Gaussian units

In physics, in particular in electromagnetic theory, Gaussian units are a set of units for electric and magnetic quantities. The units are named for the German mathematician and physicist Carl Friedrich Gauss, who was the first to define magnetic units.

The most common and most elaborate set of units are the SI units (formerly known as metric or MKSA units). Their main advantage is that they are very widespread and well defined by international committees for all different areas of engineering and science. The entire engineering world uses SI units, so almost any discussion of electrical equipment or experimental apparatus is nowadays in terms of SI units.

The main advantage of Gaussian units is that they simplify more than the SI units the fundamental physical issues and theoretical relations involving electromagnetic phenomena. Especially, the theories of relativity and electrodynamics are simpler, more transparent and more elegant in Gaussian units than in SI units. In addition, the various formulas of electromagnetism are easier to remember in Gaussian units than in SI units. Because they are superior for fundamental physical questions, it is unlikely that Gaussian units will ever be completely abandoned.

Conversion of electric units

Symbol	Property	SI Unit	Factor	Gaussian
I	Electric current	ampere (A)	10c	statampere (statA)
Q	Charge	coulomb(C)	10c	statcoulomb (statC)
V	Electric potential	volt (V)	106/c	statvolt (statV)
R	Resistance	ohm (Ω)	105/c2	statohm (statΩ)
G	Conductance	siemens (S)	10−5c2	statsiemens (statS)
L	Self-inductance	henry (H)	105/c2	abhenry (abH)
C	Capacitance	farad (F)	10−5c2	cm
E	Electric field	V/m	104/c	statV/cm
ρ	Electric charge density	C/m3	c/105	statC/cm3
D	Electric displacement	C/m2	4π10-3c	statV/cm

c is the speed of light in m/s (≈ 3⋅10⁸ m/s).
Example: 1 A = 10c statA.

Conversion of magnetic units

Gaussian units are the same as cgs emu for magnetostatics.

Mx = maxwell, G = gauss, Oe = oersted ; Wb = weber, V = volt, s = second, T = tesla, m = meter, A = ampere, J = joule, kg = kilogram, H = henry

Symbol	Property	Gaussian → SI
Φ	magnetic flux	1 Mx → 10−8 Wb = 10−8 V⋅s
B	magnetic flux density	1 G → 10−4 T = 10−4 Wb/m2
	magnetic induction
H	magnetic field	1 Oe → 103/(4π) A/m
m	magnetic moment	1 erg/G = 1 emu → 10−3 A⋅m2 = 10−3 J/T
M	magnetization	1 erg/(G⋅cm3) = 1 emu/cm3 → 103 A/m
4πM	magnetization	1 G → 103/(4π) A/m
σ	mass magnetization	1 erg/(G⋅g) = 1 emu/g → 1 A⋅m2/kg
	specific magnetization
j	magnetic dipole moment	1 erg/G = 1 emu → 4π ⋅ 10−10 Wb⋅m
J	magnetic polarization	1 erg/(G⋅cm3) = 1 emu/cm3 → 4π ⋅ 10−4 T
χ, κ	susceptibility	1 → 4π
χρ	mass susceptibility	1 cm3/g → 4π ⋅ 10−3 m3/kg
μ	permeability	1 → 4π ⋅ 10−7 H/m = 4π ⋅ 10−7 Wb/(A⋅m)
μr	relative permeability	μ → μr
w, W	energy density	1 erg/cm3 → 10−1 J/m3
N, D	demagnetizing factor	1 → 1/(4π)