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
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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 |
 ¯¹ |
m¯²•kg¯¹•s³•A² |
| capacitance |
farad |
F |
C / V |
m¯²•kg¯¹•s^4•A² |
| conductance |
siemens |
S |
¯¹ |
m¯²•kg¯¹•s³•A² |
| electrical resistance |
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 |
|
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 |
|
V / A |
m²•kg•s¯³•A¯² |
| stress |
pascal |
Pa |
N/m² |
m¯¹•kg•s¯² |
| susceptance |
siemens |
S |
¯¹ |
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 |
•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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1][Table 2][Table 3][Table
4] |
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