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SI System and Units

Submitted by Hermit Barber on Tue, 2011-07-12 08:04

Source: Wikipedia (Compilation from multiple pages, with footnotes removed)

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The SI System (The International System of Units (abbreviated SI from French: Système international d'unités))

Standard prefixes for the SI units of measure
Multiples Name   deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yotta-
Symbol   da h k M G T P E Z Y
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024
 
Fractions Name   deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Symbol   d c m μ n p f a z y
Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24

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.

SI base units
Name Unit symbol Quantity Symbol
metre m length l (a lowercase L)
kilogram kg mass m
second s time t
ampere A electric current I (a capital i)
kelvin K thermodynamic temperature T
candela cd luminous intensity Iv (a capital i with lowercase v subscript)
mole mol amount of substance n

The names of SI units are always written in lowercase. The symbols of units named after persons, however, are always written with an initial capital letter (e.g., the symbol of hertz is Hz; but metre becomes m).

Examples of derived quantities and units

Compound units derived from SI units
Name Symbol Quantity Expression in terms
of SI base units
square metre m2 area m2
cubic metre m3 volume m3
metre per second m/s speed, velocity m·s−1
cubic metre per second m3/s volumetric flow m3·s−1
metre per second squared m/s2 acceleration m·s−2
metre per second cubed m/s3 jerk, jolt m·s−3
metre per quartic second m/s4 snap, jounce m·s−4
radian per second rad/s angular velocity s−1
newton second N·s momentum, impulse m·kg·s−1
newton metre second N·m·s angular momentum m2·kg·s−1
newton metre N·m = J/rad torque, moment of force m2·kg·s−2
newton per second N/s yank m·kg·s−3
reciprocal metre m−1 wavenumber m−1
kilogram per square metre kg/m2 area density m−2·kg
kilogram per cubic metre kg/m3 density, mass density m−3·kg
cubic metre per kilogram m3/kg specific volume m3·kg−1
mole per cubic metre mol/m3 amount of substance concentration m−3·mol
cubic metre per mole m3/mol molar volume m3·mol−1
joule second J·s action m2·kg·s−1
joule per kelvin J/K heat capacity, entropy m2·kg·s−2·K−1
joule per kelvin mole J/(K·mol) molar heat capacity, molar entropy m2·kg·s−2·K−1·mol−1
joule per kilogram kelvin J/(K·kg) specific heat capacity, specific entropy m2·s−2·K−1
joule per mole J/mol molar energy m2·kg·s−2·mol−1
joule per kilogram J/kg specific energy m2·s−2
joule per cubic metre J/m3 energy density m−1·kg·s−2
newton per metre N/m = J/m2 surface tension kg·s−2
watt per square metre W/m2 heat flux density, irradiance kg·s−3
watt per metre kelvin W/(m·K) thermal conductivity m·kg·s−3·K−1
square metre per second m2/s kinematic viscosity, diffusion coefficient m2·s−1
pascal second Pa·s = N·s/m2 dynamic viscosity m−1·kg·s−1
coulomb per square metre C/m2 electric displacement field, polarization vector m−2·s·A
coulomb per cubic metre C/m3 electric charge density m−3·s·A
ampere per square metre A/m2 electric current density A·m−2
siemens per metre S/m conductivity m−3·kg−1·s3·A2
siemens square metre per mole S·m2/mol molar conductivity kg-1·s3·mol−1·A2
farad per metre F/m permittivity m−3·kg−1·s4·A2
henry per metre H/m permeability m·kg·s−2·A−2
volt per metre V/m electric field strength m·kg·s−3·A−1
ampere per metre A/m magnetic field strength A·m−1
candela per square metre cd/m2 luminance cd·m−2
coulomb per kilogram C/kg exposure (X and gamma rays) kg−1·s·A
gray per second Gy/s absorbed dose rate m2·s−3
ohm metre Ω·m resistivity m3·kg·s−3·A−2

Derived units with special names

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, 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

 

In addition to the SI units, there is also a set of non-SI units accepted for use with SI, which includes some commonly used non-coherent units.

This is a list of units that are not defined as part of the International System of Units (SI), but are otherwise mentioned in the SI[1][2], because either the General Conference on Weights and Measures (CGPM) accepts their use as being multiples or submultiples of SI-units, they have important contemporary application worldwide, or are otherwise commonly encountered worldwide.

Units officially accepted for use with the SI

Name Symbol Quantity Equivalent SI unit
Widely used units expected to be used indefinitely
minute min time (SI unit multiple) 1 min = 60 s
hour h time (SI unit multiple) 1 h = 60 min = 3600 s
day d time (SI unit multiple) 1 d = 24 h = 1440 min = 86400 s
degree of arc ° angle (dimensionless unit) 1° = (π/180) rad
minute of arc ′ angle (dimensionless unit) 1′ = (1/60)° = (π/10800) rad
second of arc ″ angle (dimensionless unit) 1″ = (1/60)′ = (1/3600)° = (π/648000) rad
hectare ha area (decimal unit multiple) 1 ha = 100 a = 10000 m2 = 1 hm2
litre l or L volume (decimal unit multiple) 1 L = 1 dm3 = 0.001 m3
tonne t mass (decimal unit multiple) 1 t = 103 kg = 1 Mg
Logarithmic units
neper Np dimensionless ratio of field quantities LF = ln(F/F0) Np
    dimensionless ratio of power quantities LP = 1⁄2ln(P/P0) Np
bel, decibel B, dB dimensionless ratio of field quantities LF = 2 log10(F/F0) B
    dimensionless ratio of power quantities LP = log10(P/P0) B
Units with experimentally determined values
electron-volt eV energy 1 eV = 1.60217653(14)×10−19 J
atomic mass unit
dalton		 u
Da		 mass 1 u = 1 Da = 1.66053886(28)×10−27 kg
astronomical unit ua length 1 ua = 1.49597870691(6)×1011 m
Natural units (n.u.)
speed of light c0 speed 299,792,458 m/s (exact)
reduced Planck constant ħ action 1.05457168(18)×10−34 J·s
electron rest mass me mass 9.1093826(16)×10−31 kg
n.u. of time \hbar/(m_e c_0 ^2) time 1.2880886677(86)×10−21 s
Atomic units (a.u.)
elementary charge e electric charge 1.60217653(14)×10−19 C
Bohr radius a0 length 0.5291772108(18)×10−10 m
Hartree energy Eh energy 4.35974417(75)×10−18 J
a.u. of time ħ/Eh time 2.418884326505(16)×10−17 s

Common units not officially sanctioned

Name Symbol Quantity Equivalent SI unit
Ångström, angstrom Å length 1 Å = 0.1 nm = 10−10 m
nautical mile nm length 1 nautical mile = 1852 m
knot kt speed 1 knot = 1 nautical mile per hour = (1852/3600) m/s
are a area 1 a = 1 dam2 = 100 m2
barn b area 1 b = 10−28 m2
bar bar pressure 1 bar = 105 Pa
millibar mbar pressure 1 mbar = 1 hPa = 100 Pa
atmosphere atm pressure 1 atm = 1013.25 mbar = 1013.25 hPa = 1.01325×105 Pa (commonly used in atmospheric meteorology, in oceanology and for pressures within liquids, or in the industry for pressures within containers of liquified gas)

 

 

History

 

According to the CIA Factbook only Burma (Myanmar), Liberia, and the United States have yet to adopt the International System of Units as their official system of measurement. However, they all have adopted metric measures to some degree through international trade and standardisation for example, Liberia switched to selling fuel by the litre in May 2011. The United States mandated the acceptance of the metric system in 1866 for commercial and legal proceedings, without displacing their customary units. Both Liberia and Myanmar are substantially metric countries, trading internationally in metric units. Visitors also report that they use metric units for many things internally with exceptions such as old petrol pumps in Myanmar, calibrated in British Imperial gallons.

However, a number of jurisdictions have laws mandating or permitting other systems of measurement in some or all contexts, such as the United Kingdom, which still uses many imperial measures, such as miles and yards for road-sign distances, road speed limits in miles per hour, lb/oz, pints, etc. for many products, and inches for clothes. Most countries have adopted the metric system officially over a transitional period where both units are used for a set period of time. Some countries such as Guyana, for example, have officially adopted the metric system, but have had some trouble over time implementing it. Antigua, also 'officially' metric, is moving toward total implementation of the metric system, but slower than expected. Other Caribbean countries such as Saint Luciaare officially metric but are still in the process toward full conversion.

In the European Union, the European Council (of Ministers) used the Units of Measure Directive to achieve a common system of weights and measures and to facilitate the European Single Market. Throughout the 1990s, the European Commission helped accelerate the process for member countries to complete their metric conversion processes. During these negotiations, the United Kingdom secured permanent exemptions for the mile and yard in road markings, and (with Ireland) for the pint of beer sold in pubs (see Metrication in the United Kingdom). In 2007, the European Commission also announced that (to facilitate trade with the United States) it was to abandon the requirement for metric-only labelling on packaged goods, and to allow dual metric-imperial marking to continue indefinitely.

Other countries using the old imperial system completed metrication during the second half of the 20th century. The most recent to complete this process was the Republic of Ireland, which began metric conversion in the 1970s and finalised it in early 2005.

In January 2007 NASA agreed to use metric units for all future moon missions due to pressure from other space agencies.

The United States and the United Kingdom have some active opposition to metrication. Other countries, like France and Japan, that once had significant popular opposition to metrication now have complete acceptance of metrication.

 Year of Adoption of the Metric System


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