Appendix:SI units
The International System of Units (abbreviated SI from French Système international d'unités^{[1]}) is the modern form of the metric system and is 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]}
SI 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 a different physical quantity. The prefixes may be combined with the base units and derived units to describe the number of those units. For example, 3×10^{15} newton = 3 petanewton, 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 unit and SI derived unit.
Base units (with symbols in parentheses; see full descriptions below)[edit]
Derived units (with symbols in parentheses; see full descriptions below)[edit]
- becquerel (Bq)
- coulomb (C)
- degree Celsius (°C)
- farad (F)
- gray (Gy)
- henry (H)
- hertz (Hz)
- joule (J)
- katal (kat)
- lumen (lm)
- lux (lx)
- newton (N)
- ohm (Ω)
- pascal (Pa)
- radian (rad) (classified as a supplementary unit until 1995)
- siemens (S)
- sievert (Sv)
- steradian (sr) (classified as a supplementary unit until 1995)
- tesla (T)
- volt (V)
- watt (W)
- weber (Wb)
Alternative names for SI units and their multiples and submultiples[edit]
- amp (for ampere)
- cycle (alternate name for hertz)
- Multiples:
- cycle per second (alternate name for hertz)
- kilo (short for kilogram)
- micron (alternate name for micrometre)
- fermi (alternate name for femtometre, sometimes used in nuclear physics)
Former names for SI units[edit]
SI prefixes[edit]
Prefix | Symbol | 1000^{m} | 10^{n} | Decimal | Short scale | Long scale | Since^{[n 1]} |
---|---|---|---|---|---|---|---|
quetta | Q | 1000^{10} | 10^{30} | 1000000000000000000000000000000 | Nonillion | Quintillion | 2022 |
ronna | R | 1000^{9} | 10^{27} | 1000000000000000000000000000 | Octillion | Quadrillard | 2022 |
yotta | Y | 1000^{8} | 10^{24} | 1000000000000000000000000 | Septillion | Quadrillion | 1991 |
zetta | Z | 1000^{7} | 10^{21} | 1000000000000000000000 | Sextillion | Trilliard | 1991 |
exa | E | 1000^{6} | 10^{18} | 1000000000000000000 | Quintillion | Trillion | 1975 |
peta | P | 1000^{5} | 10^{15} | 1000000000000000 | Quadrillion | Billiard | 1975 |
tera | T | 1000^{4} | 10^{12} | 1000000000000 | Trillion | Billion | 1960 |
giga | G | 1000^{3} | 10^{9} | 1000000000 | Billion | Milliard | 1960 |
mega | M | 1000^{2} | 10^{6} | 1000000 | Million | 1960 | |
kilo | k | 1000^{1} | 10^{3} | 1000 | Thousand | 1795 | |
hecto | h | 1000^{2/3} | 10^{2} | 100 | Hundred | 1795 | |
deca | da | 1000^{1/3} | 10^{1} | 10 | Ten | 1795 | |
1000^{0} | 10^{0} | 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 |
ronto | r | 1000^{−9} | 10^{−27} | 0.000000000000000000000000001 | Octillionth | Quadrillardth | 2022 |
quecto | q | 1000^{−10} | 10^{−30} | 0.000000000000000000000000000001 | Nonillionth | Quintillionth | 2022 |
Notes:
Binary prefixes[edit]
The following prefixes are not part of SI. They were adopted by the IEC to express binary multiples.
prefix | sym | multiplier |
---|---|---|
yobi- | Yi | 2^{80} |
zebi- | Zi | 2^{70} |
exbi- | Ei | 2^{60} |
pebi- | Pi | 2^{50} |
tebi- | Ti | 2^{40} |
gibi- | Gi | 2^{30} |
mebi- | Mi | 2^{20} |
kibi- | Ki | 2^{10} |
Former prefixes[edit]
These prefixes have been used informally at times, but were never part of SI.
prefix | multiplier | equivalent |
---|---|---|
hectokilo- | 10^{5} | |
myria- | 10^{4} | |
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:
- Units are ordered alphabetically by their symbol. Prefixes are ordered from largest to smallest.
- It is the gram (g) that takes prefixes, not the kilogram.
- Some combinations have special names; for example, 10^{6} grams is called a tonne, not a "megagram".
- The multiples in the grey columns are not in official scientific usage.
- The table lists multiples of SI units only. Other units that use the SI prefixes, such as kilobyte and millibar, are not given here.
- The table is currently incomplete. More links will be added later.
(Sources: ; Oxford English Dictionary, 2nd ed.)
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 | |||||||||||||||
MJ | kJ | J | ||||||||||||||||||
K | ||||||||||||||||||||
kat | ||||||||||||||||||||
lm | ||||||||||||||||||||
klx | lx | |||||||||||||||||||
km | hm | dam | m | dm | cm | mm | μm | nm | pm | fm | ||||||||||
mol | mmol | μmol | nmol | pmol | fmol | ymol | ||||||||||||||
MN | kN | N | ||||||||||||||||||
GΩ | MΩ | kΩ | Ω | mΩ | ||||||||||||||||
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 | ||||||||||||||||
EW | PW | TW | GW | MW | kW | W | mW | μW | ||||||||||||
kWb | Wb | mWb | μWb |
Base units[edit]
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 is 60 minutes, and each minute is 60 seconds. 24×60×60 = 86,400. So a second is (^{1}⁄_{86,400}) day. Cesium-133 is the only stable isotope of cesium. |
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) |
^{1}⁄_{107} 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 (1/1,000) cubic metre. Note that this unit has the kilo- prefix and is used by convention and for historical reasons, rather than the base gram. |
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 ^{2}H per mole of ^{1}H, 0.000 379 9 mole of ^{17}O per mole of ^{16}O, and 0.002 005 2 mole of ^{18}O per mole of ^{16}O." (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." |
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 × 10^{12} 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.
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 | m^{2}/m^{2} | dimensionless |
newton | N | force, weight | kg·m/s^{2} | kg·m·s^{−2} |
pascal | Pa | pressure, stress | N/m^{2} | kg·m^{−1}·s^{−2} |
joule | J | energy, work, heat | N·m = C·V = W·s | kg·m^{2}·s^{−2} |
watt | W | power, radiant flux | J/s = V·A | kg·m^{2}·s^{−3} |
coulomb | C | electric charge or quantity of electricity | s·A | s·A |
volt | V | voltage, potential difference, electromotive force | W/A = J/C | kg·m^{2}·s^{−3}·A^{−1} |
farad | F | capacitance | C/V | kg^{−1}·m^{−2}·s^{4}·A^{2} |
ohm | Ω | electrical resistance, impedance, reactance | V/A | kg·m^{2}·s^{−3}·A^{−2} |
siemens | S | electrical conductance | 1/Ω = A/V | kg^{−1}·m^{−2}·s^{3}·A^{2} |
weber | Wb | magnetic flux | J/A | kg·m^{2}·s^{−2}·A^{−1} |
tesla | T | magnetic field strength, magnetic flux density | V·s/m^{2} = Wb/m^{2} = N/(A·m) | kg·s^{−2}·A^{−1} |
henry | H | inductance | V·s/A = Wb/A | kg·m^{2}·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/m^{2} | m^{−2}·cd |
becquerel | Bq | radioactivity (decays per unit time) | 1/s | s^{−1} |
gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m^{2}·s^{−2} |
sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m^{2}·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]
Notes:
- *
- The kilogram is the SI base unit for mass, not the gram, which is obviously (1/1000) kilogram.
- +
- The candela is still considered an SI base unit, though it is no longer fundamental, being defined in terms of other SI units.
Variations in other languages[edit]
Finnish[edit]
- yotta- = jotta-
- zetta- = tsetta-
- exa- = eksa-
- peta- = peta-
- tera- = tera-
- giga- = giga-
- mega- = mega-
- kilo- = kilo-
- hecto- = hehto-
- deca- = deka-
- deci- = desi-
- centi- = sentti-
- milli- = milli-
- micro- = mikro-
- nano- = nano-
- pico- = piko-
- femto- = femto-
- atto- = atto-
- zepto- = tsepto-
- yocto- = jokto-
~~
- meter = metri
- kilogram = kilogramma
- second = sekunti
- ampere = ampeeri
- kelvin = kelvin
- mole = mooli
- candela = kandela
~~
- hertz = hertsi
- joule = joule
- watt = watti
- volt = voltti
- ampere = ampeeri
- ohm = ohmi
- farad = faradi
- henry = henry
- radian = radiaani
- steradian = steradiaani
- lumen = lumen
- lux = luksi
French[edit]
In French, accents appear in the following prefixes and unit-names:
German[edit]
In German, common nouns (including the names of SI units) are capitalized. Some spelling variations also appear:
- hecto- = hekto-
- deca- = deka-
- deci- = dezi-
- centi- = zenti-
- micro- = mikro-
- pico- = piko-
- yocto- = yokto-
Greek[edit]
- quetta- = κουεττα-
- ronna- = ροννα-
- yotta- = γιοττα-
- zetta- = ζεττα-
- exa- = εξα-
- peta- = πετα-
- tera- = τερα-
- giga- = γιγα-
- mega- = μεγα-
- kilo- = χιλιο-
- hecto- = εκατο-
- deca- = δεκα-
- deci- = δεκατο-
- centi- = εκατοστο-
- milli- = χιλιοστο-
- micro- = μικρο-
- nano- = νανο-
- pico- = πικο-
- femto- = φέμτο-
- atto- = αττο-
- zepto- = ζεπτο-
- yocto- = γιοκτο-
- ronto- = ροντο-
- quecto- = κουέκτο-
~~
- meter = μέτρο
- kilogram = χιλιόγραμμο
- second = δευτερόλεπτο
- ampere = αμπέρ
- kelvin = κέλβιν
- mol = μολ
- candela = καντέλα
Spanish[edit]
- hertz = hercio
- joule = julio
- watt = vatio
- volt = voltio
- ampere = amperio
- ohm = ohmio
- farad = faradio
- henry = henrio
- radian = radián
- steradian = estereorradián
References[edit]
- ^ Resolution of the International Bureau of Weights and Measures establishing the International System of Units
- ^ Official BIPM definitions
- ^ Essentials of the SI: Introduction
- ^ 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.
– CODATA reportIn the International System of Units (SI) (BIPM, 2006), the definition of the metre fixes the speed of light in vacuum c_{0}, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) μ_{0}, and the definition of the mole fixes the molar mass of the carbon-12 atom M(^{12}C) 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 μ_{0} by ε_{0} = 1/μ_{0}c_{0}^{2}, it too is known exactly.