Appendix:SI units

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The International System of Units (abbreviated SI from the French Système international d'unités[1]) is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science.[2][3][4]

The International System of Units consists of a set of units together with a set of prefixes. The units are divided into two classes—base units and derived units. There are seven base units, each representing, by convention, different kinds of physical quantities. The prefixes may generally be combined with the base units and derived units to describe the applicable number of those units. For example, three quadrillion units of force would be expressed as three petanewtons, combining the prefix peta, for quadrillion, with the derived unit, newton.

SI units[edit]

SI is an abbreviation of Système International (d'Unités) [International System (of Units)] and is a standard metric system of units adopted for official scientific use. For more information, see Wikipedia's article on SI.

Note: this page is simply a collection of links to the names of SI units and their prefixes and multiples. For further information, see the Wikipedia articles SI base units and SI derived units.

Base units (with symbols in parentheses; see full descriptions below)[edit]

Derived units (with symbols in parentheses; see full descriptions below)[edit]

Alternative names for SI units and their multiples and submultiples[edit]

Former names for SI units[edit]

SI prefixes[edit]

SI prefixes
Prefix Symbol 1000m 10n Decimal Short scale Long scale Since[n 1]
yotta Y 10008 1024 1000000000000000000000000 Septillion Quadrillion 1991
zetta Z 10007 1021 1000000000000000000000 Sextillion Trilliard 1991
exa E 10006 1018 1000000000000000000 Quintillion Trillion 1975
peta P 10005 1015 1000000000000000 Quadrillion Billiard 1975
tera T 10004 1012 1000000000000 Trillion Billion 1960
giga G 10003 109 1000000000 Billion Milliard 1960
mega M 10002 106 1000000 Million 1960
kilo k 10001 103 1000 Thousand 1795
hecto h 10002/3 102 100 Hundred 1795
deca da 10001/3 101 10 Ten 1795
10000 100 1 One
deci d 1000−1/3 10−1 0.1 Tenth 1795
centi c 1000−2/3 10−2 0.01 Hundredth 1795
milli m 1000−1 10−3 0.001 Thousandth 1795
micro μ 1000−2 10−6 0.000001 Millionth 1960
nano n 1000−3 10−9 0.000000001 Billionth Milliardth 1960
pico p 1000−4 10−12 0.000000000001 Trillionth Billionth 1960
femto f 1000−5 10−15 0.000000000000001 Quadrillionth Billiardth 1964
atto a 1000−6 10−18 0.000000000000000001 Quintillionth Trillionth 1964
zepto z 1000−7 10−21 0.000000000000000000001 Sextillionth Trilliardth 1991
yocto y 1000−8 10−24 0.000000000000000000000001 Septillionth Quadrillionth 1991
  1. ^ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.


Notes:

1. meg- is used before a vowel, as in megohm
2. not commonly used

Binary prefixes[edit]

The following prefixes are not part of SI. They were adopted by the IEC to express binary multiples.

prefix sym multiplier
exbi- Ei 260
pebi- Pi 250
tebi- Ti 240
gibi- Gi 230
mebi- Mi 220
kibi- Ki 210

Former prefixes[edit]

These prefixes have been used informally at times, but were never part of SI.

prefix multiplier equivalent
hectokilo- 105
myria- 104
millimilli- 10–6 micro-
millimicro- 10–9 nano-
micromicro- 10–12 pico-

Commonly used multiples of units[edit]

The table below shows which prefixes are most commonly used with each unit. In theory, any combination of a prefix and a unit is possible. In practice, only those multiples that are of practical use are used. Multiples towards the left and right of the table tend to gain currency as advances in technology and miniaturisation make them meaningful.
Links are to combinations that are in relatively common scientific use. Blank entries indicate combinations that are rare or not used.
Notes:
  1. Units are ordered alphabetically by their symbol. Prefixes are ordered from largest to smallest.
  2. It is the gram (g) that takes prefixes, not the kilogram.
  3. Some combinations have special names; for example, 106 grams is called a tonne, not a "megagram".
  4. The multiples in the grey columns are not in official scientific usage.
  5. The table lists multiples of SI units only. Other units that use the SI prefixes, such as kilobyte and millibar, are not given here.
  6. The table is currently incomplete. More links will be added later.

(Sources: ; Oxford English Dictionary, 2nd ed.)


Commonly used multiples of SI units
Y Z E P T G M k h da Unit d c m μ n p f a z y
MA kA A mA μA nA
PBq TBq GBq Bq
C
°C
cd
F mF μF nF pF
t, Mg kg hg dag g dg cg mg μg
Gy
H mH μH nH
PHz THz GHz MHz kHz Hz
kJ J
K
kat
lm
klx lx
km hm dam m dm cm mm μm nm pm fm
mol mmol μmol nmol pmol fmol
MN kN N
Ω
GPa MPa kPa hPa Pa
rad mrad
S
s ms μs ns ps fs as
sr
Sv mSv µSv
T mT µT nT
MV kV V mV μV
GW MW kW W mW μW
kWb Wb mWb μWb

Base units[edit]

SI base units
Name Symbol Measure Definition Historical origin / justification
second s time "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 caesium 133 atom."
13th CGPM (1967/68, Resolution 1; CR, 103)
"This definition refers to a caesium atom at rest at a temperature of 0 K."
(Added by CIPM in 1997)
The day is divided in 24 hours, each hour divided in 60 minutes, each minute divided in 60 seconds.
A second is 1(24 × 60 × 60) of the day
metre m length "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."
17th CGPM (1983, Resolution 1, CR, 97)
110,000,000 of the distance from the Earth's equator to the North Pole measured on the circumference through Paris.
kilogram kg mass "The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram."
3rd CGPM (1901, CR, 70)
The mass of one litre of water. A litre is one thousandth of a cubic metre.
ampere A electric current "The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length."
9th CGPM (1948)
The original "International Ampere" was defined electrochemically as the current required to deposit 1.118 milligrams of silver per second from a solution of silver nitrate. Compared to the SI ampere, the difference is 0.015%.
kelvin K thermodynamic temperature "The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."
13th CGPM (1967/68, Resolution 4; CR, 104)
"This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: 0.000 155 76 mole of 2H per mole of 1H, 0.000 379 9 mole of 17O per mole of 16O, and 0.002 005 2 mole of 18O per mole of 16O."
(Added by CIPM in 2005)
The Celsius scale: the Kelvin scale uses the degree Celsius for its unit increment, but is a thermodynamic scale (0 K is absolute zero).
mole mol amount of substance "1. 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; its symbol is “mol.” 

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles."
14th CGPM (1971, Resolution 3; CR, 78)
"In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to."
(Added by CIPM in 1980)

Atomic weight or molecular weight divided by the molar mass constant, 1 g/mol.
candela cd luminous intensity "The 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 watt per steradian."
16th CGPM (1979, Resolution 3; CR, 100)
The candlepower, which is based on the light emitted from a burning candle of standard properties.

Derived units with special names[edit]

Base units can be combined to derive units of measurement for other quantities. In addition to the two dimensionless derived units radian (rad) and steradian (sr), 20 other derived units have special names.

Named units derived from SI base units
Name Symbol Quantity Expression in terms of other units Expression in terms of SI base units
hertz Hz frequency 1/s s−1
radian rad angle m/m dimensionless
steradian sr solid angle m2/m2 dimensionless
newton N force, weight kg·m/s2 kg·m·s−2
pascal Pa pressure, stress N/m2 kg·m−1·s−2
joule J energy, work, heat N·m = C·V = W·s kg·m2·s−2
watt W power, radiant flux J/s = V·A kg·m2·s−3
coulomb C electric charge or quantity of electricity s·A s·A
volt V voltage, electrical potential difference, electromotive force W/A = J/C kg·m2·s−3·A−1
farad F electric capacitance C/V kg−1·m−2·s4·A2
ohm Ω electric resistance, electrical impedance, reactance V/A kg·m2·s−3·A−2
siemens S electrical conductance 1/Ω = A/V kg−1·m−2·s3·A2
weber Wb magnetic flux J/A kg·m2·s−2·A−1
tesla T magnetic field strength, magnetic flux density V·s/m2 = Wb/m2 = N/(A·m) kg·s−2·A−1
henry H inductance V·s/A = Wb/A kg·m2·s−2·A−2
degree Celsius °C temperature relative to 273.15 K K K
lumen lm luminous flux cd·sr cd
lux lx illuminance lm/m2 m−2·cd
becquerel Bq radioactivity (decays per unit time) 1/s s−1
gray Gy absorbed dose (of ionizing radiation) J/kg m2·s−2
sievert Sv equivalent dose (of ionizing radiation) J/kg m2·s−2
katal kat catalytic activity mol/s s−1·mol

Other common units, such as the litre, are not SI units, but are accepted for use with SI.

Multiples of base units by prefix[edit]

Multiples of SI base units
Multiple Prefix Mass Time Length Electrical current Temperature Quantity Luminous intensity
1024 yotta- (Y) yottagram (Yg) yottasecond (Ys) yottametre, yottameter (Ym) yottaampere (YA) yottakelvin (YK) yottamole (Ymol) yottacandela (Ycd)
1021 zetta- (Z) zettagram (Zg) zettasecond (Zs) zettametre, zettameter (Zm) zettaampere (ZA) zettakelvin (ZK) zettamole (Zmol) zettacandela (Zcd)
1018 exa- (E) exagram (Eg) exasecond (Es) exametre, exameter (Em) exaampere (EA) exakelvin (EK) examole (Emol) exacandela (Ecd)
1015 peta- (P) petagram (Pg) petasecond (Ps) petametre, petameter (Pm) petaampere (PA) petakelvin (PK) petamole (Pmol) petacandela (Pcd)
1012 tera- (T) teragram (Tg) terasecond (Ts) terametre, terameter (Tm) teraampere (TA) terakelvin (TK) teramole (Tmol) teracandela (Tcd)
109 giga- (G) gigagram (Gg) gigasecond (Gs) gigametre, gigameter (Gm) gigaampere (GA) gigakelvin (GK) gigamole (Gmol) gigacandela (Gcd)
106 mega- (M) megagram (Mg) megasecond (Ms) megametre, megameter (Mm) megaampere (MA) megakelvin (MK) megamole (Mmol) megacandela (Mcd)
103 kilo- (k) kilogram (kg) * kilosecond (ks) kilometre, kilometer (km) kiloampere (kA) kilokelvin (kK) kilomole (kmol) kilocandela (kcd)
102 hecto- (h) hectogram (hg) hectosecond (hs) hectometre, hectometer (hm) hectoampere (hA) hectokelvin (hK) hectomole (hmol) hectocandela (hcd)
101 deca-, deka- (da) decagram, dekagram (dag) decasecond, dekasecond (das) decametre, dekametre, decameter, dekameter (dam) decaampere, dekaampere (daA) decakelvin, dekakelvin (daK) decamole, dekamole (damol) decacandela, dekacandela (dacd)
100 Unit gram (g) * second (s) metre, meter (m) ampere (A) kelvin (K) mole (mol) candela (cd) +
10−1 deci- (d) decigram (dg) decisecond (ds) decimetre, decimeter (dm) deciampere (dA) decikelvin (dK) decimole (dmol) decicandela (dcd)
10−2 centi- (c) centigram (cg) centisecond (cs) centimetre, centimeter (cm) centiampere (cA) centikelvin (cK) centimole (cmol) centicandela (ccd)
10−3 milli- (m) milligram (mg) millisecond (ms) millimetre, millimeter (mm) milliampere (mA) millikelvin (mK) millimole (mmol) millicandela (mcd)
10−6 micro- (µ, not μ, nor u) microgram (µg, μg, ug) microsecond (µs, μs, us) micrometre, micrometer (µm, μm, um) microampere (µA, μA, uA) microkelvin (µK, μK, uK) micromole (µmol, μmol, umol) microcandela (µcd, μcd, ucd)
10−9 nano- (n) nanogram (ng) nanosecond (ns) nanometre, nanometer (nm) nanoampere (nA) nanokelvin (nK) nanomole (nmol) nanocandela (ncd)
10−12 pico- (p) picogram (pg) picosecond (ps) picometre, picometer (pm) picoampere (pA) picokelvin (pK) picomole (pmol) picocandela (pcd)
10−15 femto- (ff) femtogram (fg) femtosecond (fs) femtometre, femtometer (fm) femtoampere (fA) femtokelvin (fK) femtomole (fmol) femtocandela (fcd)
10−18 atto- (a) attogram (ag) attosecond (as) attometre, attometer (am) attoampere (aA) attokelvin (aK) attomole (amol) attocandela (acd)
10−21 zepto- (z) zeptogram (zg) zeptosecond (zs) zeptometre, zeptometer (zm) zeptoampere (zA) zeptokelvin (zK) zeptomole (zmol) zeptocandela (zcd)
10−24 yocto- (y) yoctogram (yg) yoctosecond (ys) yoctometre, yoctometer (ym) yoctoampere (yA) yoctokelvin (yK) yoctomole (ymol) yoctocandela (ycd)

Notes:

The kilogram is the SI base unit for mass, not the gram, which is defined as 1/1000th of a kilogram.
The candela is still considered an SI base unit, although it is no longer fundamental, being defined in terms of other SI units.

Variations in other languages[edit]

French[edit]

In French, accents appear in the following prefixes and base units:

German[edit]

In German, common nouns (including the names of SI units) are capitalized. Some spelling variations also appear:

Spanish[edit]

References[edit]

  1. ^ Resolution of the International Bureau of Weights and Measures establishing the International System of Units
  2. ^ Official BIPM definitions
  3. ^ Essentials of the SI: Introduction
  4. ^ An extensive presentation of the SI units is maintained on line by NIST, including a diagram of the interrelations between the derived units based upon the SI units. Definitions of the basic units can be found on this site, as well as the CODATA report listing values for special constants such as the electric constant, the magnetic constant and the speed of light, all of which have defined values as a result of the definition of the metre and ampere.

    In the International System of Units (SI) (BIPM, 2006), the definition of the metre fixes the speed of light in vacuum c0, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) μ0, and the definition of the mole fixes the molar mass of the carbon 12 atom M(12C) to have the exact values given in the table [Table 1, p.7]. Since the electric constant (also called the permittivity of vacuum) is related to μ0 by ε0 = 1/μ0c02, it too is known exactly.

     – CODATA report