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Cover of brochure The International System of Units.
Cover of brochure The International System of Units.

The International System of Units (abbreviated SI from the French language name Système international d'unités) is the modern form of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science. English units are still used in some scientific applications, but note also that parsecs in astronomy, calories and mmHg in the medical sciences, and electronvolts in physics are not part of the specific system of units known as SI, to just scratch the surface.

The older metric system included several groupings of units. The SI was developed in 1960 from the metre-kilogram-second (mks) system, rather than the centimetre-gram-second (cgs) system which, in turn, had many variants.

The SI introduced several newly named units. The SI is not static; it is a living set of standards where units are created and definitions are modified with international agreement as measurement technology progresses.

With few exceptions, the system is used in every country in the world, and many countries do not maintain official definitions of other units. In the United States, industrial use of SI is increasing, but popular use is still limited. In the United Kingdom, conversion to metric units is official policy but not yet complete. Those countries that still recognize non-SI units (e.g. the U.S. and UK) have redefined their traditional non-SI units in terms of SI units.

Contents

History

See main articles: metre, kilogram, second, ampere, kelvin, candela, and mole.

The metric system was conceived by a group of scientists (among them, Lavoisier) which had been commissioned by king Louis XVI of France to create a unified and rational system of measures. After the French Revolution, the system was adopted by the new government. On August 1, 1793 the National Convention adopted the new decimal "metre" with a provisional length as well as the other decimal units with preliminary definitions and terms. On April 7, 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms "gravet" (correctly "milligrave") and "grave".

A month after the coup of 18 Brumaire, the metric system was definitively adopted in France by the First Consul Bonaparte, (the later Napoleon I) on December 10, 1799. During the history of the metric system a number of variations have evolved and their use spread around the world replacing many traditional measurement systems.

By the end of World War II a number of different systems of measurement were still in use throughout the world. Some of these systems were metric system variations while others were based on the Imperial and American systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.

Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units recommended were the metre, kilogram, second, ampere, Kelvin degree (later renamed the kelvin), and the candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name: Template:Lang. The seventh base unit, the mole, was added in 1970 by the 14th CGPM.

Units

The international system of units consists of a set of units together with a set of prefixes. The units of SI can be divided into two subsets. There are the seven base units. Each of these base units are nominally dimensionally independent. From these seven base units several other units are derived. In addition to the SI units there are also a set of non-SI units accepted for use with SI.

SI base units
Name Symbol Quantity
metre m Length
kilogram kg Mass
second s Time
ampere A Electrical current
kelvin K Thermodynamic temperature
mole mol Amount of substance
candela cd Luminous intensity

A prefix may be added to units to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.

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

Base units

The international system (SI) of units defines seven SI base units: physical units defined by an operational definition. All other physical units can be derived from these base units: these are known as SI derived units. Derivation is by dimensional analysis. Use SI prefixes to abbreviate long numbers. The following are the base units from which all others are derived. They are dimensionally independent, with the exception of the metre and candela. The candela was formerly a fundamental unit but has been redefined in terms of the other SI base units. The metre also was a fundamental unit, but has since been redefined in terms of the second. They are still considered "base units" for historical reasons, but are in fact dependent on the other units for their definition.

SI base units
Name Symbol Measure Definition Historical Origin/Justification
metre or meter m length The unit of length is equal to the length of the path travelled by light in a vacuum during the time interval of 1/299 792 458 of a second. Defined by: 17th CGPM (1983) Resolution 1, CR 97 1/10 000 000 of the distance from the earth's equator to the North Pole measured through Paris.
kilogram kg mass The unit of mass is equal to the mass of the international prototype kilogram (a platinum-iridium cylinder) kept at the Bureau International des Poids et Mesures (BIPM), Sèvres, Paris (1st CGPM (1889), CR 34-38). Note that the kilogram is the only base unit with a prefix. See the kilogram article for an alternative definition. The mass of one litre of water. Kilogram was originally named "grave" and symbolized G. The gram is defined as a derived unit, equal to 1/1000 of a kilogram; prefixes such as mega are applied to the gram, not the kg; e.g. Gg, not Mkg. It is also the only unit still defined by a physical prototype instead of a measurable natural phenomenon.
second s time The unit of time is the duration of exactly 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-133 atom at a temperature of 0 K. Defined by: 13th CGPM (1967-1968) Resolution 1, CR 103 1/86400 of the day
ampere A electrical current The unit of electrical current is the constant current which, if maintained in two straight parallel conductors, of infinite length and negligible cross-section, placed 1 metre apart in a vacuum, would produce a force between these conductors equal to 2×10 −7 newtons per metre of length. Defined by: 9th CGPM (1948) Resolution 7, CR 70
kelvin K thermodynamic temperature The unit of thermodynamic temperature (or absolute temperature) is the fraction 1/273.16 (exactly) of the thermodynamic temperature at the triple point of water. Defined by: 13th CGPM (1967) Resolution 4, CR 104 1/100 of the difference between the boiling and freezing points of water
mole mol quantity of matter (mass/mass) A mole is the quantity of substance that contains the same number of elementary entities (atoms, molecules, ions, electrons or particles, depending on the substance) as there are atoms in 0.012 kilograms of pure carbon-12; this number (NA) is approximately equal to 6.02214199×1023. Defined by: 14th CGPM (1971) Resolution 3, CR 78 one gram per atomic mass unit
candela cd luminous intensity The unit of luminous intensity 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. Defined by: 16th CGPM (1979) Resolution 3, CR 100 the candlepower

SI derived units are part of the SI system of measurement units and are derived from the seven SI base units.

Dimensionless derived units

The following SI units are actually dimensionless ratios, formed by dividing two identical SI units. They are therefore considered by the BIPM to be derived. Formally, their SI unit is simply the number 1, but they are given these special names, for use whenever the lack of a unit might be confusing.

Dimensionless SI units
Name Symbol Quantity Definition
radian rad Angle The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are 2π radians in a circle.
steradian sr Solid angle The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are 4π steradians on a sphere.

Derived units with special names

Base units can be put together to derive units of measurement for other quantities. Some have been given 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
newton N Force, Weight m∙kg/s2 m∙kg∙s−2
joule J Energy, Work, Heat N∙m m2∙kg∙s−2
watt W Power, Radiant flux J/s m2∙kg∙s−3
pascal Pa Pressure, Stress N/m2 m−1∙kg∙s−2
lumen lm Luminous flux cd∙sr cd
lux lx Illuminance lm/m2 m−2∙cd
coulomb C Electric charge or flux s∙A s∙A
volt V Electrical potential difference, Electromotive force W/A = J/C m2∙kg∙s−3∙A−1
ohm Ω Electric resistance, Impedance, Reactance V/A m2∙kg∙s−3∙A−2
farad F Electric capacitance C/V m−2∙kg−1∙s4∙A2
weber Wb Magnetic flux J/A m2∙kg∙s−2∙A−1
tesla T Magnetic flux density, magnetic induction V∙s/m2 = Wb/m2 kg∙s−2∙A−1
henry H Inductance V∙s/A = Wb/A m2∙kg∙s−2∙A−2
siemens S Electric conductance 1/Ω m−2∙kg−1∙s3∙A2
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
degree Celsius °C Thermodynamic temperature T°C = TK − 273.15</span>
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Other 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−1 speed, velocity m·s−1
metre per second squared m·s−2 acceleration m·s−2
metre per second cubed m·s−3 jerk m·s−3
radian per second rad·s−1 angular velocity s−1
newton second N·s momentum, impulse kg·m·s−1
newton metre second N·m·s angular momentum kg·m2·s−1
newton metre N·m torque, moment of force kg·m2·s−2
reciprocal metre m−1 wavenumber m−1
kilogram per cubic metre kg·m−3 density, mass density kg·m−3
cubic metre per kilogram kg−1·m3 specific volume kg−1·m3
mole per cubic metre m−3·mol amount (-of-substance) concentration m−3·mol
cubic metre per mole m3·mol−1 molar volume m3·mol−1
joule per kelvin J·K−1 heat capacity, entropy kg·m2·s−2·K−1
joule per kelvin mole J·K−1·mol−1 molar heat capacity, molar entropy kg·m2·s−2·K−1·mol−1
joule per kilogram kelvin J·K−1·kg−1 specific heat capacity, specific entropy m2·s−2·K−1
joule per mole J·mol−1 molar energy kg·m2·s−2·mol−1
joule per kilogram J·kg−1 specific energy m2·s−2
joule per cubic metre J·m−3 energy density kg·m−1·s−2
newton per metre N·m−1 = J·m−2 surface tension kg·s−2
watt per square metre W·m−2 heat flux density, irradiance kg·s−3
watt per metre kelvin W·m−1·K−1 thermal conductivity kg·m·s−3·K−1
square metre per second m2·s−1 kinematic viscosity, diffusion coefficient m2·s−1
pascal second Pa·s = N·s·m−2 dynamic viscosity kg·m−1·s−1
coulomb per cubic metre C·m−3 electric charge density m−3·s·A
ampere per square metre A·m−2 electric current density A·m−2
siemens per metre S·m−1 conductivity kg−1·m−3·s3·A2
siemens square metre per mole S·m2·mol−1 molar conductivity kg-1·s3·mol−1·A2
farad per metre F·m−1 permittivity kg−1·m−3·s4·A2
henry per metre H·m−1 permeability kg·m·s−2·A−2
volt per metre V·m−1 electric field strength kg·m·s−3·A−1
ampere per metre A·m−1 magnetic field strength A·m−1
candela per square metre cd·m−2 luminance cd·m−2
coulomb per kilogram C·kg−1 exposure (X and gamma rays) kg−1·s·A
gray per second Gy·s−1 absorbed dose rate m2·s−3
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SI writing style

  • Symbols are written in lower case, except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa" whereas the unit itself is written "pascal".
    • The one exception is the litre, whose original symbol "l" is unsuitably similar to the numeral "1", at least in many English-speaking countries. The American National Institute of Standards and Technology recommends that "L" be used instead, a usage which is common in the U.S., Canada and Australia (but not elsewhere). This has been accepted as an alternative by the CGPM in 1979. The cursive "ℓ" is occasionally seen, especially in Japan, but this is not currently recommended by any standards body. For more information, see Litre.
  • Abbreviated symbols, unlike spelt-out full names of units, should not be pluralised—for example "25 kg", not "25 kgs"—though they sometimes are. For spelt-out unit names in English, all are made plural by adding an 's', except lux, hertz, and siemens, all of which are the same in singular and plural.<
  • Symbols do not have an appended period/full stop (.) unless at the end of a sentence.
  • It is preferable to write symbols in upright Roman type (m for metres, L for litres), so as to differentiate from the italic type used for mathematical variables (m for mass, l for length).
  • A space should separate the number and the symbol, e.g. "2.21 kg", "7.3Template:E m2", "22 °C" [1]. Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
  • Spaces may be used to group decimal digits in threes, e.g. 1 000 000 or 342 142 (in contrast to the commas or dots used in other systems, e.g. 1,000,000 or 1.000.000). This is presumably to reduce confusion because a comma is used as a decimal in some countries (such as France). In print, the space used for this purpose is typically narrower than that between words.
  • The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". In practice, the decimal point is used in English, and the comma in most other European languages.
  • Symbols for derived units formed from multiple units by multiplication are joined with a space or centre dot (·), e.g. N m or N·m.
  • Symbols formed by division of two units are joined with a solidus (/), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s−1", "m·s−1" or \frac{{m}}{{s}}. A solidus should not be used if the result is ambiguous, i.e. "kg·m−1·s−2" is preferable to "kg/m·s2". (Taylor (page 13) specifically calls for the use of a solidus. Many computer users will type the / character provided on American computer keyboards, which in turn produces the Unicode character U+002F, which is named solidus. Taylor does not offer suggestions about which mark should be used when more sophisticated typesetting options are available.)
  • In countries using ideographic writing systems such as Chinese and Japanese, often the full symbol for the unit, including prefixes, is placed in one square. (See the "Letterlike Symbols" Unicode subrange)

Spelling variations

  • Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre' in keeping with standard American English spelling. In addition, the official US spelling for the SI prefix 'deca' is 'deka'.[2]
  • The unit 'ampere' is often shortened to 'amp' (singular) or 'amps' (plural).

Conversion factors

The relationship between the units used in different systems is determined by convention or from the basic definition of the units. Conversion of units from one system to another is accomplished by use of a conversion factor. There are several compilations of conversion factors; see, for example Appendix B of NIST SP 811.

Cultural Issues

The worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardize the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our decimal numeral system.

There are many units in everyday and scientific use that are not derived from the seven SI base units — metre, kilogram, second, ampere, Kelvin, mole and candela — combined with the SI prefixes. In some cases these deviations have been approved by the BIPM.[3] Examples include:

  • the many units of time—minute(min), hour(h), day, week, month, year, century—in use besides the SI second.
  • the Celsius temperature scale; Kelvin is never employed in everyday use
  • electric energy is often billed in kilowatt-hours instead of megajoules
  • use of kilometre per hour (km/h) instead of the SI metre per second for automotive speed; fuel usage is often given in litres per 100 km (L/100km).
  • the nautical mile and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 nautical mile = 1852 m ≅ 1 minute of latitude).
  • astronomical distances measured in astronomical units, parsecs and light years instead of, say, petametres (a light year is about 9.461 Pm or about 9 461 000 000 000 000 m)
  • atomic scale units used in physics and chemistry, such at the ångström, electron volt, atomic mass unit, and barn
  • some physicists still use the centimetre-gram-second (CGS) units
  • In some countries, the informal cup measurement has become 250 ml, and prices for items are sometimes given per 100 g rather than per kilogram
  • In the U.S., blood glucose measurements are recorded in milligrams per decilitre (mg/dl); in Europe, the standard is millimole/litre (mmol/l).

The fine-tuning that has happened to the metric base unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the U.S. customary units, are nowadays defined in terms of SI units, any change in the definition of the SI units results in a change of the definition of the older units as well.

Trade

The European Union has a directive banning non-SI markings after 31 December 2009 on any goods imported into the European Union. This applies to all markings on products, enclosed directions and papers, packaging, and advertisements.

Related

References and external articles

Official
Information
Pro-metric pressure groups
Pro-customary measures pressure groups
Proposed adjustment to the International system
Further reading
  • I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical Chemistry, 2nd ed., Blackwell Science Inc 1993, ISBN 0-632-03583-8.

See also

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