Tables of SI Units and Prefixes
edited by Stanislav Sýkora, Extra Byte, Via R.Sanzio 22C, Castano Primo, Italy 20022
in Stan's Library, Ed.S.Sykora, Vol.I. First release February 1, 2005.
Permalink via DOI:  10.3247/SL1Phys06.002
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Table I. Basic Units

defined by Conférence Générale des Poids et Mesures (CGPM) in the latest SI-brochure of 1998.

Quantity Unit Symbol Definition
Length  meter  m  1983, 17th CGPM:  The path travelled by light in vacuum during a time interval of 1/299792458 seconds. This fixes the speed of light to exactly 299792458 m/s.
Mass  kilogram  kg  1901, 3rd CGPM:  Mass of the platinum-iridium prototype at BIPM in Sevres.
Time  second  s  1968, 13th CGPM:  On second equals 9192631770 periods of the radiation due to the transition between the two hyperfine levels of the ground state of Cesium 133.
Electric current  ampere  A  1948, 9th CGPM:  Given two parallel, rectilinear conductors of negligible circular cross-section positioned 1 m apart in vacuum, one ampere is the electric current which, passing through both of them, makes them attract each other by the force of 2.10-7 newtons per every meter of length. This fixes the permeability of vacuum to exactly 2π*10-7 H/m.
Temperature  kelvin  K  1968, 13th CGPM:  One degree K equals 1/273.16 of the thermodynamic temperature of the triple point of water.
Quantity of substance  mole  mol  1971, 14th CGPM:  The amount of a substance composed of as many specified elementary units (molecules, atoms) as there are atoms in 0.012 kg of Carbon 12.
Luminosity  candle  cd  1979, 16th CGPM:  The candle (or candela) is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540.1012 hertz and that has a radiant intensity in that direction of 1/683 W/sr.

Table II. Derived units with assigned names

defined by BIPM in the latest SI-brochure (1998) and its supplement (2000).

Quantity Unit Symbol Equals Definition / Note
Space and time:
Plane angle  radian  rad    The plain angle which,  when centered in a circle, cuts off an arc whose length is equal to the circle radius.
Solid angle  steradian  sr    The solid angle which,  when centered in a sphere, cuts off a cap whose surface equals that of a square having the radius as side.
Frequency  hertz  Hz  1 s-1 [number of events or cycles]/[time]. 
Mechanics:
Force  newton  N  1 kg.m.s-2 [mass].[acceleration]. 
Pressure  pascal  Pa  1 N.m-2 [force]/[area]. Also: stress. 
Energy  joule  J  1 N.m  [force].[length]. Also: Work, Heat 
Power  watt  W  1 J.s-1 [energy]/[time]. Also: Radiant flux 
Thermodynamics:
Temperature  celsius  oC  1 K  T [oC] = T [K] -273.15 (the offset is exact!). 
Electromagnetism:
Charge  coulomb  C  1 A.s  [current].[time]. 
Potential  volt  V  1 W.A-1 [power]/[current]. Only differences are measurable! 
Resistance  ohm  Ω  1 V.A-1 [Δpotential]/[current]. 
Conductance  siemens  S  1 A.V-1 [current]/[Δpotential]. 
Capacitance  farad  F  1 C.V-1 [charge]/[Δpotential]. 
Inductance  henry  H  1 V.s.A-1 [Δpotential]/[rate of change of current]. 
Magnetic flux  weber  Wb  1 J.A-1 [energy]/[current]. 
Magnetic flux density  tesla  T  1 Wb.m-2 [magnetic flux]/[area]. Also magnetic induction. 
Optics:
Luminous flux  lumen  lm  1 cd.sr  [luminosity].[solid angle]. 
Illuminance  lux  lx  1 lm.m-2 [luminous flux]/[area]. 
Convergence  dioptry  dioptry  1 m-1 Inverse of focal length. 
Radioactivity and radiation:
Activity  becquerel  Bq  1 s-1 [number of decay events]/[time]. 
Absorbed dose  gray  Gy  1 J.kg-1 [energy]/[mass]. 
Dose equivalent  sievert  Sv  1 J.kg-1 [energy]/[mass]. Absorbed dose re-normalized by biological effects. 
Chemistry:
Katalytic activity  katal  kat  1 mol.s-1 [quantity of substance]/[time]. 

Table III a. SI Units prefixes

with examples of correct usage.

Prefix Symbol Factor Examples of usage Origin
Yotta  Y  1024 0.2 YW, 1.23Y [W]  Greek 'octo' (eight, 10008)
Zetta  Z  1021 3.33 Zs, 3.33Z [s]  French 'sept' (seven, 10007)
Exa  E  1018 1.23 Ekg, 1.23E [kg]  Greek 'six' (10006)
Peta  P  1015 7.5 Ps, 7.5P [s]  Greek 'five' (10005)
Tera  T  1012 0.5 Tm, 0.5T [m]  Greek 'teras' = monster 
Giga  G  109 1.2 GΩ, 1.2G [Ω]  Greek 'gigas' = giant 
Mega  M  106 7 MW, 7M [W]  Greek 'megas' = large 
Kilo  K, k  103 33 km, 33K [m]  Greek 'kilioi' = thousand 
hecto  h  100  Deprecated by SI  Greek 'hekaton' = hundred 
deca  da  10  Deprecated by SI  Greek 'deka' = ten 
deci  d  0.1  Deprecated by SI  Latin 'decima pars' = one tenth 
centi  c  0.01  Deprecated by SI  Latin 'centesima pars' = one hundredth 
milli  m, k  10-3 22 mm , 1.2m [m]  Latin 'millesima pars' = one thousandth 
micro  µ, u  10-6 2.7 uJ , 2.7µ [J]  Greek 'mikros' = small 
nano  n  10-9 2.2 nF, 2.2n [F]  Latin 'nanus' = dwarf 
pico  p  10-12 1.5 pA, 1.5p [A]  Spanish 'pico' = minimal measure 
femto  f  10-15 4.8 fs, 4.8f [s]  Danish and Norvegian 'femten' = fifteen (10-15)
atto  a  10-18 1.2 ag, 1.2a [g]  Danish and Norvegian 'atten' = eighteen (10-18)
zepto  z  10-21 0.2 zm, 1.2z [m]  French 'sept' (seven, 1000-7)
yocto  y  10-24 1 ys, 1y [s]  Greek 'octo' (eight, 1000-8)

Table III b. Binary prefixes for Bytes

which are not a part of SI but which are in common use in informatics [see the note].

Prefix Symbol Factor Value Examples
Kilo  KB  210 1024  12345 KB = 12 641 280 bytes 
Mega  MB  210 1 048 576  420 MB fits in my PC's dynamic RAM 
Giga  GB  230 1 073 741 824  16 GB flash-memory pen drive costs $20 
Tera  TB  240 1 099 511 627 776  3.9 TB hard disks are a reality 
Peta  PB  250 1 125 899 906 842 624  13.5 PB is the CIA total memory capacity 
Exa  EB  260 1 152 921 504 606 846 976  1 EB is still a bit out of reach (AD 2010) 
Zetta  ZB  270 1 180 591 620 717 411 303 424  How many ZB to hard-copy a human being ??? 
Yotta  YB  280 1 208 925 819 614 629 174 706 176  1 YYB is still nothing compared with the Universe 

Table IV. Accepted non-SI units

compiled according to the US Federal Register (ref.4).

Unit of Symbol Equals Definition / Note
Degree of arc  plain angle  o (π/180) rad   
Minute of arc  plain angle  '  (1/60) o  
Second of arc  plain angle  "  (1/60)'   
Minute  time  min  60 s   
Hour  time  h  60 min   
Day  time  d  24 h  Notice that the duration of a day is not linked to Earth motion! 
Liter  volume  L, l  0.001 m3 Often used sub-units are deciliter (dl) and centiliter.(cl). 
Gram  mass  g  0.001 kg  A tolerated anomaly: the basic unit of mass (kg) has a prefix. 
Ton  mass  t  1000 kg  More precise term: metric ton. 
Bit  information  bit  -  The smallest, dimensionless quantum of information 
Baud rate  info flux  Baud  1 bit.s-1 [amount of information]/[time] 
Neper  ratio  Np  log(A/B)  Measure of a ratio A/B. The logarithms are in base 10. 
Bel  ratio  B  0.5 Np  Mostly used as decibel (dB): 1 dB = (1/20) Np. 

Table V. Accepted non-SI units with experimental values.

For the most recent values of these constantly improving units, see Constants of Physics.

Unit of Symbol Equals Note
Electronvolt  energy  eV  1.60217733(49).10-19 J Energy to move an electron across a potential difference of 1 V. 
Astronomical unit  length  au, AU, ua  1.49597870(30).10+11 m Mean Earth-to-Sun distance. Also denoted as ua. 
Atomic mass unit  mass  u  1.6605402(10).10-27 kg 1/12 of the rest mass of an unbound 12C atom in ground state. 

Table VI. Units deprecated by the SI

which are still in current use in most countries.

Unit of Symbol Equals Note
Nautical mile  length  mile  1852 m   
Knot  velocity  knot  1 mile.h-1 A nautical unit. 
Are  area  are  100 m2  
Hectar  area  ha  100 are  10000 m2 
Bar  pressure  bar  100000 Pa  Almost 1 atm = 101325 Pa (an obsolete unit) 
Calory  energy  cal  4.1868 J  Note: the conversion factor is fixed by convention. 
Ångström  length  Å  10-10 m Used in atomic and molecular physics. 
Barn  area  b  10-28 m2 Used in particle physics (collision cross-sections). 
Radioactivity and radiation:
Curie  Radioactivity  b  3.7*10+10 Bq Note: the conversion factor is fixed by convention. 
Röntgen  Radiation dose  R  0.000258 Ci.kg-1 Note: the conversion factor is fixed by convention. 
Rad  Radiation dose  rad  0.01 Gy   
Rem  Equivalent dose  rem  0.01 Sv   

Spelling differences

The symbols of various units are international. This, however, is not true about the names of the units. Thus, for example, the US meter corresponds to the French metre, Italian metro, Czech metr, etc. In particular, UK English uses the French spelling. Consequently, the US terms meter, gram and liter become, respectively, metre, gramm and litre in the British Commonwealth. Throughout this document, I have used the US spelling.

Note on binary prefixes

These prefixes are so far NOT defined by the SI system, but they are widely used when specifying amounts of information or that of an information storage capacity. This stems from the ubiquitous use of the binary system in electronics information-handling devices. The prefixes themselves are a combination of binary and decimal concepts (2 as the base, elevated to a decimal exponent) stemming from the approximate equality of 10^3 (1000) and 2^10 (1024). They are used exclusively in combination with the letter "B" standing for "Bytes". Sometimes, a distinction is made between capital "B" (when the prefix is binary) and small "b" (when the prefix is decadic). In such contexts, therefore, 1 KB equals 1.024 Kb. However, be careful because this convention is not universally accepted and can not be counted upon.

References

  • The International System of Units (SI),
    Bureau International des Poids et Measures (BIPM), 7th Edition, 1998.
    Better known as the SI brochure, this document is publicly available from the BIPM site.
  • Taylor B.N,
    The International System of Units (SI),
    NIST Special Publication 330, 2001 Edition (supersedes the 1991 Edition).
  • Metric System of Measurement: Interpretation of the International System of Units for the United States,
    Federal Register 63, No.144, July 28, 1998.
  • For more, see References on Systems of Units of Measurements

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Copyright ©2005,2006 Stanislav Sýkora    DOI: 10.3247/SL1Phys06.002 Designed by Stan Sýkora