SI Derived Units
 SI DERIVED UNITS.  
Reference tables.
Four Tables of SI DERIVED UNITS
momentum radioactivity disintergration rate rotational frequency specific volume wave number tension thermal conductivity torque
go to [ Table 2 ][ Table 3 ][ Table 4 ][ return to SI metric home page ]
admittance lar entropy moment of force permeability permittivity radiant intensity reluctance resistivity surface
Table 1. SI DERIVED UNITS EXPRESSED IN TERMS OF SI BASE UNITS AND SI SUPPLEMENTARY UNITS
QUANTITY
NAME
SYMBOL
acceleration metre per second squared m/s
angular acceleration radian per second squared rad/s
angular momentum kilogram metre squared per second kgm/s
angular velocity radian per second rad/s
area square metre m
cfficient of linear expansion 1 per kelvin K
concentration (of amount of substance) mole per cubic metre mol/m
density kilogram per cubic metre kg/m
diffusion cfficient metre squared per second m/s
electric current density ampere per square metre A/m
exposure rate (ionising radiation) ampere per kilogram A/kg
kinematic viscosity metre squared per second m/s
luminance candela per square metre cd/m
magnetic field strength ampere per metre A/m
magnetic moment ampere metre squared Am
mass flow rate kilogram per second kg/s
mass per unit area kilogram per square metre kg/m
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 m/mol
moment of inertia kilogram metre squared kgm
moment of momentum kilogram metre squared per second kgm/s
momentum kilogram metre per second kgm/s
radioactivity (disintergration rate) 1 per second s
rotational frequency 1 per second s
specific volume cubic metre per kilogram m/kg
speed metre per second m/s
velocity metre per second m/s
volume cubic metre m
wave number 1 per metre m
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Table 2. SI SUPPLIMENTARY UNITS
QUANTITY
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.
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Table 3. SI 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 ohm mkgsA
capacitance farad F C / V mkgs^4A
conductance siemens S ohm mkgsA
electrical resistance ohm ohm V / A mkgsA
electric charge coulomb C As sA
electric flux coulomb C As sA
electric potential volt V W / A mkgsA
electromotive force volt V W / A mkgsA
energy joule J Nm mkgs
energy flux watt W J/s mkgs
flux of displacement coulomb C As sA
force newton N kgm/s mkgs
frequency hertz Hz s s
illuminance lux lx lm/m mcdsr
impedance ohm ohm V / A mkgsA
inductance henry H Wb/A (Vs/A) mkgsA
luminous flux lumen lm cdsr cdsr
magnetic flux weber Wb Vs mkgsA
magnetic flux density tesla T Wb/m kgsA
magnetic induction tesla T Wb/m kgsA
magnetic polarization tesla T Wb/m kgsA
permeance henry H Wb/A (Vs/A) mkgsA
potential difference volt V W / A mkgsA
power watt W J/s mkgs
pressure pascal Pa N/m mkgs
quantity of electricity coulomb C As sA
quantity of heat joule J Nm mkgs
reactance ohm ohm V / A mkgsA
stress pascal Pa N/m mkgs
susceptance siemens S ohm mkgsA
weight newton N kgm/s mkgs
work joule J Nm mkgs
NOTES to ABOVE TABLE:
The expressions in the fourth coulumn 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=ma) so the definition of the unit of force, the newton (N) is given by 1 N = 1 kgm/s
Mechanical energy must not be expressed in newton metres (Nm) 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.
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Table 4. SI DERIVED UNITS EXPRESSED IN TERMS OF SI DERIVED UNITS WITH SPECIAL NAMES AS WELL AS SI BASE UNITS AND SI SUPPLEMENTARY UNITS (ie. the lot!)
QUANTITY
NAME
SYMBOL
Expression in terms of SI Base units and SI Supplementary units
absorbed dose joul per kilogram J/kg ms
cfficient of heat transfer watt per metre squared kelvin W/mK kgsK
conductivity siemens per metre S/m mkgsA
dialectric polarization coulomb per square metre C/m msA
displacement coulomb per square metre C/m msA
dynamic viscosity pascal second Pas mkgs
electric charge density coulomb per cubic metre C/m msA
electric dipole moment coulomb metre Cm msA
electric field strength volt per metre V /m mkgsA
energy density joul per cubic metre J/m mkgs
entropy joule per kelvin J/K mkgsK
exposure (ionizing radiation) coulomb per kilogram C/kg kgsA
heat capacity joule per kelvin J/K mkgsK
heat flux density watt per square metre W /m kgs
magnetic dipole moment weber metre Wbm mkgsA
molar energy joule per mole J/mol mkgsmol
molar entropy joule per mole kelvin J/molK mkgsKmol
molar heat capacity joule per mole kelvin J/molK mkgsKmol
moment of force newton metre Nm mkgs
permeability henry per metre H/m mkgsA
permittivity farad per metre F/m mkgs^4A
radiant intensity watt per steradian W /sr mkgssrl
reluctance 1 per henry H mkgsA
resistivity ohm metre ohmm mkgsA
specific energy joule per kilogram J/kg ms
specific entropy joule per kilogram kelvin J/kgK msK
specific heat capacity joule per kilogram kelvin J/kgK msK
specific latent heat joule per kilogram J/kg ms
surface charge density coulombe per square metre C/m msA
surface tension newton per metre N/m kgs
thermal conductivity watt per metre kelvin W /mK mkgsK
torque newton metre Nm mkgs
NOTES to the ABOVE TABLE:
In the interests of uniformity it is preferable to define, as far as possible, the SI 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/Am = 1 Nm/sAm = 1 N/C.

Torque of moment of force should not be expressed in joules (J) but only in newton metres (Nm)

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.
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