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.
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)  ML^{2}T^{3}  10^{7}  10^{7} 
Electric Current  I  ampere (A)  I=M^{½}L^{1½}T^{2}  10c  0.1 
Charge  Q  coulomb (C)  TI  10c  0.1 
Electric Potential  V  volt (V)  ML^{2}T^{3}I^{1}  10^{6}/c  10^{8} 
Resistance  R  ohm ()  ML^{2}T^{3}I^{2}  10^{5}/c^{2}  10^{9} 
Conductance  G  siemens (S)  M^{1}L^{2}T^{3}I^{2}  10^{5}c^{2}  10^{9} 
Inductance  H  henry (H)  ML^{2}T^{2}I^{2}  10^{5}/c^{2}  10^{9} 
Capacitance  C  farad (F)  M^{1}L^{2}T^{4}I^{2}  10^{5}c^{2}  10^{9} 
Electric Field Strength  E  volt/metre (V m^{1})  MLT^{3}I^{1}  10^{4}/c  10^{6} 
Electric Charge Density  coulomb/cu.m. (C m^{3})  L^{3}TI  c/10^{5}  10^{7}  
Electric displacement
Electric flux density 
D  coulomb/sq.m. (C m^{2})  L^{2}TI  410^{3}c  410^{5} 
Magnetic Potential  ampere (A)  I  410c  410^{1}  
Magnetic Field Strength  H  ampere/metre (A m^{1})  L^{1}I  4c/10  410^{3} 
Magnetic flux  weber (Wb)  ML^{2}T^{2}I^{1}  10^{6}/c  10^{8}  
Magnetic Induction
Magnetic Flux Density 
B  tesla (T)  MT^{2}I^{1}  100/c  10^{4} 
Magnetic susceptibility  _{e}  none  none  10^{4}c^{2}/(4)  1/(4) 
Magnetic Moment  m  ampere metre^{2} (A m^{2})  L^{2}I  10^{5}c  10^{3} 
Magnetisation (Magnetic moment/unit volume)  M  ampere/metre (A m^{1})  L^{1}I  10^{1}c  10^{3} 
Magnetic Polarisation  J  tesla (T)  MT^{2}I^{1}  10^{2}/(4c)  10^{4}/(4) 
Magnetic Pole Strength  P  ampere metre (A m)  LI  10^{3}c  10 
Magneto Motive Force  F_{m}  ampere (A)  I  410c  410^{1} 
Magnetic Reluctance  S  ampere/weber(A Wb^{1})  I^{2}M^{1}L^{2}T^{2}  410^{9}  410^{9} 
Permittivity of space  farad/metre (F m^{1})  M^{1}L^{3}T^{4}I^{2} 



Permeability of space  henry/metre (H m^{1})  MLT^{2}I^{2} 


Notes:
c (the speed of light) = 299792458 metre/second exactly (by definition
of the metre)
= 1/(410^{7}c^{2})
= 8.85418781762039 x 10^{12} farad/metre (approx)
= 410^{7}
= 1.25663706143592 x 10^{6} henry/metre (approx)
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  ML^{2}T^{3}  ML^{2}T^{3}  erg/second  erg/second 
Electric Current  I  I  M^{½}L^{1½}T^{2}  statamp  biot 
Charge  Q  TI  M^{½}L^{1½}T^{1}  franklin  abcoulomb 
Electric Potential  V  ML^{2}T^{3}I^{1}  M^{½}L^{½}T^{1}  statvolt  abvolt
(lines/second) 
Resistance  R  ML^{2}T^{3}I^{2}  L^{1}T  statohm  abohm 
Conductance  G  M^{1}L^{2}T^{3}I^{2}  LT^{1}  statsiemens  absiemens 
Inductance  L  ML^{2}T^{2}I^{2}  L^{1}T^{2}  stathenry  abhenry 
Capacitance  C  M^{1}L^{2}T^{4}I^{2}  L  cm  abfarad 
Electric field strength  E  MLT^{3}I^{1}  M^{½}L^{½}T^{1}  statvolt/cm  abvolt/cm 
Electric displacement  D  L^{2}TI  M^{½}L^{1½}T^{1}  statcoulomb cm^{2}  abcoulomb cm^{2} 
Dielectric constant  M^{1}L^{3}T^{4}I^{2}  none  none  none  
Magnetic pole  P  LI  M^{½}L^{2½}T^{2}  unit pole
dyne cm^{1} = 4 lines of force 

Magnetic Potential  I  M^{½}L^{1½}T^{2}  gilbert  
Magnetic field strength  H  L^{1}I  M^{½}L^{½}T^{2}  oersted  
Magnetic flux  ML^{2}T^{2}I^{1}  M^{½}L^{½}  maxwell
= 1 line 

Magnetic Induction
(Magnetic flux density) 
B  MT^{2}I^{1}  M^{½}L^{1½}  gauss
= 1 line cm^{2} 

Magnetic permeability  MLT^{2}I^{2}  L^{2}T^{2}  darcy  
Magnetic susceptibility  (or k)  M^{½}L^{1½}T^{2}I^{1}  none  none  none 
Intensity of Magnetisation  M (or I)
= J 
L^{1}I  M^{½}L^{½}T^{2}  pole cm^{2}  
Magnetic Moment  m  L^{2}I  M^{½}L^{3½}T^{2}  pole cm  
Magneto Motive force  G  I  M^{½}L^{1½}T^{2}  gilbert  
Magnetic Reluctance  S  L^{2}M^{1}T^{2}I^{2}  LT^{2}  gilbert/biot 
Notes:
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.
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/cm^{2}  ESU statcoulomb/cm^{2} 
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 
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) 
B  B 
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 
On conversion to SI units these become:
On simplifying
Then using we get:
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  1 V/metre 
Electric displacement  265 nC/metre  8000 C/metre 