Difference between revisions of "International System of Units"
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The '''International System of Units''' (commonly abbreviated to '''SI''' from its French name ''Système Internationale d'Unités'') is the international system of [[Unit of measurement|units of measurement]] established under the [[Metre Convention]]. It is based on seven "base units", with a potentially limitless number of "derived units". | The '''International System of Units''' (commonly abbreviated to '''SI''' from its French name ''Système Internationale d'Unités'') is the international system of [[Unit of measurement|units of measurement]] established under the [[Metre Convention]]. It is based on seven "base units", with a potentially limitless number of "derived units". | ||
+ | |||
+ | The definitions of the base units and other fundamental aspects of the system are approved by the [[General Conference on Weights and Measures]] (CGPM), a diplomatic conference which meets every four years, based on recommendations from the [[International Committee for Weights and Measures]] (CIPM). The CIPM is also charged with agreeing many of the technical details of the system, such as the methods of [[realization]] of units and other details of conventional measurement techniques. | ||
==Base units== | ==Base units== | ||
Line 47: | Line 49: | ||
The six original base units were selected in 1956 by the 9th CGPM (the [[mole]] was added in 1972). They represent a conventional choice: the choice made in the International System of Units is not the only possible choice of base units, nor is there any physical significance that the [[ampere]] was chosen as the base for electromagnetic units rather than, e.g., the [[coulomb]]. | The six original base units were selected in 1956 by the 9th CGPM (the [[mole]] was added in 1972). They represent a conventional choice: the choice made in the International System of Units is not the only possible choice of base units, nor is there any physical significance that the [[ampere]] was chosen as the base for electromagnetic units rather than, e.g., the [[coulomb]]. | ||
− | The inclusion of the [[candela]] as a base unit is for both historical and practical reasons. There is an obvious technical need to classify many everyday light sources on the basis of their effect on the human eye. This is acheived by multiplying the [[radient | + | The inclusion of the [[candela]] as a base unit is for both historical and practical reasons. There is an obvious technical need to classify many everyday light sources on the basis of their effect on the human eye. This is acheived by multiplying the [[radient intensity]] (measured in [[watt]]s per [[steradian]]) by a [[standard luminosity function]] that models the response of the human eye: the result is the candela, which is also the base for a series of other luminosity units. |
==Derived units== | ==Derived units== | ||
+ | A derived unit is formed from a combination of base units, particularly a product of base units raised to non-zero powers: for example, the metre per second ({{nowrap|m s<sup>−1</sup>}}) as a unit of [[speed]]. A derived unit is said to be "coherent" if there is no numerical factor other than one before product of the base units (raised, if necessary, to their different powers). For example, the metre per second squared ({{nowrap|m s<sup>−2</sup>}}) is the coherent SI derived unit for [[acceleration]], whereas the centimetre per second squared<ref group="note">This unit is better known as the [[gal]] (symbol: Gal).</ref> is a valid derived SI unit but is not coherent because of the factor of 10<sup>−2</sup> implied by the prefix "centi" (''[[#Multiples and submultiples|see below]]''). | ||
+ | |||
+ | The number of possible derived units is without practical limit, but certain coherent derived units have special names and symbols within the SI. | ||
+ | |||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! Name | ||
+ | ! Symbol | ||
+ | ! Physical quantity | ||
+ | ! Definition | ||
+ | ! Notes | ||
+ | |- | ||
+ | | [[becquerel]] || Bq || [[activity (radionuclide)|activity]] || s<sup>−1</sup> || | ||
+ | |- | ||
+ | | [[coulomb]] || C || [[electric charge]] || s A || | ||
+ | |- | ||
+ | | [[farad]] || F || [[capacitance]] || m<sup>−2</sup> kg<sup>−1</sup> s<sup>4</sup> A<sup>2</sup> = C/V || | ||
+ | |- | ||
+ | | [[gray]] || Gy || [[absorbed dose (ionizing radiation)|absorbed dose]] || m<sup>2</sup> s<sup>−2</sup> = J/kg || | ||
+ | |- | ||
+ | | [[henry]] || H || [[inductance]] || m<sup>2</sup> kg s<sup>−2</sup> A<sup>−2</sup> = Wb/A || | ||
+ | |- | ||
+ | | [[hertz]] || Hz || [[frequency]] || s<sup>−1</sup> || | ||
+ | |- | ||
+ | | [[joule]] || J || [[energy]]<br/>[[work]]<br/>amount of [[heat]] || m<sup>2</sup> kg s<sup>−2</sup> = N m || | ||
+ | |- | ||
+ | | [[katal]] || kat || [[catalytic activity]] || s<sup>−1</sup> mol || | ||
+ | |- | ||
+ | | [[lumen]] || lm || [[luminous flux]] || cd sr = cd || | ||
+ | |- | ||
+ | | [[lux]] || lx || [[illuminance]] || m<sup>−2</sup> cd = lm/m<sup>2</sup> || | ||
+ | |- | ||
+ | | [[newton]] || N || [[force]] || m kg s<sup>−2</sup> || | ||
+ | |- | ||
+ | | [[ohm]] || Ω || [[electric resistance]] || m<sup>2</sup> kg s<sup>−3</sup> A<sup>−2</sup> = V/A || | ||
+ | |- | ||
+ | | [[pascal]] || Pa || [[pressure]]<br/>[[stress]] || m<sup>−1</sup> kg s<sup>−2</sup> = N/m<sup>2</sup> || | ||
+ | |- | ||
+ | | [[siemens]] || S || [[electric conductance]] || m<sup>−2</sup> kg<sup>−1</sup> s<sup>3</sup> A<sup>2</sup> = A/V || | ||
+ | |- | ||
+ | | [[sievert]] || Sv || [[dose equivalent]] || m<sup>2</sup> s<sup>−2</sup> = J/kg || | ||
+ | |- | ||
+ | | [[tesla]] || T || [[magnetic flux density]] || kg s<sup>−2</sup> A<sup>−1</sup> = Wb/m<sup>2</sup> || | ||
+ | |- | ||
+ | | [[volt]] || V || [[electric potential difference]]<br/>[[electromotive force]] || m<sup>2</sup> kg s<sup>−3</sup> A<sup>−1</sup> = W/A = J/C || | ||
+ | |- | ||
+ | | [[watt]] || W || [[power]]<br/>[[radiant flux]] || m<sup>2</sup> kg s<sup>−3</sup> = J/s || | ||
+ | |- | ||
+ | | [[weber]] || Wb || [[magnetic flux]] || m<sup>2</sup> kg s<sup>−2</sup> A<sup>−1</sup> = V s || | ||
+ | |- | ||
+ | | [[degree Celsius]] || °C || [[Celsius temperature]] || K || | ||
+ | |- | ||
+ | | [[radian]] || rad || [[plane angle]] || m/m = 1 || | ||
+ | |- | ||
+ | | [[steradian]] || sr || [[solid angle]] || m<sup>2</sup>/m<sup>2</sup> = 1 || | ||
+ | |- | ||
+ | |} | ||
==Multiples and submultiples== | ==Multiples and submultiples== | ||
Line 138: | Line 197: | ||
==Units used with the SI== | ==Units used with the SI== | ||
+ | There are several sets of units which are not SI units but which have some degree of acceptance for use with the International System of Units. | ||
+ | |||
+ | ===Common units with exact conversion factors=== | ||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! Name | ||
+ | ! Symbol | ||
+ | ! Physical<br/>quantity | ||
+ | ! Value | ||
+ | ! Notes | ||
+ | |- | ||
+ | | [[minute]] | ||
+ | | min | ||
+ | | time | ||
+ | | 1 min = 60 s | ||
+ | | | ||
+ | |- | ||
+ | | [[hour]] | ||
+ | | h | ||
+ | | time | ||
+ | | 1 h = 60 min = 3600 s | ||
+ | | | ||
+ | |- | ||
+ | | [[day]] | ||
+ | | d | ||
+ | | time | ||
+ | | 1 d = 86 400 s | ||
+ | | | ||
+ | |- | ||
+ | | [[degree]] | ||
+ | | ° | ||
+ | | plane angle | ||
+ | | 1° = (π/180) rad | ||
+ | | | ||
+ | |- | ||
+ | | [[Arcminute|minute]] | ||
+ | | ′ | ||
+ | | plane angle | ||
+ | | 1′ = (1/60)° = (π/10 800) rad | ||
+ | | | ||
+ | |- | ||
+ | | [[Arcsecond|second]] | ||
+ | | ″ | ||
+ | | plane angle | ||
+ | | 1″ = (1/60)′ = (π/648 000) rad | ||
+ | | | ||
+ | |- | ||
+ | | [[hectare]] | ||
+ | | ha | ||
+ | | area | ||
+ | | 1 ha = 1 hm<sup>2</sup> = 0.01 km<sup>2</sup> = 10<sup>4</sup> m<sup>2</sup> | ||
+ | | | ||
+ | |- | ||
+ | | [[litre]] | ||
+ | | L, l | ||
+ | | [[volume]] | ||
+ | | 1 L = 1 l = 1 dm<sup>3</sup> = 10<sup>3</sup> cm<sup>3</sup> = 10<sup>−3</sup> m<sup>3</sup> | ||
+ | | <ref group="note">The spelling "liter" and the symbol L are mandatory in the U.S. interpretation of the SI.</ref> | ||
+ | |- | ||
+ | | [[tonne]] | ||
+ | | t | ||
+ | | mass | ||
+ | | 1 t = 1000 kg | ||
+ | | | ||
+ | |- | ||
+ | |} | ||
+ | |||
+ | ===Units with empirical conversion factors=== | ||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! Name | ||
+ | ! Symbol | ||
+ | ! Physical<br/>quantity | ||
+ | ! Value | ||
+ | ! Notes | ||
+ | |- | ||
+ | | [[electronvolt]] | ||
+ | | eV | ||
+ | | energy | ||
+ | | 1 eV = 1.602 176 487(40){{e|−19}} J | ||
+ | | align=center | <ref name="CODATA2006">{{CODATA 2006}}.</ref> | ||
+ | |- | ||
+ | | [[dalton]] | ||
+ | | Da | ||
+ | | rowspan=2 | mass | ||
+ | | rowspan=2 | 1 Da = 1 u = 1.660 538 782(83){{e|−27}} kg | ||
+ | | rowspan=2 align=center | <ref name="CODATA2006"/> | ||
+ | |- | ||
+ | | [[atomic mass unit]] | ||
+ | | u | ||
+ | |- | ||
+ | | [[astronomical unit]] | ||
+ | | ua | ||
+ | | length | ||
+ | | 1 ua = 149 597 870 700(3) m | ||
+ | | <ref>{{citation | last1 = Pitjeva | first1 = E. V. | last2 = Standish | first2 = E. M. | year = 2009 | title = Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit | url = http://www.springerlink.com/content/21885q7262104u76/ | journal = Celest. Mech. Dynam. Astron. | volume = 103 | issue = 4 | pages = 365–72 | doi = 10.1007/s10569-009-9203-8}}.</ref><ref>{{citation | title = IAU WG on NSFA Current Best Estimates | url = http://maia.usno.navy.mil/NSFA/CBE.html | accessdate = 2009-09-25}}.</ref><ref>{{citation | url = http://www.astronomy2009.com.br/10.pdf | newspaper = Estrella d'Alva | date = 2009-08-14 | page = 1 | title = The Final Session of the General Assembly}}.</ref><br/><ref group="note">There are several different symbols for the astronomical unit, including ua, au, AU and A.</ref> | ||
+ | |- | ||
+ | |} | ||
==Notes and references== | ==Notes and references== |
Latest revision as of 11:28, 23 March 2010
The International System of Units (commonly abbreviated to SI from its French name Système Internationale d'Unités) is the international system of units of measurement established under the Metre Convention. It is based on seven "base units", with a potentially limitless number of "derived units".
The definitions of the base units and other fundamental aspects of the system are approved by the General Conference on Weights and Measures (CGPM), a diplomatic conference which meets every four years, based on recommendations from the International Committee for Weights and Measures (CIPM). The CIPM is also charged with agreeing many of the technical details of the system, such as the methods of realization of units and other details of conventional measurement techniques.
Contents
Base units
Unit name | Unit symbol | Physical quantity | Notes |
---|---|---|---|
metre | m | length | |
kilogram | kg | mass | |
second | s | time | |
ampere | A | electric current | |
kelvin | K | thermodynamic temperature | |
candela | cd | luminous intensity | |
mole | mol | amount of substance |
The six original base units were selected in 1956 by the 9th CGPM (the mole was added in 1972). They represent a conventional choice: the choice made in the International System of Units is not the only possible choice of base units, nor is there any physical significance that the ampere was chosen as the base for electromagnetic units rather than, e.g., the coulomb.
The inclusion of the candela as a base unit is for both historical and practical reasons. There is an obvious technical need to classify many everyday light sources on the basis of their effect on the human eye. This is acheived by multiplying the radient intensity (measured in watts per steradian) by a standard luminosity function that models the response of the human eye: the result is the candela, which is also the base for a series of other luminosity units.
Derived units
A derived unit is formed from a combination of base units, particularly a product of base units raised to non-zero powers: for example, the metre per second (m s−1) as a unit of speed. A derived unit is said to be "coherent" if there is no numerical factor other than one before product of the base units (raised, if necessary, to their different powers). For example, the metre per second squared (m s−2) is the coherent SI derived unit for acceleration, whereas the centimetre per second squared[note 1] is a valid derived SI unit but is not coherent because of the factor of 10−2 implied by the prefix "centi" (see below).
The number of possible derived units is without practical limit, but certain coherent derived units have special names and symbols within the SI.
Name | Symbol | Physical quantity | Definition | Notes |
---|---|---|---|---|
becquerel | Bq | activity | s−1 | |
coulomb | C | electric charge | s A | |
farad | F | capacitance | m−2 kg−1 s4 A2 = C/V | |
gray | Gy | absorbed dose | m2 s−2 = J/kg | |
henry | H | inductance | m2 kg s−2 A−2 = Wb/A | |
hertz | Hz | frequency | s−1 | |
joule | J | energy work amount of heat |
m2 kg s−2 = N m | |
katal | kat | catalytic activity | s−1 mol | |
lumen | lm | luminous flux | cd sr = cd | |
lux | lx | illuminance | m−2 cd = lm/m2 | |
newton | N | force | m kg s−2 | |
ohm | Ω | electric resistance | m2 kg s−3 A−2 = V/A | |
pascal | Pa | pressure stress |
m−1 kg s−2 = N/m2 | |
siemens | S | electric conductance | m−2 kg−1 s3 A2 = A/V | |
sievert | Sv | dose equivalent | m2 s−2 = J/kg | |
tesla | T | magnetic flux density | kg s−2 A−1 = Wb/m2 | |
volt | V | electric potential difference electromotive force |
m2 kg s−3 A−1 = W/A = J/C | |
watt | W | power radiant flux |
m2 kg s−3 = J/s | |
weber | Wb | magnetic flux | m2 kg s−2 A−1 = V s | |
degree Celsius | °C | Celsius temperature | K | |
radian | rad | plane angle | m/m = 1 | |
steradian | sr | solid angle | m2/m2 = 1 |
Multiples and submultiples
Multiples | Submultiples | |||||
---|---|---|---|---|---|---|
Symbol | Prefix | Prefix | Symbol | |||
da | deca | 101 | 10−1 | deci | d | |
h | hecto | 102 | 10−2 | centi | c | |
k | kilo | 103 | 10−3 | milli | m | |
M | mega | 106 | 10−6 | micro | µ | |
G | giga | 109 | 10−9 | nano | n | |
T | tera | 1012 | 10−12 | pico | p | |
P | peta | 1015 | 10−15 | femto | f | |
E | exa | 1018 | 10−18 | atto | a | |
Z | zetta | 1021 | 10−21 | zepto | z | |
Y | yotta | 1024 | 10−24 | yocto | y |
Units used with the SI
There are several sets of units which are not SI units but which have some degree of acceptance for use with the International System of Units.
Common units with exact conversion factors
Name | Symbol | Physical quantity |
Value | Notes |
---|---|---|---|---|
minute | min | time | 1 min = 60 s | |
hour | h | time | 1 h = 60 min = 3600 s | |
day | d | time | 1 d = 86 400 s | |
degree | ° | plane angle | 1° = (π/180) rad | |
minute | ′ | plane angle | 1′ = (1/60)° = (π/10 800) rad | |
second | ″ | plane angle | 1″ = (1/60)′ = (π/648 000) rad | |
hectare | ha | area | 1 ha = 1 hm2 = 0.01 km2 = 104 m2 | |
litre | L, l | volume | 1 L = 1 l = 1 dm3 = 103 cm3 = 10−3 m3 | [note 2] |
tonne | t | mass | 1 t = 1000 kg |
Units with empirical conversion factors
Name | Symbol | Physical quantity |
Value | Notes |
---|---|---|---|---|
electronvolt | eV | energy | 1 eV = 1.602 176 487(40) × 10−19 J | [1] |
dalton | Da | mass | 1 Da = 1 u = 1.660 538 782(83) × 10−27 kg | [1] |
atomic mass unit | u | |||
astronomical unit | ua | length | 1 ua = 149 597 870 700(3) m | [2][3][4] [note 3] |
Notes and references
Notes
References
- ↑ 1.0 1.1 Mohr, Peter J.; Taylor, Barry N.; Newell, David B. CODATA Recommended Values of the Fundamental Physical Constants: 2006. Rev. Mod. Phys. 2008, 80 (2), 633–730. doi:10.1103/RevModPhys.80.633, <http://physics.nist.gov/cuu/Constants/codata.pdf>.
- ↑ Pitjeva, E. V.; Standish, E. M. Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit. Celest. Mech. Dynam. Astron. 2009, 103 (4), 365–72. doi:10.1007/s10569-009-9203-8, <http://www.springerlink.com/content/21885q7262104u76/>.
- ↑ IAU WG on NSFA Current Best Estimates, <http://maia.usno.navy.mil/NSFA/CBE.html>. (accessed 25 September 2009).
- ↑ The Final Session of the General Assembly. Estrella d'Alva 2009-08-14, 1, <http://www.astronomy2009.com.br/10.pdf>.
External links
See also the corresponding article on Wikipedia. |
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