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MathPhysicalConstants is a Julia package which has the values of a range of mathematical and physical constants updated with most recent available dataset from BIPM in 2018. Currently MKS and CGS units and International System of Units. Updated CODATA 2017 and redefinition of SI base units following ISU, BIPM, CGPM, CIPM approved resolutions and scheduled to come into force on 20 May 2019. See


The package can be installed directly from its github repository:



Usage is pretty straightforward. Start off by loading the package.

julia> using MathPhysicalConstants

Query and retrieve the Planck Constant using the most updated International System of Units (SI)

julia> MathPhysicalConstants.SI.PlanckConstantH

julia> big(MathPhysicalConstants.SI.PlanckConstantH)

Let’s have a look at ƛe ≡ ħ/m_e.c the reduced Compton electron wavelength radius formula. Try it with BigFloat and Measurement

julia> big(MathPhysicalConstants.SI.PlanckConstantHbar)/(big(MathPhysicalConstants.SI.MassElectron)*big(MathPhysicalConstants.SI.SpeedOfLight))

Now let’s have a look at determined with the following equation: R_H = 2ħ^2/(G.m_e.m_p.m_n) as described in

julia> R3mn=(2*SI.PlanckConstantHbar^2)/(SI.SanchezGravitationalConstant*SI.MassElectron*SI.MassProton*SI.MassNeutron)

One converts the result in Gly with SI.GigaLightYear:

julia> 1.3056254088279212e26/SI.GigaLightYear

Other examples of MathPhysicalConstants Let’s switch to Earth’s gravitational acceleration in MKS units.

julia> MathPhysicalConstants.MKS.GravAccel

Or in CGS units.

julia> MathPhysicalConstants.CGS.GravAccel

last but not least in International System of Units (SI)

julia> MathPhysicalConstants.SI.GravAccel

SI Constant List

Symbol Name Formula Dimension Value Unit
π pi - - 3.1415926535897932 pure number
e Euler's number - - 2.7182817284590452 pure number
γ euler_gamma - - 0.5772156649015329 pure number
TSSGP 26 sporadic group Product exp(841.2869278) - 2.3241836455143e365 pure number
HFP Happy Family product exp(674.5210288) - 8.7249055755086e292 pure number
O_M Monster Group Cardinal - - 8.080174248 × 10^53 pure number
O_B Baby Monster Group Cardinal - - 4.15478148 × 10^33 pure number
c Speed of light in vacuum - - 2.99792458e8 m.s^-1
ħ Reduced Planck constant $\hbar=h/2\pi$ - 1.054571800e-34 m^2 kg s^-1
G' constant of gravitation CODATA2019 - M^-1L^3T^-2 6.67408(31)e-11 m^3 kg^-1 s^-2
G F.M.Sanchez constant of gravitation $F_{gr}=Gmm’/ d^{2}$ M^-1L^3T^-2 6.675453818e-11 m^3 kg^-1 s^-2
a Electric constant $F_{qq}=\hbarc/ad^{2}$ dimensionless 137.035999139^-1 pure number
R_U Universe Hubble radius (F.M.Sanchez) $R_U=2G.M_{U}/c)^{2}$ L 1.3065e26 m
G_F Fermi Coupling Constant(F.M.Sanchez) $G_F=(ħc)^3/E_{F}^{2}$ ML^5T^-2 1.4358509(7)e-62 J.m^3
a_G Gravit Sanchez Coupling Constant $a_G=ħc/Gm_pm_H$ - 1.691936465e38 pure number
M_U Universe Sanchez Mass $M_U=(ħc/G)^2/m_e.m_p.m_H$ M 8.7936e52 kg
t_cc Kotov Cosmic Periodicity - s 9600.061(2) s
r_H(0) Bare Hydrogen radius $a\hbar/m_{e}c$ L 5.291772103e-11 m
H Hydrogen-electron mass ratio $m_H/m_e$ dimensionless 1837.152645 m_e
p Proton-electron mass ratio $m_p/m_e$ dimensionless 1836.152672 m_e
n Neutron-electron mass ratio $m_n/m_e$ dimensionless 1838.683659 m_e
m_e electron mass - M 9.10938356(11)e-31 kg
μ' Muon electron mass ratio CODATA2019 - dimensionless 206.7682826(41) m_e
μ Muon mass F.M.Sanchez - dimensionless 206.7682869 m_e
f' Strg Nuc Coupling Constant CODATA2019 - dimensionless 1/0.1181(11) pure number
f Strg Nuc Coupling Constant C.Bizouard $F^{2}/2\pi(pH)^{3}/2$ dimensionless 8.434502892 pure number
F' Fermi Constant reduced mass CODAT2019 $E_{F}/m_{e}c^{2}$ dimensionless 573007.33(25) pure number
F Fermi Constant reduc mass F.M.Sanchez - dimensionless 573007.3652 pure number
d_e electron magnetic moment excess - dimensionless 1.00115965218091(26) pure number
θ' CMB Temperature CODATA2019 - - 2.7255(6) K K
θ CMB Temperature F.M.Sanchez - - 2.725820831 K K
k_B Boltzman Energy-temperature Convers° - - 1.3806488e10-23 J K^-1
W Intermed vector boson Red. Mass - dimensionless 157298(23) pure number
W_s In vector boson Red. Mass F.M.Sanchez - dimensionless 157340 pure number
Z Intermediate vector boson Red. Mass - dimensionless 178450.0(41) pure number
Z_s In vector boson Red. Mass F.M.Sanchez - dimensionless 178452 pure number
Π± Pion / Pi Meson Reduced Mass - dimensionless 273.13203(68) pure number
Π0 Pion / Pi Meson Reduced Mass - dimensionless 264.1426(18) pure number


The MathPhysicalConstants.jl package is licensed under the MIT “Expat” License. The original author is La Guer.

Please, cite this paper ( if you employ this package in your research work.