Some physical constants and quantities in SI and natural units

Layout by Krister Henriksson, krister.henriksson@helsinki.fi (rev. April 7 2003)

Physical constants in SI units

Constant	Symbol	Value
Pi	$\pi$	3.141592654
Universal gravitational constant	G	6.67259 . 10-11 Nm2/kg2
Standard acceleration of gravity	gn	9.80665 m/s2
Standard temperature	T0	273.15 K
Standard pressure	p0	1 atm = 760 Torr = 101325 Pa = 1.01325 bar
Molar volume at STP	Vm	22.42420 . 10-3 m3/mol
Avogadro's constant	NA	6.0221367 . 1023 1/mol
Gas constant	R	8.314510 J/(mol . K)
Boltzmann's constant, R/NA	kB	1.380658 . 10-23 J/K
		= 8.617385 . 10-5 eV/K
Speed of light in vacuum	c	2.99792458 . 108 m/s
Fundamental unit of electric charge	e	1.60217733 . 10-19 C
Mass of electron	me	9.1093897 . 10-31 kg
		= 0.51099906 MeV/c2
Mass of proton	mp	1.6726231 . 10-27 kg
		= 938.27231 MeV/c2
Mass of neutron	mn	1.6749286 . 10-27 kg
		= 939.56563 MeV/c2
Universal atomic mass unit	u	1.6605402 . 10-27 kg
		= 931.49435 MeV/c2
Permeability of vacuum	$\mu_{0}^{}$	4$\pi$ . 10-7 N/A2
		= 1.256637061 . 10-6 N/A2
Permittivity of vacuum	$\varepsilon_{0}^{}$ = 1/($\mu_{0}^{}$c2)	8.85418782 . 10-12 F/m
Coefficient in Coulomb's law	1/(4$\pi$$\varepsilon_{0}^{}$)	8.98755 . 109 Nm2/C2
Planck's constant	h	6.6260755 . 10-34 Js
		= 4.1356692 . 10-15 eVs
	$\hbar$ = h/(2$\pi$)	1.05457266 . 10-34 Js
		= 6.5821220 . 10-16 eVs
Electromagnetic coupling constant	$\alpha$ = e2/(4$\pi$$\varepsilon_{0}^{}$$\hbar$c)	7.29735308 . 10-3
(fine structure constant)		= 1/137.0359895
Rydberg's constant	R$\infty$ = mec$\alpha^{2}_{}$/(2h)	1.0973731534 . 107 1/m
Stefan & Boltzmann's constant	$\sigma$ = $\pi^{2}_{}$kB4/(60$\hbar^{3}_{}$c2)	5.67051 . 10-8 W/(m2 . K4)
		= 3.53925 . 1011 eV/(m2 . K4)

Physical quantities in SI units

Quantity	Symbol	Unit	Symbol of unit	Dependence on
				other SI units
Electric charge	Q	coulomb	C
current	I	ampere	A	A=C/s
voltage	$\Delta$Ve, Ue	volt	V	V=N/C
resistance	R	ohm	$\Omega$	$\Omega$=V/A=Vs/C
capacitance	C	farad	F	F=C/V=$\Omega$s
conductivity	G = 1/R	siemens	Si
Magnetic flow	$\Phi$	weber	Wb	Wb=Vs
Rate of magnetic flow	B	tesla	T	T=Wb/m2
Magnetic inductance	L	henry	H	H=Wb/A=Vs/A
Activity	A	bequerel	Bq	Bq=1/s
Equivalent dose	E	sievert	Sv	Sv=J/kg
Absorbed dose	D	gray	Gy	Gy=J/kg

Physical quantities in natural units ( c = k_B = $\hbar$ = 1)

Quantity	Natural unit
s	2.99792458 . 108 m	2.99792458 . 1023 fm
J	3.163025 . 1025 m-1	6.241506 . 1018 eV
kg	2.842785 . 1042 m-1	5.609586 . 1035 eV
K	436.7056 m-1	8.617386 . 10-5 eV
eV	5.067727 . 106 m-1	5.067727 . 10-9 fm-1
pc	3.0856 . 1016 m	3.0856 . 1031 fm
H0	h . 100 km/(s . Mpc) = h . 1.0810 . 10-26 m-1	= h . 2.1331 . 10-33 eV

Note the following dependence that holds for natural units:

fm ^. GeV = 5.067727

Physical constants in natural units

Constant	Symbol	Value
Planck mass	mPl = 1/$\sqrt{{G}}$	1.22 . 1019 GeV
Reduced Planck mass	MPl = mPl/$\sqrt{{8 \pi}}$ = 1/$\sqrt{{8 \pi G}}$	2.436 . 1018 GeV

Values taken from
David R. Lide et al., CRC Handbook of Chemistry and Physics,
76th Edition, CRC Press, 1995.