltzmann constant 1.380 649 × 10−23 J K−1 Physico-chemical exact k Boltzmann constant in eV/K 8.617 333 262… × 10−5 eV K−1 Physico-chemical exact k/h Boltzmann constant in Hz/K 2.083 661 912… × 1010 Hz K−1 Physico-chemical exact k/hc Boltzmann constant in inverse meter per kelvin 69.503 480 04… m−1 K−1 Electromagnetic exact G0 Conductance quantum 7.748 091 729… × 10−5 S Units exact eV Electron volt 1.602 176 634 × 10−19 J Electromagnetic exact e Elementary charge 1.602 176 634 × 10−19 C Physico-chemical exact F Faraday constant 96 485.332 12… C mol−1 Physico-chemical exact c1 First radiation constant 3.741 771 852… × 10−16 W m2 Physico-chemical exact c1L First radiation constant for spectral radiance 1.191 042 972… × 10−16 W m2 sr−1 Electromagnetic exact G0−1 Inverse of conductance quantum 12 906.403 72… Ω Electromagnetic exact KJ Josephson constant 483 597.8484… × 109 Hz V−1 Physico-chemical exact n0 Loschmidt constant (273.15 K, 100 kPa) 2.651 645 804… × 1025 m−3 Physico-chemical exact n0 Loschmidt constant 2.686 780 111… × 1025 m−3 Electromagnetic exact Φ0 Flux quantum 2.067 833 848… × 10−15 Wb Physico-chemical exact R Gas constant 8.314 462 618… J mol−1 K−1 Physico-chemical exact NAh Molar Planck constant 3.990 312 712… × 10−10 J Hz−1 mol−1 Physico-chemical exact Vm Molar volume of ideal gas (273.15 K, 100 kPa) 22.710 954 64… × 10−3 m3 mol−1 Physico-chemical exact Vm Molar volume of ideal gas 22.413 969 54… × 10−3 m3 mol−1 Units exact ℏ Natural unit of action 1.054 571 817… × 10−34 J s Units exact ℏ Natural unit of action in eV s 6.582 119 569… × 10−16 eV s

…and 10 more, including most of the energy equivalents.

What became measured

Fixing the elementary charge and the Planck constant had a price: some quantities that used to be exact by definition must now be measured. The main ones are the magnetic and electric constants, whose uncertainty is now that of the fine-structure constant, and the molar mass of carbon-12.

Units e2/a0Eh Atomic unit of permittivity 1.112 650 056 20(17) × 10−10 F m−1 Universal Z0 Impedance of free space 376.730 313 412(59) Ω Physico-chemical Mu Molar mass constant 1.000 000 001 05(31) × 10−3 kg mol−1 Physico-chemical M(12C) Molar mass of carbon-12 12.000 000 0126(37) × 10−3 kg mol−1 Universal ε0 Electric constant 8.854 187 8188(14) × 10−12 F m−1 Universal μ0 Magnetic constant 1.256 637 061 27(20) × 10−6 N A−2

Lists computed by comparing NIST's files: a value counts as “became exact” if it was listed with an uncertainty in any adjustment up to 2014 and as exact in 2022.