Quantity
Name
acceleration
metre per second squared
angular acceleration
radian per second squared
angular momentum
kilogram metre squared per second
angular velocity
radian per second
area
square metre
coefficient of linear expansion
1 per kelvin
concentration (of amount of substance) mole per cubic metre
density
kilogram per cubic metre
diffusion coefficient
metre squared per second
electric current density
ampere per square metre
exposure rate (ionizing radiation)
ampere per kilogram
cinematic viscosity
metre squared per second
luminance
candela per square metre
magnetic field strength
ampere per metre
magnetic moment
ampere metre squared
mass flow rate
kilogram per second
mass per unit area
kilogram per square metre
mass per unit length
kilogram per metre
molality
mole per kilogram
molar mass
kilogram per mole
molar volume
cubic metre per mole
moment of inertia
kilogram metre squared
moment of momentum
kilogram metre squared per second
momentum
kilogram metre per second
radioactivity (disintegration rate)
1 per second
rotational frequency
1 per second
specific volume
cubic metre per kilogram
speed
metre per second
velocity
metre per second
volume
cubic metre
wave number
1 per metre
Table 2. SI supplementary units
Quality
Name
plane
radian
angle
Symbol
rad
solid
steradian sr
angle
Definition
The radian is the plane
angle between two radii of
a circle which cut off on the
circumference an arc equal
in length to the radius
The steradian is the solid
angle which, having it's
vertex in the centre of a
sphere, cuts off an area of
the surface of the sphere
equal to that of a square
Symbol
m/s2
rad/s2
kg·m2/s
rad/s
m2
K−1
mol/m3
kg/m3
m2/s
A/m2
A/kg
m2/s
cd/m2
A/m
A·m2
kg/s
kg/m2
kg/m
mol/kg
kg/mol
m3/mol
kg·m2
kg·m2/s
kg·m/s
s−1
s−1
m3/kg
m/s
m/s
m3
m−1
with sides of length equal
to the radius of the sphere.
Table 3. Derived units with special names
Quantity
Name
Expression
in terms
Expression in
of other SI
Symbol
terms
units and
of SI Base units
definition of
unit.
admittance siemens S
capacitance farad
F
conductance siemens S
electrical
ohm

resistance
electric
coulomb C
charge
electric flux coulomb C
electric
volt
V
potential
electromotive
volt
V
force
energy
joule
J
energy flux watt
W
flux of
coulomb C
displacement
force
newton N
frequency
hertz
Hz
illuminance lux
lx
impedance ohm

−1
C/V
−1
m−2·kg−1·s3·A2
m−2·kg−1·s4·A2
m−2·kg−1·s3·A2
V/A
m2·kg·s−3·A−2
A·s
s·A
A·s
s·A
W/A
m2·kg·s−3·A−1
W/A
m2·kg·s−3·A−1
N·m
J/s
m2·kg·s−2
m2·kg·s−3
A·s
s·A
m·kg·s−2
s−1
m−2·cd·sr
m2·kg·s−3·A−2
luminous flux lumen
magnetic flux weber
magnetic flux
tesla
density
magnetic
tesla
induction
magnetic
tesla
polarization
lm
Wb
kg·m/s2
s−1
lm/m2
V/A
Wb/A
(V·s/A)
cd·sr
V·s
T
Wb/m2
kg·s−2·A−1
T
Wb/m2
kg·s−2·A−1
T
Wb/m2
kg·s−2·A−1
permeance
henry
H
Wb/A
(V·s/A)
m2·kg·s-2·A−2
volt
V
W/A
m2·kg·s−3·A−1
watt
W
J/s
m2·kg·s-3
pascal
Pa
N/m2
m−1·kg·s−2
inductance
potential
difference
power
pressure,
stress
henry
H
m2·kg·s−2·A−2
cd·sr
m2·kg·s-2·A−1
quantity of
electricity
quantity of
heat
reactance
stress
susceptance
weight
work
coulomb C
A·s
s·A
joule
N·m
m2·kg·s−2
V/A
N/m2
−1
kg·m/s2
N·m
m2·kg·s−3·A−2
m−1·kg·s−2
m−2·kg−1·s 3·A2
m·kg·s−2
m2·kg·s−2
J
ohm

pascal Pa
siemens S
newton N
joule
J
Notes to the above table
The expressions in the fourth column represent the definitions of the respective
units in symbolic form. For instance, the quantity force is defined as the product of
mass and acceleration (F = m·a) so the definition of the unit of force, the newton
(N) is given by
1 N = 1 kg·m/s2.
Mechanical energy must not be expressed in newton metres (N·m) but only in
joules (J).
The former unit is used only for torque or moment of force.
In the expressions for the lumen (lm) and lux (lx) in the fifth column, the steradian
(sr) is treated as a base unit.
Table 4. SI derived units expressed in terms of SI derived units with
special names as well as SI based units and SI supplementary units:
Quality
absorbed dose
Name
joul per kilogram
watt per metre squared
coefficient of heat transfer
kelvin
conductivity
siemens per metre
dialectric polarization
coulomb per square metre
displacement
coulomb per square metre
dynamic viscosity
pascal second
electric charge density
coulomb per cubic metre
electric dipole moment
coulomb metre
electric field strength
volt per metre
energy density
joul per cubic metre
entropy
joule per kelvin
exposure (ionizing
coulomb per kilogram
radiation)
heat capacity
joule per kelvin
heat flux density
watt per square metre
magnetic dipole moment weber metre
molar energy
joule per mole
molar entropy
joule per mole kelvin
Expression in terms
of
Symbol
SI Base units and SI
Supplementary units
J/kg
m2·s−2
W/m2·K kg·s−3·K−1
S/m
C/m2
C/m2
Pa·s
C/m3
C·m
V /m
J/m3
J/K
m−3·kg−1·s 3·A2
m−2·s·A
m−2·s·A
m−1·kg·s−1
m-3·s·A
m·s·A
m·kg·s−3·A−1
m-1·kg·s−2
m2·kg·s−2·K−1
C/kg
kg−1·s·A
J/K
m2·kg·s−2·K−1
W /m2 kg·s-3
Wb·m m3·kg·s−2·A−1
J/mol m2·kg·s−2·mol−1
J/mol·K m2·kg·s−2·K -1·mol−1
molar heat capacity
moment of force
permeability
permittivity
radiant intensity
reluctance
resistivity
specific energy
specific entropy
specific heat capacity
specific latent heat
surface charge density
surface tension
thermal conductivity
torque
joule per mole kelvin
newton metre
henry per metre
farad per metre
watt per steradian
1 per henry
ohm metre
joule per kilogram
joule per kilogram kelvin
joule per kilogram kelvin
joule per kilogram
coulomb per square metre
newton per metre
watt per metre kelvin
newton metre
J/mol·K m2·kg·s−2·K -1·mol−1
N·m
m2·kg·s−2
H/m
m·kg·s−2·A−2
F/m
m−3·kg−1·A2
W /sr m2·kg·s−3·srl−1
H−1
m-2·kg−1·s 2·A2
Ω·m
m3·kg·s−3·A−2
J/kg
m2·s−2
J/kg·K m2·s−2·K−1
J/kg·K m2·s−2·K−1
J/kg
m2·s−2
C/m2 m−2·s·A
N/m
kg·s−2
W /m·K m·kg·s-3·K−1
N·m
m2·kg·s−2
Notes to the above table
In the interests of uniformity it is preferable to define, as far as possible, the SI (Systeme
Internationale) derived units in accordance with the combinations given in the above tables. This
does not, however, exclude the possibility of using other equivalent combinations in special cases.
In education, for example, it may be convenient to define electric field strength initially in terms of
the force experienced by unit charge and to use the corresponding unit newton per coulomb (N/C)
instead of volt per metre (V/m).
Note that: 1 V/m = 1 W/A·m = 1 N·m/s·A·m = 1 N/C.
Torque of moment of force should not be expressed in joules (J) but only in newton metres (N·m).
The values of certain so-called dimensionless quantities such as index of refraction, relative
permeability and relative permittivity are expressed as pure numbers. Each of these quantities
does have an SI unit but this consists of the ratio of two identical SI units and thus may be
expressed by the number 1.
SI Derived Units / Abgeleitete SI-Einheiten
English/German
Frequency / Frequenz
hertz: Hz = 1/s
Force / Kraft
newton: N = m kg/s2
Pressure, stress / Druck, mechanische Spannung
pascal: Pa = N/m2= kg/m s2
Energy, work, quantity of heat / Energie, Arbeit, Wärmemenge
joule: J = N m = m2kg/s2
Power, radiant flux / Leistung
watt: W = J/s = m2kg/s3
Quantity of electricity, electric charge / elektrische Ladung
coulomb: C = s A
Electric potential / elektrische Spannung
volt: V = W/A = m2kg/s3 A
Capacitance / Kapazität
farad: F = C/V = s4A2/m2 kg
Electric resistance / elektrischer Widerstand
ohm: Omega = V/A = m2kg/s3 A2
Conductance / elektr.Leitfähigkeit
siemens: S = A/V = s3A2/m2 kg
Magnetic flux / magnetischer Fluss
weber: Wb = V s = m2kg/s2 A
Magnetic flux density, magnetic induction / Magnetische Induktion
tesla: T = Wb/m2 = kg/s2 A
Inductance / Induktivität
henry: H = Wb/A = m2kg/s2 A2
Luminous flux / Lichtstrom
lumen:lm = cd sr
Illuminance / Beleuchtungsstärke
lux:lx = lm/m2 = cd sr/m2
Activity (ionizing radiations) / Radioaktivität
becquerel: Bq = 1/s
Absorbed dose / Absorbierte Strahlendosis
gray: Gy = J/kg = m2/s2
Dynamic viscosity / Dynamische Viskosität
pascal second: Pa s = kg/m s
Moment of force / Drehmoment
meter newton: N m = m2 kg/s2
Surface tension / Oberflächenspannung
newton per meter:N/m = kg/s2
Heat flux density, irradiance / Wärmeflussdichte
watt per squaremeter: W/m2 = kg/s3
Heat capacity, entropy / Wärmekapazität,Entropie
joule per kelvin:J/K = m2 kg/s2 K
Specific heat capacity, specific entropy /Spez. Wärmekapazität, spez. Entropie
joule per kilogramkelvin: J/kg K = m2/s2 K
Specific energy / Spezifische Energie
joule per kilogram:J/kg = m2/s2
Thermal conductivity / Thermische Leitfähigkeit
watt per meterkelvin: W/m K = m kg/s3 K
Energy density / Energiedichte
joule per cubicmeter: J/m3 = kg/m s2
Electric field strength / Elektrische Feldstärke
volt per meter: V/m = m kg/s3 A
Electric charge density / Elektrische Ladungsdichte
coulomb per cubicmeter: C/m3 = s A/m3
Electric displacement, electric flux density /Elektrische Flussdichte
coulomb per squaremeter: C/m2 = s A/m2
Permittivity / Influenz
farad per meter: F/m = s4 A2/m3 kg
Permeability / Permeabilität
henry per meter: H/m = m kg/s2 A2
Molar energy / Molare Energie
joule per mole:J/mol = m2 kg/s2 mol
Molar entropy, molar heat capacity / Molare Entropie, molare Wärmekapazität
joule per molekelvin: J/mol K = m2 kg/s2 K mol
Exposure (ionizing radiations) / Exposition
coulomb per kilogram: C/kg = s A/kg
Absorbed dose rate / Absorbierte Dosisrate
gray per second: Gy/s = m2/s3
cgs Units / cgs-Einheiten
erg
1erg = E-7 J
dyne
1 dyn = E-5 N
poise
1 P = 1 dyn s/cm2 = 0.1 Pa s
stokes
1 St = 1 cm2/s = E-4 m2/s
gauss
1G = E-4 T
oersted
1Oe = (1000/(4∙pi)) A/m
maxwell
1Mx = E-8 Wb
stilb
1sb = 1 cd/cm2 = E4 cd/m2
phot
1ph = E4 lx