Constants

Each constant is accessed as a function from Microsoft SQL Server.  To access Euler-Mascheroni Constant use the dbo.EulerMascheroni() function.  When constants already exist in MS SQL Server, such as PI(), testing has shown SQL Server functions to be faster.

Mathematical Constants

Constant Description
E The number e
Log2E The number log[2](e) 
Log10E The number log[10](e)
Ln2 The number log[e](2)
Ln10 The number log[e](10)
LnPi The number log[e](pi)
Ln2PiOver2 The number log[e](2*pi)/2
InvE The number 1/e
SqrtE The number sqrt(e)
Sqrt2 The number sqrt(2)
Sqrt1Over2 The number sqrt(1/2) = 1/sqrt(2) = sqrt(2)/2
HalfSqrt3 The number sqrt(3)/2
Pi The number pi
Pi2 The number 2*pi
OneOverPi The number 1/pi
PiOver2 The number pi/2
PiOver4 The number pi/4
SqrtPi The number sqrt(pi)
Sqrt2Pi The number sqrt(2pi)
Sqrt2PiE The number sqrt(2*pi*e)
LogSqrt2Pi The number log(sqrt(2*pi))
LogSqrt2PiE The number log(sqrt(2*pi*e))
LogTwoSqrtEOverPi The number log(2 * sqrt(e / pi))
InvPi The number 1/pi
TwoInvPi The number 2/pi
InvSqrtPi The number 1/sqrt(pi)
InvSqrt2Pi The number 1/sqrt(2pi)
TwoInvSqrtPi The number 2/sqrt(pi)
TwoSqrtEOverPi The number 2 * sqrt(e / pi)
Degree The number (pi)/180 - factor to convert from Degree (deg) to Radians (rad).
Grad The number (pi)/200 - factor to convert from NewGrad (grad) to Radians (rad).
PowerDecibel The number ln(10)/20 - factor to convert from Power Decibel (dB) to Neper (Np). Use this version when the Decibel represent a power gain but the compared values are not powers (e.g. amplitude, current, voltage).
NeutralDecibel The number ln(10)/10 - factor to convert from Neutral Decibel (dB) to Neper (Np). Use this version when either both or neither of the Decibel and the compared values represent powers.
Catalan The Catalan constant: Sum(k=0 -> inf){ (-1)^k/(2*k + 1)2 }
EulerMascheroni The Euler-Mascheroni constant: lim(n -> inf){ Sum(k=1 -> n) { 1/k - log(n) } }
GoldenRatio The number (1+sqrt(5))/2, also known as the golden ratio
Glaisher The Glaisher constant: e^(1/12 - Zeta(-1))
Khinchin The Khinchin constant: prod(k=1 -> inf){1+1/(k*(k+2))^log(k,2)}
SizeOfDouble The size of a double in bytes. Not a SqlDouble but a double for the SQL Server processor.
SizeOfInt The size of an int in bytes. Not a SqlInt32/SqlInt64 but an int for the SQL Server processor.
SizeOfFloat The size of a float in bytes. Not a SqlFloat but a float for the SQL Server processor.
SizeOfComplex The size of a complex number based on two int's.
SizeOfComplex32 The size of a complex number based on two 32 bit int's.

 

Universal Constants

Constant Description
SpeedOfLight Speed of Light in Vacuum: c_0 = 2.99792458e8 [m s^-1] (defined, exact; 2007 CODATA)
MagneticPermeability Magnetic Permeability in Vacuum: mu_0 = 4*Pi * 10^-7 [N A^-2 = kg m A^-2 s^-2] (defined, exact; 2007 CODATA)
ElectricPermittivity Electric Permittivity in Vacuum: epsilon_0 = 1/(mu_0*c_0^2) [F m^-1 = A^2 s^4 kg^-1 m^-3] (defined, exact; 2007 CODATA)
CharacteristicImpedanceVacuum Characteristic Impedance of Vacuum: Z_0 = mu_0*c_0 [Ohm = m^2 kg s^-3 A^-2] (defined, exact; 2007 CODATA)
GravitationalConstant Newtonian Constant of Gravitation: G = 6.67429e-11 [m^3 kg^-1 s^-2] (2007 CODATA)
PlancksConstant Planck's constant: h = 6.62606896e-34 [J s = m^2 kg s^-1] (2007 CODATA)
DiracsConstant Reduced Planck's constant: h_bar = h / (2*Pi) [J s = m^2 kg s^-1] (2007 CODATA)
PlancksMass Planck mass: m_p = (h_bar*c_0/G)^(1/2) [kg] (2007 CODATA)
PlancksTemperature Planck temperature: T_p = (h_bar*c_0^5/G)^(1/2)/k [K] (2007 CODATA)
PlancksLength Planck length: l_p = h_bar/(m_p*c_0) [m] (2007 CODATA)
PlancksTime Planck time: t_p = l_p/c_0 [s] (2007 CODATA)

 

Electromagnetic Constants

Constant Description
ElementaryCharge Elementary Electron Charge: e = 1.602176487e-19 [C = A s] (2007 CODATA)
MagneticFluxQuantum Magnetic Flux Quantum: theta_0 = h/(2*e) [Wb = m^2 kg s^-2 A^-1] (2007 CODATA)
ConductanceQuantum Conductance Quantum: G_0 = 2*e^2/h [S = m^-2 kg^-1 s^3 A^2] (2007 CODATA)
JosephsonConstant Josephson Constant: K_J = 2*e/h [Hz V^-1] (2007 CODATA)
VonKlitzingConstant Von Klitzing Constant: R_K = h/e^2 [Ohm = m^2 kg s^-3 A^-2] (2007 CODATA)
BohrMagneton Bohr Magneton: mu_B = e*h_bar/2*m_e [J T^-1] (2007 CODATA)
NuclearMagneton Nuclear Magneton: mu_N = e*h_bar/2*m_p [J T^-1] (2007 CODATA)

 

Atomic and Nuclear Constants

Constant Description 
FineStructureConstant Fine Structure Constant: alpha = e^2/4*Pi*e_0*h_bar*c_0 [1] (2007 CODATA)
RydbergConstant Rydberg Constant: R_infty = alpha^2*m_e*c_0/2*h [m^-1] (2007 CODATA)
BohrRadius Bor Radius: a_0 = alpha/4*Pi*R_infty [m] (2007 CODATA)
HartreeEnergy Hartree Energy: E_h = 2*R_infty*h*c_0 [J] (2007 CODATA)
QuantumOfCirculation Quantum of Circulation: h/2*m_e [m^2 s^-1] (2007 CODATA)
FermiCouplingConstant Fermi Coupling Constant: G_F/(h_bar*c_0)^3 [GeV^-2] (2007 CODATA)
WeakMixingAngle Weak Mixin Angle: sin^2(theta_W) [1] (2007 CODATA)
ElectronMass Electron Mass: [kg] (2007 CODATA)
ElectronMassEnergyEquivalent Electron Mass Energy Equivalent: [J] (2007 CODATA)
ElectronMolarMass Electron Molar Mass: [kg mol^-1] (2007 CODATA)
ComptonWavelength Electron Compton Wavelength: [m] (2007 CODATA)
ClassicalElectronRadius Classical Electron Radius: [m] (2007 CODATA)
ThomsonCrossSection Tomson Cross Section: [m^2] (2002 CODATA)
ElectronMagneticMoment Electron Magnetic Moment: [J T^-1] (2007 CODATA)
ElectronGFactor Electon G-Factor: [1] (2007 CODATA)
MuonMass  Muon Mass: [kg] (2007 CODATA)
MuonMassEnegryEquivalent Muon Mass Energy Equivalent: [J] (2007 CODATA)
MuonMolarMass Muon Molar Mass: [kg mol^-1] (2007 CODATA)
MuonComptonWavelength Muon Compton Wavelength: [m] (2007 CODATA)
MuonMagneticMoment Muon Magnetic Moment: [J T^-1] (2007 CODATA)
MuonGFactor  Muon G-Factor: [1] (2007 CODATA)
TauMass Tau Mass: [kg] (2007 CODATA)
TauMassEnergyEquivalent Tau Mass Energy Equivalent: [J] (2007 CODATA)
TauMolarMass Tau Molar Mass: [kg mol^-1] (2007 CODATA)
TauComptonWavelength Tau Compton Wavelength: [m] (2007 CODATA)
ProtonMass Proton Mass: [kg] (2007 CODATA)
ProtonMassEnergyEquivalent Proton Mass Energy Equivalent: [J] (2007 CODATA)
ProtonMolarMass Proton Molar Mass: [kg mol^-1] (2007 CODATA)
ProtonComptonWavelength Proton Compton Wavelength: [m] (2007 CODATA)
ProtonMagneticMoment Proton Magnetic Moment: [J T^-1] (2007 CODATA)
ProtonGFactor Proton G-Factor: [1] (2007 CODATA)
ShieldedProtonMagneticMoment Proton Shielded Magnetic Moment: [J T^-1] (2007 CODATA)
ProtonGyromagneticRatio Proton Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)
ShieldedProtonGyromagneticRatio Proton Shielded Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)
NeutronMass Neutron Mass: [kg] (2007 CODATA)
NeutronMassEnegryEquivalent Neutron Mass Energy Equivalent: [J] (2007 CODATA)
NeutronMolarMass Neutron Molar Mass: [kg mol^-1] (2007 CODATA)
NeutronComptonWavelength Neuron Compton Wavelength: [m] (2007 CODATA)
NeutronMagneticMoment Neutron Magnetic Moment: [J T^-1] (2007 CODATA)
NeutronGFactor Neutron G-Factor: [1] (2007 CODATA)
NeutronGyromagneticRatio Neutron Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)
DeuteronMass Deuteron Mass: [kg] (2007 CODATA)
DeuteronMassEnegryEquivalent Deuteron Mass Energy Equivalent: [J] (2007 CODATA)
DeuteronMolarMass Deuteron Molar Mass: [kg mol^-1] (2007 CODATA)
DeuteronMagneticMoment Deuteron Magnetic Moment: [J T^-1] (2007 CODATA)
HelionMass Helion Mass: [kg] (2007 CODATA)
HelionMassEnegryEquivalent Helion Mass Energy Equivalent: [J] (2007 CODATA)
HelionMolarMass Helion Molar Mass: [kg mol^-1] (2007 CODATA)

 

Standard International Prefixes

Constant Description
Yotta The SI prefix factor corresponding to 1 000 000 000 000 000 000 000 000
Zetta The SI prefix factor corresponding to 1 000 000 000 000 000 000 000
Exa The SI prefix factor corresponding to 1 000 000 000 000 000 000
Peta The SI prefix factor corresponding to 1 000 000 000 000 000
Tera The SI prefix factor corresponding to 1 000 000 000 000
Giga The SI prefix factor corresponding to 1 000 000 000
Mega The SI prefix factor corresponding to 1 000 000
Kilo The SI prefix factor corresponding to 1 000
Hecto The SI prefix factor corresponding to 100
Deca The SI prefix factor corresponding to 10
Deci The SI prefix factor corresponding to 0.1
Centi The SI prefix factor corresponding to 0.01
Milli The SI prefix factor corresponding to 0.001
Micro The SI prefix factor corresponding to 0.000 001
Nano The SI prefix factor corresponding to 0.000 000 001
Pico The SI prefix factor corresponding to 0.000 000 000 001
Femto The SI prefix factor corresponding to 0.000 000 000 000 001
Atto The SI prefix factor corresponding to 0.000 000 000 000 000 001
Zepto The SI prefix factor corresponding to 0.000 000 000 000 000 000 001
Yocto The SI prefix factor corresponding to 0.000 000 000 000 000 000 000 001

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