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Tables of Gaussian and SI Units

Mechanical

Quantity SI CGS–ESU Gaussian CGS–EMU
Force, F newton (N) = kg m s−2 dyne (dyn) = g cm s−2
M L T−2
Energy, E joule (J) = N⋅m = kg m2 s−2 erg = dyn⋅cm = g cm2 s−2
M L2 T−2
Angular momentum, L J⋅s = kg m2 s−1 erg⋅s = g cm2 s−1
M L2 T−1

Electric

Quantity SI CGS–ESU Gaussian CGS–EMU
Charge, Q, q coulomb (C) = A⋅s franklin (Fr) = statcoulomb (statC) = esu charge = dyn1/2⋅cm = erg1/2⋅cm1/2 = g1/2 cm3/2 s−1 Bi⋅s = abcoulomb (abC) = emu charge = dyn1/2⋅s = g1/2 cm1/2
T I M1/2 L3/2 T−1 M1/2 L1/2
Charge density, ρ C/m3 Fr/cm3 = dyn1/2/cm2 = g1/2 cm−3/2 s−1 abC/cm3 = Bi⋅s/cm3
L−3 T I M1/2 L−3/2 T−1 M1/2 L−5/2
Electric potential/voltage, V volt (V) = J/C = kg m2 s−3 A−1 statvolt (statV) = erg/Fr = Fr/cm = g1/2 cm1/2 s−1 abvolt (abV) = erg/(Bi⋅s) = dyn1/2⋅cm/s = g1/2 cm3/2 s−2
M L2 T−3 I−1 M1/2 L1/2 T−1 M1/2 L3/2 T−2
Electric field, E V/m = N/C = kg m s−3 A−1 statV/cm = dyn/Fr = Fr/cm2 = g1/2 cm−1/2 s−1 abV/cm
M L T−3 I−1 M1/2 L−1/2 T−1 M1/2 L1/2 T−2
Electric displacement field, D C/m2 Fr/cm2 Bi⋅s/cm2
L−2 T I M1/2 L−1/2 T−1 M1/2 L−3/2
Polarization density, P C/m2 Fr/cm2
L−2 T I M1/2 L−1/2 T−1
Electric flux, ΦE V⋅m = N⋅m2/C = kg m3 s−3 A−1 Fr
M L3 T−3 I−1 M1/2 L3/2 T−1
The other electric flux, ΦD C Fr
T I M1/2 L3/2 T−1
Electric dipole moment, p C⋅m Fr⋅cm
L T I M1/2 L5/2 T−1
Electric permittivity, ε F/m = C/(V⋅m) = C2/(N⋅m2) = kg−1 m−3 s4 A2 cm/cm s2/cm2
M−1 L−3 T4 I2 1 L−2 T2

Magnetic

Quantity SI CGS–ESU Gaussian CGS–EMU
Current, I, j ampere (A) = C/s Fr/s = statampere (statA) = esu current = dyn1/2⋅cm/s = g1/2 cm3/2 s−2 biot (Bi) = abampere (abA) = emu current = dyn1/2 = g1/2 cm1/2 s−1
I M1/2 L3/2 T−2 M1/2 L1/2 T−1
Current density, J, j A/m2 statA/cm2 Bi/cm2
L−2 I M1/2 L−1/2 T−2 M1/2 L−3/2 T−1
Magnetic vector potential, A V⋅s/m = kg⋅m/(s⋅C) = N/A = kg m s−2 A−1 statWb/cm = statT⋅cm Mx/cm = G⋅cm
M L T−2 I−1 M1/2 L−1/2 M1/2 L1/2 T−1
Magnetic flux density, B tesla (T) = Wb/m2 = N⋅s/(C⋅m) = N/(A⋅m) = V⋅s/m2 = kg s−2 A−1 stattesla (statT) = statWb/cm2 gauss (G) = Mx/cm2 = g/(Bi⋅s2)
M T−2 I−1 M1/2 L−3/2 M1/2 L−1/2 T−1
Magnetic field strength, H A/m statA/cm oersted (Oe) = dyn/Mx
L−1 I M1/2 L1/2 T-2 M1/2 L−1/2 T−1
Magnetic flux, ΦB weber (Wb) = V⋅s = kg m2 s−2 A−1 statweber (statWb) = statV⋅s maxwell (Mx) = G⋅cm2
M L2 T−2 I−1 M1/2 L1/2 M1/2 L3/2 T−1
Magnetic dipole moment, μ, m A⋅m2 = N⋅m/T = J/T statA⋅cm2 erg/G = g1/2 cm5/2 s−1
L2 I M1/2 L7/2 T−2 M1/2 L5/2 T−1
Magnetization, M, 4πM A/m erg/(G⋅cm3)
L−1 I
Magnetic permeability, μ H/m s2/cm2 cm/cm
M L T−2 I−2 L−2 T2 1
Magnetomotive force, ℱ A Gi
I
Magnetic reluctance, ℛ H−1 Gi/Mx
M−1 L−2 T2 I2

Other

Quantity SI CGS–ESU Gaussian CGS–EMU
Capacitance, C farad (F) = C/V = kg−1 m−2 s4 A2 statfarad (statF) = cm abfarad (abF)
M−1 L−2 T4 I2 L
Inductance, L henry (H) = Wb/A = kg m2 s−2 A−2 stathenry (statH) = s2/cm abhenry (abH) = abΩ⋅s
M L2 T−2 I−2 L−1 T2 L
Resistance, R ohm (Ω) = V/A = kg m2 s−3 A−2 statohm (statΩ) = s/cm abohm (abΩ) = abV/Bi
M L2 T−3 I−2 L−1 T L T−1
Conductance, G siemens (S) = mho (℧) = Ω−1 = kg−1 m−2 s3 A2 cm/s
M−1 L−2 T3 I2 L T−1
Resistivity, ρ Ω⋅m = kg m3 s−3 A−2 s abΩ⋅cm
M L3 T−3 I−2 T L2 T−1
Conductivity, σ S/m = ℧/m = kg−1 m−3 s3 A2 s−1
M−1 L−3 T3 I2 T−1

Closures

To define the value of a unit, we're required to set a physical constant to a measurable value (Colton, 2024). The SI and Gaussian system take different approaches to "closing" the system of electromagnetic equations.

  • SI:

    Set magnetic permeability μ₀ to 4π × 10⁻⁷ N/A²

  • Gaussian:

    Set electric permittivity ε₀ to 1/4π (or, Coulomb's constant k<sub>c</sub> to 1)

Sources