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SI - INTERNATIONAL SYSTEM OF UNITS

The name Système International d'Unités, (International System of Units) and the abbreviation SI, were established by the 11th General Conference on Weights and Measures (CGPM) in 1960.

The base quantities used in the SI are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The base quantities are by convention assumed to be independent. The corresponding base units of the SI were chosen by the CGPM to be the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. The derived units of the SI are then formed as products of powers of the base units, according to the algebraic relations that define the corresponding derived quantities in terms of the base quantities. When the product of powers includes no numerical factor other than one, the derived units are called coherent derived units.

Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets. Note that symbols for quantities are only recommendations, in contrast to symbols for units whose style and form is mandatory.

The value of a quantity is expressed as the product of a number and a unit, and the number multiplying the unit is the numerical value of the quantity expressed in that unit. The numerical value of a quantity depends on the choice of unit. Thus the value of a particular quantity is independent of the choice of unit, although the numerical value will be different for different units. The same value of a speed v = dx/dt of a particle might be given by either of the expressions v = 25 m/s = 90 km/h, where 25 is the numerical value of the speed in the unit metres per second, and 90 is the numerical value of the speed in the unit kilometres per hour.

 

 

 

SI base units

Base quantity SI base unit
Name of base quantity Symbol Name of SI base unit Symbol
length l, x, r, etc. metre m
mass m kilogram kg
time, duration t second s
electric current I, i ampere A
thermodynamic temperature T kelvin K
amount of substance n mole mol
luminous intensity Iv candela cd

 

 

Examples of coherent derived units in the SI expressed in terms of base units

Derived quantity SI coherent derived unit
Name Symbol Name Symbol
area A square metre m2
volume V cubic metre m3
speed, velocity v metre per second m s-1
acceleration a metre per second squared m s-2
wavenumber σ reciprocal metre m-1
density, mass density ρ kilogram per cubic metre kg m-3
surface density ρA kilogram per square metre kg m-2
specific volume v cubic metre per kilogram m3kg-1
current density j ampere per square metre A m-2
magnetic field strength H ampere per metre A m-1
amount concentration, concentration c mole per cubic metre mol m-3
mass concentration ρ, γ kilogram per cubic metre kg m-3
luminance Lv candela per square metre cd m-2
refractive index n (the number) one 1
relative permeability μr (the number) one 1

 

 

Coherent derived units in the SI with special names and symbols

  SI coherent derived unit
Derived quantity Name Symbol Expressed in terms of other SI units Expressed in terms of SI base units
plane angle radian rad 1 m m-1
solid angle steradian sr 1 m2 m-2
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, amount of heat joule J N m m2 kg s-2
power, radiant flux watt W J/s m2 kg s-3
electric charge, amount 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 Ω 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 cd
luminance lux lx lm/m2 m-2 cd
activity referred to a radionuclide becquerel Bq   s-1
absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2 s-2
dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent sievert Sv J/kg m2 s-2
catalytic activity katal kat   s-1 mol

 

 

Examples of SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols

  SI coherent derived unit
Derived quantity Name Symbol Expressed in terms of SI base units
dynamic viscosity pascal second Pa s m-1 kg s-1
moment of force newton metre N m m2 kg s-2
surface tension newton per metre N/m kg s-2
angular velocity radian per second rad/s m m-1 s-1 = s-1
angular acceleration radian per second squared rad/s2 m m-1 s-2 = s-2
heat flux density, irradiance watt per square metre W/m2 kg s-3
heat capacity, entropy joule per kelvin J/K m2 kg s-2 K-1
specific heat capacity, specific entropy joule per kilogram kelvin J/(kg K) m2 s-2 K-1
specific energy joule per kilogram J/kg m2 s-2
thermal conductivity watt per metre kelvin W/(m K) m kg s-3 K-1
energy density joule per cubic metre J/m3 m -1 kg s-2
electric field strength volt per metre V/m m kg s-3 A-1
electric charge density coulomb per cubic metre C/m3 m-3 s A
surface charge density coulomb per square metre C/m2 m-2 s A
electric flux density, electric displacement coulomb per square metre C/m2 m-2 s A
permittivity farad per metre F/m m-3 kg-1 s4 A2
permeability henry per metre H/m m kg s-2 A-2
molar energy joule per mole J/mol m2 kg s-2 mol-1
molar entropy, molar heat capacity joule per mole kelvin J/(mol K) m2 kg s-2 K-1 mol-1
exposure (x- and γ-rays) coulomb per kilogram C/kg kg-1 s A
absorbed dose rate gray per second Gy/s m2 s-3
radiant intensity watt per steradian W/sr m4 m-2 kg s-3 = m2 kg s-3
radiance watt per square metre steradian W/(m2 sr) m2 m-2 kg s-3 = kg s-3
catalytic activity concentration katal per cubic metre kat/m3 m-3 s-1 mol

 

 

Non-SI units accepted for use with the International System of Units

Quantity Name of unit Symbol for unit Value in SI units
time, duration minute min 1 min = 60 s
  hour h 1 h = 60 min = 3 600 s
  day d 1 d = 24 h = 86 400 s
plane angle degree ° 1° = (π/180) rad
  minute ' 1' = (1/60)° = (π/10 800) rad
  second " 1" = (1/60)' = (π/648 000) rad
area hectare ha 1 ha = 1hm2 = 104 m2
volume litre L, l 1 L = 1 dm3 = 10-3 m3
mass tonne t 1 t = 103 kg

 

 

Non-SI units whose values in SI units must be obtained experimentally

Quantity Name of unit Symbol for unit Value in SI units
Units accepted for use with the SI
   energy electronvolt eV 1 eV = 1.602 176 53(14)×10-19 J
   mass dalton, Da 1 Da = 1.660 538 86(28)×10-27 kg
  unified atomic mass unit u 1 u = 1 Da
   length astronomical unit ua 1 ua = 1.495 978 706 91(6)×1011 m
Natural units (n.u.)
   speed, velocity natural unit of speed (speed of light in vacuum) co 299 792 458 m s-1
   action natural unit of action (reduced Planck constant) ℏ 1.054 571 68(18)×10-34 Js
   mass natural unit of mass (electron mass) me 9.109 382 6(16)×10-31 kg
   time, duration natural unit of time ℏ/(meco2) 1.288 088 667 7(86)×10-21 s
Atomic units (a.u.)
   charge atomic unit of charge, (elementary charge) e 1.602 176 53(14)×10-19 C
   mass atomic unit of mass, (electron mass) me 9.109 382 6(16)×10-31 kg
   action atomic unit of action, (reduced Planck constant) ℏ 1.054 571 68(18)×10-34 Js
   length atomic unit of length, bohr (Bohr radius) ao 0.529 177 210 8(18)×10-10 m
   energy atomic unit of energy, hartree (Hartree energy) Eh 4.359 744 17(75)×10-18 J
   time, duration atomic unit of tim ℏ/Eh 2.418 884 326 505(16)×10-17 s

 

 

Other non-SI units

Quantity Name of unit Symbol for unit Value in SI units
pressure bar bar 1 bar = 0.1 MPa = 105 Pa
  millimetre of mercury mmHg 1 mmHg ≈ 133.322 Pa
length angström Å 1 Å = 0.1 nm = 10-10 m
distance nautical mile M 1 M = 1852 m
area barn b 1 b = 100 fm2 = 10-28 m2
speed, velocity knot kn 1 kn = (1852/3600) m s-1
logarithmic ratio quantities neper Np  
  bel B  
  decibel dB  

 

 

Non-SI units associated with the CGS system of units

Quantity Name of unit Symbol for unit Value in SI units
energy erg erg 1 erg = 10-7 J
force dyne dyn 1 dyn = 10-5 N
dynamic viscosity poise P 1 P = 1 dyn s cm-2 = 0.1 Pa s
kinematic viscosity stokes St 1 St = 1 cm2 s-1 = 10-4 m2 s-1
luminance stilb sb 1 sb = 1 cd cm-2 = 104 cd m-2
illuminance phot ph 1 ph = 1 cd sr cm-2 = 104 lx
acceleration gal Gal 1 Gal = 1 cm s-2 = 10-2 m s-2
magnetic flux maxwell Mx 1 Mx = 1 G cm2 = 10-8 Wb
magnetic flux density gauss G 1 G = 1 Mx cm-2 = 10-4 T
magnetic field œrsted Oe 1 Oe ≙ (103/4π) A m-1

 

 

SI prefixes

  Factor Name Symbol      Factor Name Symbol
 
  101 deca da   10-1 deci d
  102 hecto h   10-2 centi c
  103 kilo k   10-3 milli m
  106 mega M   10-6 micro μ
  109 giga G   10-9 nano n
  1012 tera T   10-12 pico p
  1015 peta P   10-15 femto f
  1018 exa E   10-18 atto a
  1021 zetta Z   10-21 zepto z
  1024 yotta Y   10-24 yocto y

 

Names and symbols for decimal multiples and submultiples of the unit of mass are formed by attaching prefix names to the unit name 'gram', and prefix symbols to the unit symbol 'g'.

These SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (for example, one kilobit represents 1000 bits and not 1024 bits). The names and symbols for the prefixes corresponding to 210, 220, 230, 240, 250, and 260 are, respectively: kibi, Ki; mebi, Mi; gibi, Gi; tebi, Ti; pebi, Pi; and exbi, Ei. Thus, for example, one kibibyte would be written: 1 KiB = 210 B = 1024 B, where B denotes a byte. Although these prefixes are not part of the SI, they should be used in the field of information technology to avoid the incorrect usage of the SI prefixes.

 

Bibliography:

  1. "The International System of Units (SI)." Bureau International des Poids et Mesures. 30 Nov 2010. <http://www.bipm.org/en/si/>.
  2. "The International System of Units from NIST." Oct 2000. National Institute of Standards and Technology. 30 Nov 2010. <http://physics.nist.gov/cuu/Units/>.