4 The Two Classes of SI Units and the SI Prefixes
Since the 1995 edition of this Guide, the 20th CGPM, which met October 9  12, 1995, decided to eliminate the class of supplementary units as a separate unit class in the SI. The SI now consists of only two classes of units: base units and derived units. The radian and steradian, which were the two supplementary units, are now subsumed into the class of SI derived units. Thus the SI units are currently divided into base units and derived units, which together form what is called “the coherent system of SI units.”^{2} The SI also includes the prefixes to form decimal multiples and submultiples of SI units.
Table 1 gives the seven base quantities, assumed to be mutually independent, on which the SI is founded, and the names and
symbols of their respective units, called “SI base units.” Definitions of the SI base units are given in Appendix A.
The kelvin and its
symbol K are also used to express the value of a temperature interval or a temperature
difference (see Sec. 8.5).
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 
Derived units are expressed algebraically in terms of base units or other derived units.
The symbols for derived units are obtained by means of the mathematical operations of multiplication and division.
For example, the derived unit for the derived quantity molar mass (mass divided by amount of substance) is
the kilogram per mole, symbol kg/mol. Additional examples of derived units expressed in terms of SI base units are
given in Table 2. (The rules and style conventions for printing and using SI unit symbols are given in Sec.
6.1.1 to 6.1.8.)
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} 
wavenumber  reciprocal meter  m^{1} 
density, 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 
luminance  candela per square meter  cd/m^{2} 
amountofsubstance concentration  
amount concentration , concentration  mole per cubic meter  mol/m^{3} 
4.2.1 SI coherent derived units with special names and symbols
Certain SI coherent derived units have special names and symbols; these are given in Table 3.
Consistent with the discussion in Sec. 4, the radian and steradian, which are the two former supplementary units,
are included in Table 3. The last four units in Table 3 were introduced into the SI for reasons of safeguarding human health.
SI coherent derived unit ^{(a)}



Special Name  Special symbol 
Expression in terms of other SI units 
Expression in terms of SI base units 

plane angle  radian^{(b)}  rad  1^{(b)}  m/m 
solid angle  steradian^{(b)}  sr^{(c)}  1^{(b)}  
frequency  hertz^{(d)}  Hz  
force  newton  N  
pressure, stress  pascal  Pa  N/m^{2}  
energy, work, amount of heat 
joule  J  N · m  
power, radiant flux  watt  W  J/s  
electric charge, amount of electricity 
coulomb  C  
electric potential difference^{(e)}, electromotive force 
volt  V  W/A  
capacitance  farad  F  C/V  
electric resistance  ohm  Ω  V/A  
electric conductance  siemens  S  A/V  
magnetic flux  weber  Wb  V · s  
magnetic flux density  tesla  T  Wb/m^{2}  kg · s^{2} · A^{1} 
inductance  henry  H  Wb/A  
Celsius temperature  degree Celsius ^{(f)}  °C  K  
luminous flux  lumen  lm  cd · sr^{(c)}  Cd 
illuminance  lux  lx  lm/m^{2}  m^{2}· cd 
activity referred to a radionuclide^{(g)} 
becquerel^{(d)}  Bq  s^{1}  
absorbed dose, specific energy (imparted), kerma 
gray  Gy  J/kg  m^{2}· s^{2} 
dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent 
sievert ^{(h)}  Sv  J/kg  m^{2}· s^{2} 
catalytic activity  katal  kat  s^{1}· mol 
(a) The SI prefixes may be used with any of the special names and symbols, but when this is done the
resulting unit will no longer be coherent. (See Sec. 6.2.8.)
(b) The radian and steradian are special names for the number one that may be
used to convey information about the quantity concerned. In practice the symbols rad
and sr are used where appropriate, but the symbol for the derived unit one is generally
omitted in specifying the values of dimensionless quantities. (See Sec 7.10)
(c) In photometry the name steradian and the symbol sr are usually retained in expressions for units.
(d) The hertz is used only for periodic phenomena, and the becquerel is used only for
stochastic processes in activity referred to a radionuclide.
(e) Electric potential difference is also called “voltage” in the United States.
(f) The degree Celsius is the special name for the kelvin used to express Celsius temperatures.
The degree Celsius and the kelvin are equal in size, so that the numerical value of a temperature difference or
temperature interval is the same when expressed in either degrees Celsius or in kelvins. (See Secs. 4.2.1.1 and 8.5.)
(g) Activity referred to a radionuclide is sometimes incorrectly called radioactivity.
(h) See Refs. [1, 2], on the use of the sievert.
In addition to the quantity thermodynamic temperature (symbol T), expressed in the unit kelvin, use is also made of the quantity Celsius temperature (symbol t) defined by the equation t = T  T_{0} , where T_{0} = 273.15 K by definition. To express Celsius temperature, the unit degree Celsius, symbol °C, which is equal in magnitude to the unit kelvin, is used; in this case, “degree Celsius” is a special name used in place of “kelvin.” An interval or difference of Celsius temperature, however, can be expressed in the unit kelvin as well as in the unit degree Celsius (see Sec. 8.5). (Note that the thermodynamic temperature T_{0} is exactly 0.01 K below the thermodynamic temperature of the triple point of water (see Sec. A.6).)
4.2.2 Use of SI derived units with special names and symbols
Examples of SI derived units that can be expressed with the aid of SI derived units having special names
and symbols are given in Table 4.
SI coherent derived unit



Derived quantity  Name  Symbol  Expression in terms of SI base units 
dynamic viscosity  pascal second  Pa · s  
moment of force  newton meter  N · m  
surface tension  newton per meter  N/m  kg · s^{2} 
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}  kg · s^{3} 
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}  
surface charge density  coulomb per square meter  C/m^{2}  
electric flux density, electric displacement 
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 (χ and γ 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}  m^{3} · s^{1} · mol 
The advantages of using the special names and symbols of SI derived units are apparent in Table 4. Consider, for example, the quantity molar entropy: the unit J/ (mol · K) is obviously more easily understood than its SI baseunit equivalent, m^{2} · kg · s^{2} · K^{1} · mol^{1}. Nevertheless, it should always be recognized that the special names and symbols exist for convenience;either the form in which special names or symbols are used for certain combinations of units or the form in which they are not used is correct. For example, because of the descriptive value implicit in the compoundunit form, communication is sometimes facilitated if magnetic flux (see Table 3) is expressed in terms of the volt second (V · s) instead of the weber (Wb) or the combination of SI base units, m^{2} · kg · s^{2} · A^{1}.
Tables 3 and 4 also show that the values of several different quantities are expressed in the same SI unit. For example, the joule per kelvin (J/K) is the SI unit for heat capacity as well as for entropy. Thus the name of the unit is not sufficient to define the quantity measured.
A derived unit can often be expressed in several different ways through the use of base units and derived units with special names. In practice, with certain quantities, preference is given to using certain units with special names, or combinations of units, to facilitate the distinction between quantities whose values have identical expressions in terms of SI base units. For example, the SI unit of frequency is specified as the hertz (Hz) rather than the reciprocal second (s^{1}), and the SI unit of moment of force is specified as the newton meter (N · m) rather than the joule (J).
Similarly, in the field of ionizing radiation, the SI unit of activity is designated as the becquerel (Bq) rather than the reciprocal second (s^{1}), and the SI units of absorbed dose and dose equivalent are designated as the gray (Gy) and the sievert (Sv), respectively, rather than the joule per kilogram (J/kg).
4.3 Decimal multiples and submultiples of SI units: SI prefixes
Table 5 gives the SI prefixes that are used to form decimal multiples and submultiples of units. They allow very large or very small numerical values (see Sec. 7.1) to be avoided. A prefix name attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit. For example, one kilometer, 1 km, is equal to one thousand meters, 1000 m or 103 m. When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent. (See footnote 2 for a brief discussion of coherence.) The rules and style conventions for printing and using SI prefixes are given in Secs. 6.2.1 to 6.2.8. The special rule for forming decimal multiples and submultiples of the unit of mass is given in Sec. 6.2.7
Factor  Prefix  Symbol  Factor  Prefix  Symbol  



10^{24}=(10^{3})^{8}  yotta  Y    10^{1}  deci  d 
10^{21}=(10^{3})^{7}  zetta  Z    10^{2}  centi  c 
10^{18}=(10^{3})^{6}  exa  E    10^{3}=(10^{3})^{1}  milli  m 
10^{15}=(10^{3})^{5}  peta  P    10^{6}=(10^{3})^{2}  micro  μ 
10^{12}=(10^{3})^{4}  tera  T    10^{9}=(10^{3})^{3}  nano  n 
10^{9}=(10^{3})^{3}  giga  G    10^{12}=(10^{3})^{4}  pico  p 
10^{6}=(10^{3})^{2}  mega  M    10^{15}=(10^{3})^{5}  femto  f 
10^{3}=(10^{3})^{1}  kilo  k    10^{18}=(10^{3})^{6}  atto  a 
10^{2}  hecto  h    10^{21}=(10^{3})^{7}  zepto  z 
10^{1}  deka  da    10^{24}=(10^{3})^{8}  yocto  y 

Note: Alternative definitions of the SI prefixes and their symbols are not permitted. For example, it is unacceptable to use kilo (k) to represent 2^{10} = 1024, mega (M) to represent 2^{20} = 1 048 576, or giga (G) to represent 2^{30} = 1 073 741 824. See the note to Ref. [5] on page 74 for the prefixes for binary powers adopted by the IEC.