Physical Constants & Units Conversion
A. Miyoshi
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Physical Constants & Units Conversion

Physical Constants (CODATA 2018) and SI Units

Previous physical constants   2006   2010   2014  
  Here, a brief summary of physical constants based on   Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor (2019), "The 2018 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 8.0). Database developed by J. Baker, M. Douma, and S. Kotochigova. Available at http://physics.nist.gov/constants, National Institute of Standards and Technology, Gaithersburg, MD 20899.   is shown. For detail, see, Fundamental Physical Constants from NIST.
  Due to the redefinition of the SI base units effective after May 29, 2019, the definition structure of the units and physical constants has been changed largely.   In addition to the speed of light in vacuum, Planck constant, elementary charge, Boltzmann constant, and Avogadro constants are now the defined values.   Because the Avogadro constant has become a constant defining the unit "mol" for amount of substance, the molar mass of carbon-12 is no longer "exactly 12 g", but it is a measured value (~11.999 999 9958 g).

Mathematical Constant

π 3.14159265358979323846

Fundamental Physical Constants (2018 CODATA)

Symbol Value UnitRel. std.
uncert.		 Quantity
c 299 792 458  (= 2.997 924 58×108) m s−1exact speed of light in vacuum
G 6.674 30(15)×10−11 m3 kg−1 s−2 2.2×10−5 Newtonian constant of gravitation
h 6.626 070 15×10−34 J Hz−1exact Planck constant
e 1.602 176 634×10−19 Cexact elementary charge
μ0 1.256 637 062 12×10−6 N A−21.5×10−10 vacuum magnetic permeability 4παħ / e2c
ε0 8.854 187 8128(13)×10−12 F m−11.5×10−10 vacuum electric permittivity 1 / μ0c2
me 9.109 383 7015(28)×10−31 kg3.0×10−10 electron mass
α 7.297 352 5693(11)×10−3 –1.5×10−10 fine-structure constant e2 / 4πε0ħc
cR∞ 3.289 841 960 2508(64)×1015 Hz 1.9×10−12 Rydberg frequency α2mec2 / 2h = Eh / 2h
R∞ 10 973 731.568 160(21)
(= 1.097 373 156 8160×107)		 m−1 1.9×10−12 Rydberg constant α2mec / 2h
k 1.380 649×10−23 J K−1exact Boltzmann constant
NA 6.022 140 76×1023 mol−1exact Avogadro constant
mu 1.660 539 066 60(50)×10−27 kg3.0×10−10 atomic mass constant
Mu 0.999 999 999 65(30)×10−3 kg mol−13.0×10−10 molar mass constant
M(12C) 11.999 999 9958(36)×10−3 kg mol−13.0×10−10 molar mass of carbon-12

Physical Constants

- derived from fundamental mathematical / physical constants

Symbol Value UnitRel. std.
uncert.		 Quantity
ħ ~ 1.054 571 818×10−34 J sexact h / 2π
R ~ 8.314 462 618 J K−1 mol−1 exact molar gas constant NA k
F ~ 96 485.332 12  (= 9.648 533 212×104) C mol−1exact Faraday constant NA e
μB 9.274 010 0784(28)×10−24 J T−13.0×10−10 Bohr magneton eħ / 2me
a0 5.291 772 109 02(80)×10−11 m1.5×10−10 Bohr radius α / 4πR∞
Eh 4.359 744 722 2071(85)×10−18 J1.9×10−12 Hartree energy 2hcR∞

Conversion of Units

SI Derived Units with Special Names

Derived QuatitySymbol Expression
in terms of
other SI units		 Expression
in terms of
SI base units
electric chargeC A s
electric potentialV J C−1m2 kg s−3 A−1
electric capacitanceF C V−1m−2 kg−1 s4 A2
Celsius temperature °C θ / °C + 273.15 ≡ T / K

Standard Values / Non-SI Units

Quantity
standard acceleration of gravity9.806 65 m s−2
pressure 1 bar ≡ 105 Pa
1 atm ≡ 101 325 Pa
1 Torr ≡ 1 / 760 atm ~ 133.322 3684 Pa
energy1 cal ≡ 4.184 J
cross section1 b (barn) ≡ 1 × 10−28 m2