SI derived units - supplementary units and notes - sengpielaudio
SI derived Units
Table 1. SI derived units expressed in terms of
SI based units and SI supplementary units
Quantity Name Symbol
acceleration metre per second squared m/s2
angular acceleration radian per second squared rad/s2
angular momentum kilogram metre squared per second kg·m2/s
angular velocity radian per second rad/s
area square metre m2
coefficient of linear expansion 1 per kelvin K−1
concentration (of amount of substance) mole per cubic metre mol/m3
density kilogram per cubic metre kg/m3
diffusion coefficient metre squared per second m2/s
electric current density ampere per square metre A/m2
exposure rate (ionizing radiation) ampere per kilogram A/kg
cinematic viscosity metre squared per second m2/s
luminance candela per square metre cd/m2
magnetic field strength ampere per metre A/m
magnetic moment ampere metre squared A·m2
mass flow rate kilogram per second kg/s
mass per unit area kilogram per square metre kg/m2
mass per unit length kilogram per metre kg/m
molality mole per kilogram mol/kg
molar mass kilogram per mole kg/mol
molar volume cubic metre per mole m3/mol
moment of inertia kilogram metre squared kg·m2
moment of momentum kilogram metre squared per second  kg·m2/s
momentum kilogram metre per second kg·m/s
radioactivity (disintegration rate) 1 per second s−1
rotational frequency 1 per second s−1
specific volume cubic metre per kilogram m3/kg
speed metre per second m/s
velocity metre per second m/s
volume cubic metre m3
wave number 1 per metre m−1

Table 2. SI supplementary units

Quality Name Symbol Definition
plane angle radian rad 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
solid angle steradian sr 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 with sides of length equal to the radius of the sphere.

Table 3. Derived units with special names

Quantity Name Symbol Expression in terms
of other SI units and
definition of unit.
Expression in terms
of SI Base units
admittance siemens S W−1 m−2·kg−1·s3·A2
capacitance farad F C / V m−2·kg−1·s4·A2
conductance siemens S W−1 m−2·kg−1·s3·A2
electrical resistance ohm W V / A m2·kg·s−3·A−2
electric charge coulomb C A·s s·A
electric flux coulomb C A·s s·A
electric potential volt V W / A m2·kg·s−3·A−1
electromotive force volt V W / A m2·kg·s−3·A−1
energy joule J N·m m2·kg·s−2
energy flux watt W J/s m2·kg·s−3
flux of displacement coulomb C A·s s·A
force newton N kg·m/s2 m·kg·s−2
frequency hertz Hz s−1 s−1
illuminance lux lx lm/m2 m−2·cd·sr
impedance ohm W V / A m2·kg·s−3·A−2
inductance henry H Wb/A (V·s/A) m2·kg·s−2·A−2
luminous flux lumen lm cd·sr cd·sr
magnetic flux weber Wb V·s m2·kg·s-2·A−1
magnetic flux density tesla T Wb/m2 kg·s−2·A−1
magnetic induction tesla T Wb/m2 kg·s−2·A−1
magnetic polarization tesla T Wb/m2 kg·s−2·A−1
permeance henry H Wb/A (V·s/A) m2·kg·s-2·A−2
potential difference volt V W / A m2·kg·s−3·A−1
power watt W J/s m2·kg·s-3
pressure, stress pascal Pa N/m2 m−1·kg·s−2
quantity of electricity coulomb C A·s s·A
quantity of heat joule J N·m m2·kg·s−2
reactance ohm W V / A m2·kg·s−3·A−2
stress pascal Pa N/m2 m−1·kg·s−2
susceptance siemens S W−1 m−2·kg−1·s 3·A2
weight newton N kg·m/s2 m·kg·s−2
work joule J N·m m2·kg·s−2

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 Name Symbol Expression in terms of
SI Base units and SI
Supplementary units
absorbed dose joul per kilogram J/kg m2·s−2
coefficient of heat transfer watt per metre squared kelvin W/m2·K kg·s−3·K−1
conductivity siemens per metre S/m m−3·kg−1·s 3·A2
dialectric polarization coulomb per square metre C/m2 m−2·s·A
displacement coulomb per square metre C/m2 m−2·s·A
dynamic viscosity pascal second Pa·s m−1·kg·s−1
electric charge density coulomb per cubic metre C/m3 m-3·s·A
electric dipole moment coulomb metre C·m m·s·A
electric field strength volt per metre V /m m·kg·s−3·A−1
energy density joul per cubic metre J/m3 m-1·kg·s−2
entropy joule per kelvin J/K m2·kg·s−2·K−1
exposure (ionizing radiation) coulomb per kilogram C/kg kg−1·s·A
heat capacity joule per kelvin J/K m2·kg·s−2·K−1
heat flux density watt per square metre W /m2 kg·s-3
magnetic dipole moment weber metre Wb·m m3·kg·s−2·A−1
molar energy joule per mole J/mol m2·kg·s−2·mol−1
molar entropy joule per mole kelvin J/mol·K m2·kg·s−2·K -1·mol−1
molar heat capacity joule per mole kelvin J/mol·K m2·kg·s−2·K -1·mol−1
moment of force newton metre N·m m2·kg·s−2
permeability henry per metre H/m m·kg·s−2·A−2
permittivity farad per metre F/m m−3·kg−1·A2
radiant intensity watt per steradian W /sr m2·kg·s−3·srl−1
reluctance 1 per henry H−1 m-2·kg−1·s 2·A2
resistivity ohm metre Ω·m m3·kg·s−3·A−2
specific energy joule per kilogram J/kg m2·s−2
specific entropy joule per kilogram kelvin J/kg·K m2·s−2·K−1
specific heat capacity joule per kilogram kelvin J/kg·K m2·s−2·K−1
specific latent heat joule per kilogram J/kg m2·s−2
surface charge density coulomb per square metre C/m2 m−2·s·A
surface tension newton per metre N/m kg·s−2
thermal conductivity watt per metre kelvin W /m·K m·kg·s-3·K−1
torque newton metre 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

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

1erg = E-7 J
1 dyn = E-5 N
1 P = 1 dyn s/cm2 = 0.1 Pa s
1 St = 1 cm2/s = E-4 m2/s
1G = E-4 T
1Oe = (1000/(4pi)) A/m
1Mx = E-8  Wb
1sb = 1 cd/cm2  = E4 cd/m2
1ph = E4 lx

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