Units in Electricity and Magnetism

The tables below list the systems of electrical and magnetic units. They only include units of interest in the field of Radio.
The older systems were the CGS and Gaussian systems.The Gaussian system being based on a mix of Electrostatic units (ESU) and Electromagnetic units (EMU).

The current standard is the International System of Units (SI) and is sometimes referred to as rationalised MKS units.
Conversions from one system to others are given in two ways. Firstly numerically by multiplying factors. Note that c stands for  the velocity of light in space and its value is exactly 299792458 metre/second exactly (by definition of the metre).

The other method of conversion allows you to change formulas given in old books into the modern SI form. This will be particularly useful to you if, like me, you have books by Terman, Scroggie, etc. or the Admiralty Handbook of Wireless Telegraphy. There were lots of useful formulas in these old books, which can now be given new life.

I have tried to make the tables as complete and accurate as possible and have checked lots of different sources. Nevertheless there may be errors and I will be grateful for any corrections or additions. Please email me at the address given on the home page.

SI  Units

Quantity Symbol Unit & (Abbr.) Dimensions ESU EMU
Mass m kilogram (kg) M 1000 1000
Length l metre (m) L 100 100
Time t second (s) T 1 1
Power P watt (W) ML2T-3 107 107
Electric Current I ampere (A) I=M½LT-2 10c 0.1
Charge Q coulomb (C) TI 10c 0.1
Electric Potential V volt (V) ML2T-3I-1 106/c 108
Resistance R ohm () ML2T-3I-2 105/c2 109
Conductance G siemens (S) M-1L-2T3I2 10-5c2 10-9
Inductance H henry (H) ML2T-2I-2 105/c2 109
Capacitance C farad (F) M-1L-2T4I2 10-5c2 10-9
Electric Field Strength E volt/metre (V m-1) MLT-3I-1 104/c 106
Electric Charge Density coulomb/cu.m. (C m-3) L-3TI c/105 10-7
Electric displacement
Electric flux density
D coulomb/sq.m. (C m-2) L-2TI 410-3c 410-5
Magnetic Potential ampere (A) I 410c 410-1
Magnetic Field Strength H ampere/metre (A m-1) L-1I 4c/10 410-3
Magnetic flux weber (Wb) ML2T-2I-1 106/c 108
Magnetic Induction
Magnetic Flux Density
B tesla (T) MT-2I-1 100/c 104
Magnetic susceptibility e none none 10-4c-2/(4) 1/(4)
Magnetic Moment m ampere metre2 (A m2) L2I 105c 103
Magnetisation (Magnetic moment/unit volume) M ampere/metre (A m-1) L-1I 10-1c 10-3
Magnetic Polarisation J tesla (T) MT-2I-1 102/(4c) 104/(4)
Magnetic Pole Strength P ampere metre (A m) LI 103c 10
Magneto Motive Force Fm ampere (A) I 410c 410-1
Magnetic Reluctance S ampere/weber(A Wb-1) I2M-1L-2T2 410-9 410-9
Permittivity of space farad/metre (F m-1) M-1L-3T4I2
Permeability of space henry/metre (H m-1) MLT-2I-2

c (the speed of light) = 299792458 metre/second exactly (by definition of the metre)
= 1/(410-7c2) = 8.85418781762039 x 10-12 farad/metre (approx)
= 410-7 = 1.25663706143592 x 10-6 henry/metre (approx)

CGS Units

Quantity Symbol Dimensions Dimensions ESU EMU
Mass m M M gram gram
Length l L L centimetre centimetre
Time t T T second second
Power P ML2T-3 ML2T-3 erg/second erg/second
Electric Current I I M½LT-2 statamp biot
Charge Q TI M½LT-1 franklin abcoulomb
Electric Potential V ML2T-3I-1 M½L½T-1 statvolt abvolt
Resistance R ML2T-3I-2 L-1T statohm abohm
Conductance G M-1L-2T3I2 LT-1 statsiemens absiemens
Inductance L ML2T-2I-2 L-1T2 stathenry abhenry
Capacitance C M-1L-2T4I2 L cm abfarad
Electric field strength E MLT-3I-1 M½LT-1 statvolt/cm abvolt/cm
Electric displacement D L-2TI M½LT-1 statcoulomb cm-2 abcoulomb cm-2
Dielectric constant M-1L-3T4I2 none none none
Magnetic pole P LI M½LT-2   unit pole
dyne cm-1
= 4 lines of force
Magnetic Potential I M½LT-2   gilbert
Magnetic field strength H L-1I M½L½T-2   oersted
Magnetic flux ML2T-2I-1 M½L½   maxwell

= 1 line

Magnetic Induction
(Magnetic flux density)
B MT-2I-1 M½L-1½   gauss
= 1 line cm-2
Magnetic permeability MLT-2I-2 L-2T2   darcy
Magnetic susceptibility (or k) M½LT-2I-1 none none none
Intensity of Magnetisation M (or I)
= J
L-1I M½L½T-2   pole cm-2
Magnetic Moment m L2I M½LT-2   pole cm
Magneto Motive force G I M½LT-2   gilbert
Magnetic Reluctance S L-2M-1T2I2 LT-2   gilbert/biot

In the first column of Dimensions, I is used as a basic unit.
In the second it is expressed in terms of Length, Mass and Time.

Gaussian Units

The Gaussian system uses a mix of Electrostatic and Electromagnetic units
There are two common forms, Gaussian and Modified Gaussian, which defines electric current in terms of magnetic units
Quantity Symbol Gaussian Modified Gaussian
Electric Current I ESU franklin EMU biot
Charge Q ESU statcoulomb ESU statcoulomb
Electric Potential V ESU statvolt ESU statvolt
Resistance R ESU statohm ESU statohm
Inductance L EMU abhenry cm
Capacitance C cm cm
Electric field strength E ESU statvolt/cm ESU statvolt/cm
Electric displacement D ESU statcoulomb/cm2 ESU statcoulomb/cm2
Dielectric constant none none
Magnetic pole P EMU unit pole EMU unit pole
Magnetic Potential EMU gilbert EMU gilbert
Magnetic field strength H EMU oersted EMU oersted
Magnetic flux EMU maxwell
= 1 line
EMU maxwell
= 1 line
Magnetic Induction
(Magnetic flux density)
B EMU gauss EMU gauss
Magnetic permeability EMU darcy EMU darcy
Magnetic susceptibility none none
Intensity of Magnetisation M EMU pole cm-2 EMU pole cm-2
Magnetic Moment m EMU pole cm EMU pole cm
Magneto Motive force G EMU gilbert EMU gilbert
Magnetic Reluctance S EMU EMU

Conversion of Gaussian formulae into SI

To convert a formula from the Gauss form into the SI form, replace the elements on both sides of the equation using the table below. Mass, Length, Time and others not listed below are not changed.
Quantity Gaussian SI
Electric Current I I /
Electric Current in EMU I I
Charge Q Q /
Electric Potential, PD, EMF V V
Resistance R R
Inductance L L
Capacitance C C / ()
Electric field strength E E
Electric displacement D D
Dielectric constant /
Magnetic pole P P
Magnetic Potential
Magnetic field strength H H
Magnetic flux
Magnetic Induction

(Magnetic flux density)

Magnetic permeability /
Magnetic susceptibility or k e
Intensity of Magnetisation I M
Magnetic Moment m m
Magneto Motive force G G
Magnetic Reluctance S S

Example of formula conversion

Maxwell's equations

In Gaussian units:

On conversion to SI units these become:

On simplifying

Then using  we get:


Approximate ESU/EMU units in terms of SI units

Quantity 1 ESU unit 1 EMU unit
Current 334 A 10 A
Charge 334 C 10 C
Potential 300 V 10 nV
Power 100 nW 100 nW
Resistance 90 G 1 n
Conductance 1 pS 1 GS
Inductance 90 GH 1 nH
Capacitance 1 pF 1 GF
Magnetic flux 300 Wb 10 nWb
Magnetic induction 3 MT 100 T
Magnetic field strength 3 nA/metre 80 A/metre
Magnetisation 33 nA/metre 1000 A/metre
Electric field strength 30000 V/metre V/metre
Electric displacement 265 nC/metre 8000 C/metre