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For
ease of understanding and convenience, 22 SI derived units have been given
special names and symbols, as shown in Table 3.
Table 3. SI derived units with special names and symbols
|
|
SI derived unit
|
Derived quantity |
Name |
Symbol |
Expression in terms of other SI units |
Expression in terms of SI base units |
plane angle |
radian (a) |
rad |
- |
m·m-1 = 1 (b) |
solid angle |
steradian (a) |
sr (c) |
- |
m2·m-2 = 1 (b) |
frequency |
hertz |
Hz |
- |
s-1 |
force |
newton |
N |
- |
m·kg·s-2 |
pressure, stress |
pascal |
Pa |
N/m2 |
m-1·kg·s-2 |
energy, work, quantity of heat |
joule |
J |
N·m |
m2·kg·s-2 |
power, radiant flux |
watt |
W |
J/s |
m2·kg·s-3 |
electric charge, quantity of electricity |
coulomb |
C |
- |
s·A |
electric potential difference,
electromotive force |
volt |
V |
W/A |
m2·kg·s-3·A-1 |
capacitance |
farad |
F |
C/V |
m-2·kg-1·s4·A2 |
electric resistance |
ohm |
![Omega](https://webarchive.library.unt.edu/web/20080916081904im_/http://physics.nist.gov/cuu/Images/Omega.gif) |
V/A |
m2·kg·s-3·A-2 |
electric conductance |
siemens |
S |
A/V |
m-2·kg-1·s3·A2 |
magnetic flux |
weber |
Wb |
V·s |
m2·kg·s-2·A-1 |
magnetic flux density |
tesla |
T |
Wb/m2 |
kg·s-2·A-1 |
inductance |
henry |
H |
Wb/A |
m2·kg·s-2·A-2 |
Celsius temperature |
degree Celsius |
°C |
- |
K |
luminous flux |
lumen |
lm |
cd·sr (c) |
m2·m-2·cd = cd |
illuminance |
lux |
lx |
lm/m2 |
m2·m-4·cd = m-2·cd |
activity (of a radionuclide) |
becquerel |
Bq |
- |
s-1 |
absorbed dose, specific energy (imparted), kerma |
gray |
Gy |
J/kg |
m2·s-2 |
dose equivalent (d) |
sievert |
Sv |
J/kg |
m2·s-2 |
catalytic activity |
katal |
kat |
|
s-1·mol |
(a) The radian
and steradian may be used advantageously in expressions for derived
units to distinguish between quantities of a different nature but
of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where
appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit
symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient
dose equivalent, directional dose equivalent, personal dose equivalent,
and organ equivalent dose. |
|
For a graphical illustration of how the 22 derived units with special names
and symbols given in Table 3 are related to the seven SI base units, see
relationships among SI units.
Note on degree Celsius.
The derived unit in Table 3 with the special name degree Celsius and
special symbol °C deserves comment. Because of the way temperature
scales used to be defined, it remains common practice to express a thermodynamic
temperature, symbol T, in terms of its difference from the reference
temperature T0 = 273.15 K, the ice point. This temperature
difference is called a Celsius temperature, symbol t, and is
defined by the quantity equation
t= T- T0.
The unit of Celsius temperature is the degree Celsius, symbol °C. The
numerical value of a Celsius temperature t expressed in degrees
Celsius is given by
t/°C = T/K - 273.15.
It follows from the definition of t that the degree Celsius is equal
in magnitude to the kelvin, which in turn implies that the numerical
value of a given temperature difference or temperature interval whose
value is expressed in the unit degree Celsius (°C) is equal to the
numerical value of the same difference or interval when its value is
expressed in the unit kelvin (K). Thus, temperature differences or temperature
intervals may be expressed in either the degree Celsius or the kelvin
using the same numerical value. For example, the Celsius temperature
difference t
and the thermodynamic temperature difference T
between the melting point of gallium and the triple point of water may
be written as t
= 29.7546 °C = T
= 29.7546 K.
The special names and symbols of the 22 SI derived units with special names and symbols
given in Table 3 may themselves be included in the names and symbols of
other SI derived units, as shown in Table 4.
Table 4. Examples of SI derived units whose names and symbols
include SI derived units with special names and symbols
|
|
SI derived unit
|
Derived quantity |
Name |
Symbol |
dynamic viscosity |
pascal second |
Pa·s |
moment of force |
newton meter |
N·m |
surface tension |
newton per meter |
N/m |
angular velocity |
radian per second |
rad/s |
angular acceleration |
radian per second squared |
rad/s2 |
heat flux density, irradiance |
watt per square meter |
W/m2 |
heat capacity, entropy |
joule per kelvin |
J/K |
specific heat capacity, specific entropy |
joule per kilogram kelvin |
J/(kg·K) |
specific energy |
joule per kilogram |
J/kg |
thermal conductivity |
watt per meter kelvin |
W/(m·K) |
energy density |
joule per cubic meter |
J/m3 |
electric field strength |
volt per meter |
V/m |
electric charge density |
coulomb per cubic meter |
C/m3 |
electric flux density |
coulomb per square meter |
C/m2 |
permittivity |
farad per meter |
F/m |
permeability |
henry per meter |
H/m |
molar energy |
joule per mole |
J/mol |
molar entropy, molar heat capacity |
joule per mole kelvin |
J/(mol·K) |
exposure (x and
rays) |
coulomb per kilogram |
C/kg |
absorbed dose rate |
gray per second |
Gy/s |
radiant intensity |
watt per steradian |
W/sr |
radiance |
watt per square meter steradian |
W/(m2·sr) |
catalytic (activity) concentration |
katal per cubic meter |
kat/m3 |
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