List of all important Physics Constants

Here you find all important constants of modern physics together with their relative standard uncertainty. All constants are given in SI-Units.

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Table of universal constants

Quantity Symbol Value Relative Error
speed of light in vacuum `c` 299 792 458 m·s−1 by definition exact
Newtonian constant of gravitation `G` 6.67384(80)×10−11 m3·kg−1·s−2 1.2 × 10−4
Planck constant `h` 6.626 069 57(29) × 10−34 J·s 4.4 × 10−8
Newtonian constant of gravitation ` h bar = h//(2pi)` 6.67384(80)×10−11 m3·kg−1·s−2 1.2 × 10−4

Table of electromagnetic constants

Quantity Symbol Value Relative Error
magnetic constant (vacuum permeability) μ0 4π × 10−7 N·A−2 = 1.256 637 061... × 10−6 N·A−2 by definition exact
magnetic constant (vacuum permeability) `varepsilon_0=1//mu_0c^2` 8.854 187 817... × 10−12 F·m−1 by definition exact
characteristic impedance of vacuum `Z_0=mu_0c` 8.854 187 817... × 10−12 F·m−1 by definition exact
characteristic impedance of vacuum `Z_0=mu_0c` 376.730 313 461... Ω by definition exact
Coulomb`s constant `k_e=1//4pivarepsilon_0` 8.987 551 787... × 109 N·m2·C−2 by definition exact
elementary charge `e` 1.602 176 565(35) × 10−19 C 2.2 × 10−8
Bohr magneton `mu_B=ebar h//2m_e` 9.274 009 68(20) × 10−24 J·T−1 2.2 × 10−8
vconductance quantum `G_0=2e^2//h` 7.748 091 7346(25) × 10−5 S 3.2 × 10−10
inverse conductance quantum `G_0^(-1) =h//2e^2` 12 906.403 7217(42) Ω 3.2 × 10−10
Josephson constant `K_J =2e//h` 4.835 978 70(11) × 1014 Hz·V−1 2.2 × 10−8
magnetic flux quantum `phi_0h//2e` 4.835 978 70(11) × 1014 Hz·V−1 2.2 × 10−8
nuclear magneton `mu_N=ebarh//2m_p` 5.050 783 53(11) × 10−27 J·T−1 2.2 × 10−8
von Klitzing constant `R_K=h//e^2` 25 812.807 4434(84) Ω 3.2 × 10−10

Table of atomic and nuclear constants

Quantity Symbol Value Relative Error
Bohr radius ` a_0=alpha//4piR_oo` 5.291 772 1092(17) × 10−11 m 3.2 × 10−9
classical electron radius `r_e=e^2//4pivarepsilon_0m_ec^2` 2.817 940 3267(27) × 10−15 m 9.7 × 10−10
electron mass `m_e` 9.109 382 91(40) × 10−31 kg 4.4 × 10−8
Fermi coupling constant `G_F//(barhc)^3` 1.166 364(5) × 10−5GeV−2 4.3 × 10−6
fine-structure constant `alpha=mu_0e^2 c//2h=e^2//4pivarepsilon_0barhc` 7.297 352 5698(24) × 10−3 3.2 × 10−10
Hartree energy `E_h=2R_oohc` 4.359 744 34(19) × 10−18 J 4.4 × 10−8
proton mass `m_P` 1.672 621 777(74) × 10−27 kg 4.4 × 10−8
quantum of circulation `h//2m_e` 3.636 947 5520(24) × 10−4 m2 s−1 6.5 × 10−10
Rydberg constant `R_oo=alpha^2m_ec//2h` 10 973 731.568 539(55) m−1 5.0 × 10−12
Thomson cross section `(8pi//3)r_e^2` 6.652 458 734(13) × 10−29 m2 1.9 × 10−9
weak mixing angle `sin^2 thetaw=1-(m_w//m_z)^2` 0.2223(21) 9.5 × 10−3
Efimov factor 22.7 9.5 × 10−3

Table of physico-chemical constants

Quantity Symbol Value Relative Error
Atomic mass constant `m_u=1 u` 1.660 538 921(73) × 10−27 kg 4.4 × 10−8
Avogadro`s number `N_A,L` 6.022 141 29(27) × 1023 mol−1 4.4 × 10−8
Boltzmann constant `k=k_B=R//N_A` 1.380 6488(13) × 10−23 J·K−1 9.1 × 10−7
Faraday constant `F=N_Ae` 96 485.3365(21)C·mol−1 2.2 × 10−8
first radiation constant c_1=2pi=hc^2 3.741 771 53(17) × 10−16W·m2 4.4 × 10−8
c_(1L)=c_1//pi 1.191 042 869(53) × 10−16 W·m2·sr−1 4.4 × 10−8
Loschmidt constant `n_0=N_A//V_m` 2.686 7805(24) × 1025 m−3 9.1 × 10−7
gas Constant `R` 8.314 4621(75) J·K−1·mol−1 9.1 × 10−7
molar Planck constant `N_Ah` 3.990 312 7176(28) × 10−10 J·s·mol−1 7.0 × 10−10
molar volume of an ideal gas V_m=RT//p 2.271 0953(21) × 10−2 m3·mol−1 9.1 × 10−7
2.241 3968(20) × 10−2 m3·mol−1 9.1 × 10−7
Sackur-Tetrode constant S_0//R=(5)/(2)+In[(2pim_ukT//h^2)^(3//2) kT//p] −1.151 7078(23) 2.0 × 10−6
−1.164 8708(23) 1.9 × 10−6
second radiation constant `c_2=hc//k` 1.438 7770(13) × 10−2 m·K 9.1 × 10−6
Wien displacement law constant `b=hck^(-1)//4.965 114231...` 2.897 7721(26) × 10−3 m·K 9.1 × 10−7

Table of adopted values

Quantity Symbol Value Relative Error
conventional value of Josephson constant `K_J-90` 24.835 979 × 1014 Hz·V−1 by definition exact
conventional value of von Klitzing constant `R_k-90` 25 812.807 Ω by definition exact
molar mass `M_u = M^((12_C))//12` 1 × 10−3kg·mol−1 by definition exact
`M^((12_C))=N_Am^((12_C))` 1.2 × 10−2 kg·mol−1
standard acceleration of gravity (gee, free-fall on Earth) `gn` 9.806 65 m·s−2 by definition exact
standard atmosphere `atm` 101 325 Pa by definition exact

Base Planck units

Name Dimension Expression Value (given in SI Units)
Planck length Length (L) `l_P = sqrt((barhG)/(C^3))` 1.616 199(97) × 10−35m
Planck mass Mass (M) `m_P=sqrt((barhc)/(G))` 2.176 51(13) × 10−8 kg
Planck time Time (T) `t_P=(lp)/(c)=(barh)/(m_pc^2)=sqrt((barhG)/(c^5))` 5.391 06(32) × 10−44 s
Planck charge Electric charge (Q) `q_P=sqrt(4pivarepsilon_0barhc)` 1.875 545 956(41) × 10−18 C
Planck temperature Temperature (Θ `T_p=(m_pc^2)/(k_B)=sqrt((barhc^5)/(Gk_B^2)` 1.416 833(85) × 1032 K