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Constants
Math.NET Numerics contains a set of often used mathematical and scientific
constants. Mathematical and defined scientific constants are as accurate as
double precision allows, while measured constants are implemented according
to 2007 CODATA.
All constants are defined as static constant fields of the Constants class.
SI Unit Scaling
| Constant |
Factor |
Constant |
Factor |
| Deca |
$10^{1}$ |
Deci |
$10^{-1}$ |
| Hecto |
$10^{2}$ |
Centi |
$10^{-2}$ |
| Kilo |
$10^{3}$ |
Milli |
$10^{-3}$ |
| Mega |
$10^{6}$ |
Micro |
$10^{-6}$ |
| Giga |
$10^{9}$ |
Nano |
$10^{-9}$ |
| Tera |
$10^{12}$ |
Pico |
$10^{-12}$ |
| Peta |
$10^{15}$ |
Femto |
$10^{-15}$ |
| Exa |
$10^{18}$ |
Atto |
$10^{-18}$ |
| Zetta |
$10^{21}$ |
Zepto |
$10^{-21}$ |
| Yotta |
$10^{24}$ |
Yocto |
$10^{-24}$ |
Mathematical Constants
| Constant |
Definition |
Value (Rounded) |
| E |
$e$ |
2.7182818284590452354 |
| Log2E |
$\log_2{e}$ |
1.4426950408889634074 |
| Log10E |
$\log_{10}{e}$ |
0.4342944819032518277 |
| Ln2 |
$\log_e{2}$ |
0.6931471805599453094 |
| Ln10 |
$\log_e{10}$ |
2.3025850929940456840 |
| LnPi |
$\log_e{\pi}$ |
1.1447298858494001741 |
| Ln2PiOver2 |
$\frac{1}{2}\log_e{2\pi}$ |
0.9189385332046727418 |
| InvE |
$\frac{1}{e}$ |
0.3678794411714423216 |
| SqrtE |
$\sqrt{e}$ |
1.6487212707001281468 |
| Sqrt2 |
$\sqrt{2}$ |
1.4142135623730950488 |
| Sqrt3 |
$\sqrt{3}$ |
1.7320508075688772935 |
| Sqrt1Over2 |
$\sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ |
0.7071067811865475244 |
| HalfSqrt3 |
$\frac{1}{2}\sqrt{3}$ |
0.8660254037844386468 |
| Pi |
$\pi$ |
3.1415926535897932385 |
| Pi2 |
$2\pi$ |
6.2831853071795864769 |
| PiOver2 |
$\frac{1}{2}\pi$ |
1.5707963267948966192 |
| Pi3Over2 |
$\frac{3}{2}\pi$ |
4.7123889803846898577 |
| PiOver4 |
$\frac{1}{4}\pi$ |
0.7853981633974483096 |
| SqrtPi |
$\sqrt{\pi}$ |
1.7724538509055160273 |
| Sqrt2Pi |
$\sqrt{2\pi}$ |
2.5066282746310005024 |
| Sqrt2PiE |
$\sqrt{2\pi e}$ |
4.1327313541224929385 |
| LogSqrt2Pi |
$\log_e{\sqrt{2\pi}} = \frac{1}{2}\log_e{2\pi}$ |
0.9189385332046727418 |
| LogSqrt2PiE |
$\log_e{\sqrt{2\pi e}}$ |
1.4189385332046727418 |
| LogTwoSqrtEOverPi |
$\log_e{2\sqrt{\frac{e}{\pi}}}$ |
0.6207822376352452223 |
| InvPi |
$\frac{1}{\pi}$ |
0.3183098861837906715 |
| TwoInvPi |
$\frac{2}{\pi}$ |
0.6366197723675813431 |
| InvSqrtPi |
$\frac{1}{\sqrt{\pi}}$ |
0.5641895835477562869 |
| InvSqrt2Pi |
$\frac{1}{\sqrt{2\pi}}$ |
0.3989422804014326779 |
| TwoInvSqrtPi |
$\frac{2}{\sqrt{2\pi}}$ |
1.1283791670955125739 |
| TwoSqrtEOverPi |
$2\sqrt{\frac{e}{\pi}}$ |
1.8603827342052657173 |
| Catalan |
$\beta(2) = \sum_{k=0}^{\infty}{\frac{(-1)^k}{(2k+1)^2}}$ |
0.9159655941772190151 |
| EulerMascheroni |
$\gamma = \lim_{n\to\infty} {\sum_{k=1}^n{(\frac{1}{k} - \log_e{n})}}$ |
0.5772156649015328606 |
| GoldenRatio |
$\frac{1+\sqrt{5}}{2}$ |
1.6180339887498948482 |
| Glaisher |
$\exp{(\frac{1}{12} - \zeta{(-1)})}$ |
1.2824271291006226369 |
| Khinchin |
$K_0 = \prod_{k=1}^{\infty}{(1+\frac{1}{k(k+2)})^{\log_2{k}}}$ |
2.6854520010653064453 |
Universal Constants
| Constant |
Symbol |
Unit |
Value |
| SpeedOfLight |
$c_0$ |
$\frac{m}{s}$ |
2.99792458e+8 |
| MagneticPermeability |
$\mu_0$ |
$\frac{N}{A^2}$ = $\frac{kg,m}{A^2s^2}$ |
1.2566370614359172954e-6 |
| ElectricPermittivity |
$\varepsilon_0$ |
$\frac{F}{m}$ = $\frac{A^2s^4}{kg,m^3}$ |
8.8541878171937079245e-12 |
| CharacteristicImpedanceVacuum |
$Z_0$ |
$\Omega = \frac{kg,m^2}{A^2s^3}$ |
376.7303134617706554682 |
| GravitationalConstant |
$G$ |
$\frac{m^3}{kg,s^2}$ |
6.67429e-11 |
| PlancksConstant |
$h$ |
$J,s = \frac{kg,m^2}{s}$ |
6.62606896e-34 |
| DiracsConstant |
$\hbar$ |
$J,s = \frac{kg,m^2}{s}$ |
1.054571629e-34 |
| PlancksMass |
$m_p$ |
$kg$ |
2.17644e-8 |
| PlancksTemperature |
$T_p$ |
$K$ |
1.416786e+32 |
| PlancksLength |
$l_p$ |
$m$ |
1.616253e-35 |
| PlancksTime |
$t_p$ |
$s$ |
5.39124e-44 |
Electromagnetic Constants
| Constant |
Symbol |
Unit |
Value |
| ElementaryCharge |
$e$ |
$C = A,s$ |
1.602176487e-19 |
| MagneticFluxQuantum |
$\Theta_0$ |
$Wb = \frac{kg,m^2}{A,s^2}$ |
2.067833668e-15 |
| ConductanceQuantum |
$G_0$ |
$S = \frac{A^2s^3}{kg,m^2}$ |
7.7480917005e-5 |
| JosephsonConstant |
$K_J$ |
$\frac{Hz}{V}$ |
483597.891e+9 |
| VonKlitzingConstant |
$R_K$ |
$\Omega = \frac{kg,m^2}{A^2s^3}$ |
25812.807557 |
| BohrMagneton |
$\mu_B$ |
$\frac{J}{T}$ |
927.400915e-26 |
| NuclearMagneton |
$\mu_N$ |
$\frac{J}{T}$ |
5.05078324e-27 |
Atomic and Nuclear Constants
| Constant |
Symbol |
Unit |
Value |
| FineStructureConstant |
$\alpha$ |
$1$ |
7.2973525376e-3 |
| RydbergConstant |
$T_{\infty}$ |
$\frac{1}{m}$ |
10973731.568528 |
| BohrRadius |
$a_0$ |
$m$ |
0.52917720859e-10 |
| HartreeEnergy |
$E_h$ |
$J$ |
4.35974394e-18 |
| QuantumOfCirculation |
|
$\frac{m^2}{s}$ |
3.6369475199e-4 |
| FermiCouplingConstant |
|
$\frac{1}{GeV^2}$ |
1.16637e-5 |
| WeakMixingAngle |
|
|
0.22256 |
| Avogadro |
|
$\frac{1}{mol}$ |
6.0221412927e23 |
Electron
| Constant |
Unit |
Value |
| ElectronMass |
$kg$ |
9.10938215e-31 |
| ElectronMassEnergyEquivalent |
$J$ |
8.18710438e-14 |
| ElectronMolarMass |
$\frac{kg}{mol}$ |
5.4857990943e-7 |
| ComptonWavelength |
$m$ |
2.4263102175e-12 |
| ClassicalElectronRadius |
$m$ |
2.8179402894e-15 |
| ThomsonCrossSection |
$m^2$ |
0.6652458558e-28 |
| ElectronMagneticMoment |
$\frac{J}{T}$ |
-928.476377e-26 |
| ElectronGFactor |
|
-2.0023193043622 |
Muon
| Constant |
Unit |
Value |
| MuonMass |
$kg$ |
1.88353130e-28 |
| MuonMassEnegryEquivalent |
$J$ |
1.692833511e-11 |
| MuonMolarMass |
$\frac{kg}{mol}$ |
0.1134289256e-3 |
| MuonComptonWavelength |
$m$ |
11.73444104e-15 |
| MuonMagneticMoment |
$\frac{J}{T}$ |
-4.49044786e-26 |
| MuonGFactor |
|
-2.0023318414 |
Tau
| Constant |
Unit |
Value |
| TauMass |
$kg$ |
3.16777e-27 |
| TauMassEnergyEquivalent |
$J$ |
2.84705e-10 |
| TauMolarMass |
$\frac{kg}{mol}$ |
1.90768e-3 |
| TauComptonWavelength |
$m$ |
0.69772e-15 |
Proton
| Constant |
Unit |
Value |
| ProtonMass |
$kg$ |
1.672621637e-27 |
| ProtonMassEnergyEquivalent |
$J$ |
1.503277359e-10 |
| ProtonMolarMass |
$\frac{kg}{mol}$ |
1.00727646677e-3 |
| ProtonComptonWavelength |
$m$ |
1.3214098446e-15 |
| ProtonMagneticMoment |
$\frac{J}{T}$ |
1.410606662e-26 |
| ShieldedProtonMagneticMoment |
$\frac{J}{T}$ |
1.410570419e-26 |
| ProtonGFactor |
|
5.585694713 |
| ProtonGyromagneticRatio |
$\frac{1}{T,s}$ |
2.675222099e8 |
| ShieldedProtonGyromagneticRatio |
$\frac{1}{T,s}$ |
2.675153362e8 |
Neutron
| Constant |
Unit |
Value |
| NeutronMass |
$kg$ |
1.674927212e-27 |
| NeutronMassEnegryEquivalent |
$J$ |
1.505349506e-10 |
| NeutronMolarMass |
$\frac{kg}{mol}$ |
1.00866491597e-3 |
| NeutronComptonWavelength |
$m$ |
1.3195908951e-1 |
| NeutronMagneticMoment |
$\frac{J}{T}$ |
-0.96623641e-26 |
| NeutronGFactor |
|
-3.82608545 |
| NeutronGyromagneticRatio |
$\frac{1}{T,s}$ |
1.83247185e8 |
Deuteron
| Constant |
Unit |
Value |
| DeuteronMass |
$kg$ |
3.34358320e-27 |
| DeuteronMassEnegryEquivalent |
$J$ |
3.00506272e-10 |
| DeuteronMolarMass |
$\frac{kg}{mol}$ |
2.013553212725e-3 |
| DeuteronMagneticMoment |
$\frac{J}{T}$ |
0.433073465e-26 |
Helion
| Constant |
Unit |
Value |
| HelionMass |
$kg$ |
5.00641192e-27 |
| HelionMassEnegryEquivalent |
$J$ |
4.49953864e-10 |
| HelionMolarMass |
$\frac{kg}{mol}$ |
3.0149322473e-3 |
