
SI Base Units & Derived Units


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NIST, so it is in the public domain. However, this HTML
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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.
Table 1. SI base units


SI base unit

Base quantity 
Name 
Symbol 
length 
meter 
m 
mass 
kilogram 
kg 
time 
second 
s 
electric current 
ampere 
A 
thermodynamic temperature 
kelvin 
K 
amount of substance 
mole 
mol 
luminous intensity 
candela 
cd 


For detailed information on the SI base units, see
Definitions of the SI base units and
their
Historical context.
SI Derived Units
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


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/s^{2} 
heat flux density, irradiance 
watt per square meter 
W/m^{2} 
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/m^{3} 
electric field strength 
volt per meter 
V/m 
electric charge density 
coulomb per cubic meter 
C/m^{3} 
electric flux density 
coulomb per square meter 
C/m^{2} 
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/(m^{2}·sr) 
catalytic (activity) concentration 
katal per cubic meter 
kat/m^{3} 



