COMSOL 6.4 - Physical Constants

Physical constants are fundamental, universal constants that represent physical quantities. COMSOL Multiphysics includes the most widely used physical constants as built-in constants. Table 5-8 lists all supported physical constants with their names, symbol (variable name), value, and SI unit. The values are taken from Ref. 1 and include the SI unit. Constants marked by an asterisk (*) are exact by definition, although the numerical values listed for some of these are rounded since they are derived from other constants (for example hbar_const = h_const/2π).

Table 5-8: Physical Constants.
Name	Symbol	Value
Acceleration of gravity	g_const	9.80665[m/s^2]
Avogadro constant*	N_A_const	6.02214076e23[1/mol]
Bohr radius	a0_const	4piepsilon0_consthbar_const^2/(me_conste_const^2) (m) (5.2917721054432e-11[m])
Boltzmann constant*	k_B_const	1.380649e-23[J/K]
Characteristic impedance of vacuum (impedance of free space)	Z0_const	mu0_const*c_const (ohm) (376.73031341044[ohm])
Electron mass	me_const	9.109383713928e-31[kg]
Elementary charge*	e_const	1.602176634e-19[C]
Faraday constant*	F_const	N_A_const*e_const (C/mol) (96485.33212331[C/mol])
Fine-structure constant	alpha_const	7.297352564311e-3
Gravitational constant	G_const	6.6743015e-11[m^3/(kg*s^2)]
Molar volume of ideal gas (at 273.15 K and 1 atm)*	V_m_const	R_const*273.15[K]/1[atm] (m3/mol) (22.413969545014e-3[m^3/mol])
Neutron mass	mn_const	1.6749275005685e-27[kg]
Permeability of vacuum (magnetic constant)	mu0_const	2alpha_consth_const/(c_const*e_const^2) (H/m) (1.25663706126471e-6[N/A^2])
Permittivity of vacuum (electric constant)	epsilon0_const	1/mu0_const/c_const/c_const (F/m) (8.85418781882671e-12[F/m])
Planck constant*	h_const	6.62607015e-34[J*s]
Planck constant over 2 pi*	hbar_const	1.0545718176462e-34[J*s]
Proton mass	mp_const	1.6726219259552e-27[kg]
Speed of light in vacuum*	c_const	299792458[m/s]
Stefan–Boltzmann constant*	sigma_const	(pi^2/60)k_B_const^4/(hbar_const^3c_const^2) (W/(m2·K4)) (5.67037441918443e-8[W/(m^2*K^4)])
Universal gas constant (molar gas constant)*	R_const	N_A_constk_B_const (J/(mol·K)) (8.3144626185324[J/(molK)])
Wien displacement law constant*	b_const	h_constc_const/k_B_const/4.965114231744276 (m·K) (2.89777195518517e-3[mK]) The constant 4.965114... is a root of the equation x = 5(1 − e−x) [ Ref. 2 ]

Table 5-8: Physical Constants.

Name

Symbol

Value

Acceleration of gravity

4*pi*epsilon0_const*hbar_const^2/(me_const*e_const^2) (m)
(5.2917721054432e-11[m])

Boltzmann constant*

k_B_const

1.380649e-23[J/K]

Characteristic impedance of vacuum (impedance of free space)

Z0_const

mu0_const*c_const (ohm)
(376.73031341044[ohm])

Electron mass

me_const

9.109383713928e-31[kg]

N_A_const*e_const (C/mol)
(96485.33212331[C/mol])

Fine-structure constant

alpha_const

7.297352564311e-3

Gravitational constant

G_const

6.6743015e-11[m^3/(kg*s^2)]

Molar volume of ideal gas (at 273.15 K and 1 atm)*

V_m_const

R_const*273.15[K]/1[atm] (m3/mol)
(22.413969545014e-3[m^3/mol])

Neutron mass

mn_const

1.6749275005685e-27[kg]

Permeability of vacuum (magnetic constant)

mu0_const

2*alpha_const*h_const/(c_const*e_const^2) (H/m)
(1.25663706126471e-6[N/A^2])

Permittivity of vacuum (electric constant)

epsilon0_const

1/mu0_const/c_const/c_const (F/m)
(8.85418781882671e-12[F/m])

Planck constant*

h_const

6.62607015e-34[J*s]

Planck constant over 2 pi*

hbar_const

1.0545718176462e-34[J*s]

Proton mass

mp_const

1.6726219259552e-27[kg]

Speed of light in vacuum*

c_const

299792458[m/s]

Stefan–Boltzmann constant*

sigma_const

(pi^2/60)*k_B_const^4/(hbar_const^3*c_const^2) (W/(m2·K4))
(5.67037441918443e-8[W/(m^2*K^4)])

Universal gas constant (molar gas constant)*

R_const

N_A_const*k_B_const (J/(mol·K))
(8.3144626185324[J/(mol*K)])

Wien displacement law constant*

b_const

h_const*c_const/k_B_const/4.965114231744276 (m·K)
(2.89777195518517e-3[m*K])
The constant 4.965114... is a root of the equation x = 5(1 − e−x) [ Ref. 2 ]

1. The NIST Reference on Constants, Units, and Uncertainty, physics.nist.gov/cuu/Constants/index.html (“CODATA Recommended Values of the Fundamental Physical Constants: 2022”).