# 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

$$a_0$$

$$m$$

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

$$\frac{1}{mol}$$

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

$$m$$

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