Derived units - angular acceleration momentum velocity coefficient linear expansion concentration density diffusion electric current density exposure rate ionising radiation kinematic viscosity luminance
capacitance conductance electromotive force energy flux illuminance inductance impedance luminous flux permeance potential difference reactance stress susceptance absorbed dose conductivity dialectric

 SI DERIVED UNITS.  
Reference tables.

polarization displacement dynamic viscosity electric charge density dipole moment field strength entropy exposure heat flux density magnetic dipole moment momagnetic field strength moment molality molar mass moment of inertia
Four Tables of SI DERIVED UNITS
momentum radioactivity disintergration rate rotational frequency specific volume wave number tension thermal conductivity torque
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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/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
cœfficient 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 cœfficient metre squared per second m²/s
electric current density ampere per square metre A/m²
exposure rate (ionising radiation) ampere per kilogram A/kg
kinematic 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 (disintergration 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
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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 m¯²•kg¯¹•s³•A²
capacitance farad F C / V m¯²•kg¯¹•s^4•A²
conductance siemens S ohm m¯²•kg¯¹•s³•A²
electrical resistance ohm ohm 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 ohm 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 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 ohm V / A m²•kg•s¯³•A¯²
stress pascal Pa N/m² m¯¹•kg•s¯²
susceptance siemens S ohm m¯²•kg¯¹•s³•A²
weight newton N kg•m/s² m•kg•s¯²
work joule J N•m m²•kg•s¯²
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=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.
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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 m²•s¯²
cœfficient 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•s³•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•s^4•A²
radiant intensity watt per steradian W /sr m²•kg•s¯³•srl¯¹
reluctance 1 per henry H¯¹ m¯²•kg¯¹•s²•A²
resistivity ohm metre ohm •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 coulombe 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 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.
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