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

Physical Constants (CODATA 2022) and SI Units

Previous physical constants   2006   2010   2014   2018  
  Here, a brief summary of physical constants based on   Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor (2024), "The 2022 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 9.0). 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.

Mathematical Constant

π 3.14159265358979323846

Fundamental Physical Constants (2022 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 1.256 637 061 27(20)×10−6 N A−21.6×10−10 vacuum magnetic permeability 4παħ / e2c
ε0 8.854 187 8188(14)×10−12 F m−11.6×10−10 vacuum electric permittivity 1 / μ0c2
me 9.109 383 7139(28)×10−31 kg3.1×10−10 electron mass
α 7.297 352 5643(11)×10−3 –1.6×10−10 fine-structure constant e2 / 4πε0ħc
cR∞ 3.289 841 960 2500(36)×1015 Hz 1.1×10−12 Rydberg frequency α2mec2 / 2h = Eh / 2h
R∞ 10 973 731.568 157(12)
(= 1.097 373 156 8160×107)		 m−1 1.1×10−12 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 1.660 539 068 92(52)×10−27 kg3.1×10−10 atomic mass constant
Mu 1.000 000 001 05(31)×10−3 kg mol−13.1×10−10 molar mass constant
M(12C) 12.000 000 0126(37)×10−3 kg mol−13.1×10−10 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 0657(29)×10−24 J T−13.1×10−10 Bohr magneton eħ / 2me
a0 5.291 772 105 44(82)×10−11 m1.6×10−10 Bohr radius α / 4πR∞
Eh 4.359 744 722 2060(48)×10−18 J1.1×10−12 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