The data presented here is derived from publications of
NIST, so it is in the public domain. However, this HTML
implementation is not in the public domain. It is provided to make for easier access.
SI Base Units The SI is founded on seven
SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.
Other quantities,
called
derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The
SI derived units for these derived quantities are obtained from these equations and the seven SI base units.
Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities
of dimension 1 such as mass fraction is generally omitted.
Table 2. Examples of SI derived
units
SI derived unit
Derived quantity
Name
Symbol
area
square meter
m^{2}
volume
cubic meter
m^{3}
speed, velocity
meter per second
m/s
acceleration
meter per second squared
m/s^{2}
wave number
reciprocal meter
m^{1}
mass density
kilogram per cubic meter
kg/m^{3}
specific volume
cubic meter per kilogram
m^{3}/kg
current density
ampere per square meter
A/m^{2}
magnetic field strength
ampere per meter
A/m
amountofsubstance concentration
mole per cubic meter
mol/m^{3}
luminance
candela per square meter
cd/m^{2}
mass fraction
kilogram per kilogram, which may be represented by the number 1
kg/kg = 1
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)}

m^{2}·m^{2 }= 1 ^{(b)}
frequency
hertz
Hz

s^{1}
force
newton
N

m·kg·s^{2}
pressure, stress
pascal
Pa
N/m^{2}
m^{1}·kg·s^{2}
energy, work, quantity of heat
joule
J
N·m
m^{2}·kg·s^{2}
power, radiant flux
watt
W
J/s
m^{2}·kg·s^{3}
electric charge, quantity of electricity
coulomb
C

s·A
electric potential difference, electromotive force
volt
V
W/A
m^{2}·kg·s^{3}·A^{1}
capacitance
farad
F
C/V
m^{2}·kg^{1}·s^{4}·A^{2}
electric resistance
ohm
V/A
m^{2}·kg·s^{3}·A^{2}
electric conductance
siemens
S
A/V
m^{2}·kg^{1}·s^{3}·A^{2}
magnetic flux
weber
Wb
V·s
m^{2}·kg·s^{2}·A^{1}
magnetic flux density
tesla
T
Wb/m^{2}
kg·s^{2}·A^{1}
inductance
henry
H
Wb/A
m^{2}·kg·s^{2}·A^{2}
Celsius temperature
degree Celsius
°C

K
luminous flux
lumen
lm
cd·sr ^{(c)}
m^{2}·m^{2}·cd = cd
illuminance
lux
lx
lm/m^{2}
m^{2}·m^{4}·cd = m^{2}·cd
activity (of a radionuclide)
becquerel
Bq

s^{1}
absorbed dose, specific energy (imparted), kerma
gray
Gy
J/kg
m^{2}·s^{2}
dose equivalent ^{(d)}
sievert
Sv
J/kg
m^{2}·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 T_{0 }=
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 T_{0}.
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
RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling
2 MB. Its primary purpose was to provide me with ready access to commonly needed
formulas and reference material while performing my work as an RF system and circuit
design engineer. The World Wide Web (Internet) was largely an unknown entity at
the time and bandwidth was a scarce commodity. Dialup modems blazed along at 14.4 kbps
while typing up your telephone line, and a nice lady's voice announced "You've Got
Mail" when a new message arrived...
All trademarks, copyrights, patents, and other rights of ownership to images
and text used on the RF Cafe website are hereby acknowledged.