The International System of Units
Base Units
The International System of Units (Systeme International d'Unites, with the international
abbreviation SI), is the modern version of the metric system adopted by the General
Conference of Weights and measures in 1960. It has seven independent base units.
meter (metre), m: The meter is the length of the path traveled by light in vacuum during a
time interval of 1/299792458 of a second.
kilogram, kg: The kilogram is the unit of mass; it is equal to the mass of the international
prototype of the kilogram.
second, s: The second is the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the ground state of the
cesium-133 atom.
ampere, A: The ampere is the constant current which, if maintained in two straight parallel
conductors of infinite length, of negligible circular cross section, and place 1 meter apart in
vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per
meter of length.
kelvin, K: The kelvin, the unit of thermodynamic temperature, is the fraction 1/273.16 of
the thermodynamic temperature of the triple point of water. The unit kelvin and its symbol,
K, should be used to express both the thermodynamic temperature and an interval or a
difference of temperature. Just say "kelvin", not "degrees kelvin".
mole, mol: The mole is the amount of substance of a system which contains as many
elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is
used, the elementary entities must be specific and may be atoms, molecules, ions, electrons,
other particles, or specified groups of such particles.
candela. cd: The candela is the luminous intensity, in a given direction, of a source that
emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity
in that direction of 1/683 watts per steradian.
From The Physics Quick Reference Guide by E. Richard Cohen. AIP press, 1996.
Table 1. Prefixes used in SI. These prefixes are used to indicate multiples or submultiples of
the base unit, except that units for mass are formed by applying the prefix to the symbol g:
i.e., Mg not kkg and mg not μkg. Only a single prefix is permitted. Use ns rather than mμs.
The first syllable of the prefix retains its stress in compounds; thus, preferred pronunciations
are kil' oh-mee-ter and mic' roh-mee-ter, not kil-lom' e-ter or mi-crom' e-ter.
Factor
101
102
103
106
109
1012
1015
1018
1021
1024
Prefix
deka
hecto
kilo
mega
giga
tera
peta
exa
zetta
yotta
Symbol
da
h
k
M
G
T
P
E
Z
Y
Factor
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
Prefix
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
Symbol
d
c
m
μ
n
p
f
a
z
y
Derived Units
By combining SI base units, it is possible to derive all other units. A derived unit
may correspond to more than one physical quantity, but a give physical quantity, although it
may be expressed in terms of different units or different equivalent names for the same unit,
has a unique dimension and a unique coherent unit within SI. Several of the most
commonly used derived units of SI have been given special names.
becquerel, Bq: activity of a radionuclide decaying at the rate of 1 transition per second;
coulomb, C: quantity of electricity carried in one second by a current of 1 ampere
farad, F: capacitance of a capacitor between the plates of which there appears a potential
difference of 1 volt when it is charged by a quantity of electricity of 1 coulomb;
gray, G: absorbed dose when 1 joule is imparted per kilogram of matter by ionizing
radiation;
henry, H: inductance of a closed circuit in which electromotive force of 1 volt is produced
when the electric current in the circuit varies uniformly at the rate of 1 ampere per second;
hertz, Hz: frequency of a periodic phenomenon, the period of which is 1 second;
joule, J: work done when the point of application of a force of 1 newton moves a distance
of 1 meter in the direction of the force;
newton, N: force that gives to a mass of 1 kilogram an acceleration of 1 meter per second
squared.
ohm, Ω: electric resistance between two points of a conductor (not being the seat of any
electromotive force) when a constant potential difference of 1 volt, applied to these points,
produces in the conductor a current of 1 ampere;
pascal, Pa: pressure or stress of 1 newton per square meter;
tesla, T: magnetic flux density given by a magnetic flux of 1 weber per square meter;
volt, V: difference of electrical potential between two points of a conducting wire carrying
a current of 1 ampere when the power dissipated is 1 watt;
watt, W: power that, in 1 second, gives rise to energy of 1 joule.
weber, Wb: magnetic flux that, linking a circuit of 1 turn, would produce in it an
electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.
Table 2: Derived SI units with special names.
Quantity
Name
Frequency
Force
Pressure
Energy, work,
quantity of heat
Power, radiant flux
Quantity of electricity,
electric charge
Potential difference,
electric potential,
electromotive force
Capacitance
Electric resistance
Magnetic flux
Magnetic flux density,
magnetic field
Inductance
hertz
newton
pascal
joule
Symbol Expression in
terms of basic
units
Hz
sec-1
N
kg•m/s2
Pa
kg/m•s2
J
m2•kg/s2
Expression in
terms of
derived units
J/m
N/m2, J/m3
N•m
watt
W
coulomb C
m2•kg/s3
A•s
J/s
volt
V
m2•kg/s3•A
W/A, J/C
farad
ohm
weber
tesla
F
Wb
T
s4•A2/m2•kg
m2•kg/s3•A2
m2•kg/s2•A
kg/s2•A
C/V
V/A
V•s
Wb/m2
henry
H
m2•kg/s2•A2
Wb/A
Ω