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.
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 |
\(10^{-24}\) |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
Constant |
Unit |
Value |
|---|---|---|
HelionMass |
\(kg\) |
5.00641192e-27 |
HelionMassEnegryEquivalent |
\(J\) |
4.49953864e-10 |
HelionMolarMass |
\(\frac{kg}{mol}\) |
3.0149322473e-3 |