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(centimeter-gram-second) 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.
The MKS system of units is a physical system of units that expresses any given measurement using
fundamental units of the metre, kilogramme, and/or second (MKS)
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=M½L1½T-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
coulomb/cu.m. (C m-3)
L-3TI
c/105
10-7
coulomb/sq.m. (C m-2)
L-2TI
4 10-3c
4 10-5
ampere (A)
I
4 10c
4 10-1
ampere/metre (A m-1)
L-1I
4 c/10
4 10-3
weber (Wb)
ML2T-2I-1
106/c
108
tesla (T)
MT-2I-1
100/c
104
none
none
10-4c-2/(4
)
1/(4 )
Electric Charge Density
Electric displacement
Electric flux density
D
Magnetic Potential
Magnetic Field Strength
H
Magnetic flux
Magnetic Induction
Magnetic Flux Density
B
Magnetic susceptibility
e
)
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/(4
c)
104/(4 )
Magnetic Pole Strength
P
ampere metre (A m)
LI
103c
10
Magneto Motive Force
Fm
ampere (A)
I
4 10c
4 10-1
Magnetic Reluctance
S
ampere/weber(A Wb-1)
I2M-1L-2T2
4 10-9
4 10-9
Permittivity of space
farad/metre (F m-1)
M-1L-3T4I2
-
-
Permeability of space
henry/metre (H m-1)
MLT-2I-2
-
-
Notes:
c (the speed of light) = 299792458 metre/second exactly (by definition of the metre)
= 1/(4 10-7c2) = 8.85418781762039 x 10-12 farad/metre (approx)
= 4 10-7 = 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
M½L1½T-2
statamp
biot
Charge
Q
TI
M½L1½T-1
franklin
abcoulomb
Electric Potential
V
ML2T-3I-1
M½L½T-1
statvolt
abvolt
(lines/second)
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
M½L-½T-1
statvolt/cm
abvolt/cm
Electric displacement
D
L-2TI
M½L1½T-1
statcoulomb cm-2
abcoulomb cm2
Dielectric constant
Magnetic pole
P
Magnetic Potential
Magnetic field strength
H
M-1L-3T4I2
none
LI
M½L2½T-2
unit pole
dyne cm-1
= 4 lines of
force
I
M½L1½T-2
gilbert
L-1I
M½L½T-2
oersted
none
none
ML2T-2I-1
Magnetic flux
M½L½
maxwell
= 1 line
Magnetic Induction
(Magnetic flux density)
B
Magnetic permeability
Magnetic susceptibility
(or k)
MT-2I-1
M½L-1½
gauss
= 1 line cm-2
MLT-2I-2
L-2T2
darcy
M½L1½T-2I-1
none
none
none
Intensity of
Magnetisation
M (or I)
=J
L-1I
M½L½T-2
pole cm-2
Magnetic Moment
m
L2I
M½L3½T-2
pole cm
Magneto Motive force
G
I
M½L1½T-2
gilbert
Magnetic Reluctance
S
L-2M-1T2I2
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.
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
ESU statcoulomb/cm2
ESU statcoulomb/cm2
none
none
EMU unit pole
EMU unit pole
EMU gilbert
EMU gilbert
EMU oersted
EMU oersted
EMU maxwell
= 1 line
EMU maxwell
= 1 line
EMU gauss
EMU gauss
Magnetic permeability
EMU darcy
EMU darcy
Magnetic susceptibility
none
none
Electric displacement
D
Dielectric constant
Magnetic pole
P
Magnetic Potential
Magnetic field strength
H
Magnetic flux
Magnetic Induction
(Magnetic flux density)
B
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
Electric Current
I
Electric Current in EMU
I
Charge
Q
Electric Potential, PD, EMF
V
Resistance
R
SI
I/
I
Q/
V
R
Inductance
L
Capacitance
C
Electric field strength
E
Electric displacement
D
L
C/(
E
D
Dielectric constant
Magnetic pole
)
/
P
P
Magnetic Potential
Magnetic field strength
H
H
Magnetic flux
Magnetic Induction
B
B
(Magnetic flux density)
Magnetic permeability
/
Magnetic susceptibility
or k
Intensity of Magnetisation
I
Magnetic Moment
m
Magneto Motive force
G
Magnetic Reluctance
S
Example of formula conversion
Maxwell's equations
e
M
m
G
S
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
Charge
Potential
Power
Resistance
Conductance
Inductance
Capacitance
Magnetic flux
Magnetic induction
Magnetic field strength
Magnetisation
Electric field strength
Electric displacement
334 A
334 C
300 V
100 nW
90 G
1 pS
90 GH
1 pF
300 Wb
3 MT
3 nA/metre
33 nA/metre
30000 V/metre
265 nC/metre
10 A
10 C
10 nV
100 nW
1n
1 GS
1 nH
1 GF
10 nWb
100 T
80 A/metre
1000 A/metre
1 V/metre
8000 C/metre
The electrostatic system of units is a system of units used to measure electrical quantities of
electric charge, electric current, and voltage within the centimeter-gram-second (or "CGS")
system of metric units.
In electrostatic units, electrical charge is defined by the force that it exerts on other charges.
Although the CGS units have mostly been supplanted by the MKSA (meter-kilogram-secondampere) or International System of Units (SI) units, the electrostatic units are still in occasional
use in some applications, most notably in certain fields of physics such as in particle physics and
astrophysics.
The main electrostatic units are:
The statcoulomb, called the franklin or the "esu" for electric charge.