The International System of Units (abbreviated SI from the French le Système international d'unités) 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.
The older metric system included several groups of units. The SI was developed in 1960 from the old metre-kilogram-second system, rather than the centimetre-gram-second system, which, in turn, had a few variants. Because the SI is not static, units are created and definitions are modified through international agreement among many nations as the technology of measurement progresses, and as the precision of measurements improves.
The system has been nearly globally adopted. Three principal exceptions are Burma (Myanmar), Liberia, and the United States. The United Kingdom has officially adopted the International System of Units but not with the intention of replacing customary measures entirely.
It is very important to distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is carefully drawn up so that it is unique and provides a sound theoretical basis upon which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of how the definitions of some important units are realised in practice is given on the BIPM website.
A coherent SI derived unit can be expressed in SI base units with no numerical factor other than the number 1. The coherent SI derived unit of resistance, the ohm, symbol Ω, for example, is uniquely defined by the relation Ω = m2·kg·s−3·A−2, which follows from the definition of the quantity electrical resistance. However, "any method consistent with the laws of physics could be used to realise any SI unit." (p. 111).
The metric system was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier, who is known as the "father of modern chemistry") who had been commissioned by 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 1 August 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 7 April 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms gravet (correctly milligrave) and grave. On 10 December 1799 (a month after Napoleon's coup d'état), the metric system was definitively adopted in France.
The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty which established three international organizations to oversee the keeping of metric standards:
The history of the metric system has seen a number of variations, whose use has spread around the world, to replace many traditional measurement systems. At 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, whereas others were based on customary 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 that were recommended are the metre, kilogram, second, ampere, degree Kelvin (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: Le Système international d'unités. The seventh base unit, the mole, was added in 1971 by the 14th CGPM.
ISO 31 contains recommendations for the use of the International System of Units; for electrical applications, in addition, IEC 60027 has to be taken into account. As of 2008, work is proceeding to integrate both standards into a joint standard Quantities and Units in which the quantities and equations used with SI are to be referred as the International System of Quantities (ISQ).
A readable discussion of the present units and standards is found at Brian W. Petley International Union of Pure and Applied Physics I.U.P.A.P.- 39 (2004).
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 seven base units: Each of these base units represents, at least in principle, different kinds of physical quantities. From these seven base units, several other units are derived. 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 units such as the litre.
|metre||m||length||l (a lowercase L)|
|ampere||A||electric current||I (a capital i)|
|candela||cd||luminous intensity||Iv (a capital i with lowercase v subscript)|
|mole||mol||amount of substance||n|
A prefix may be added to a unit 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.
U+002F, which is named solidus but is distinct from the Unicode solidus character,
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.
Density (specific mass) is commonly expressed in SI units or in reference to water. Since a cube with sides of 1 decimetre has volume of 1 cubic decimetre, which is 1 litre and, when filled with water, has a approximate mass of 1 kilogram, water has an approximate density of 1 kilogram per litre, which is equal to 1 gram per cubic centimetre and 1 tonne per cubic metre, and will freeze at approximately 0 degrees Celsius at 1 atmosphere of pressure.
Note that this is only an approximate definition of the kilogram, as the density of water can change with temperature; the actual definition is based on a specific platinum-iridium cylinder held in a vault at the BIPM in Sèvres, France.
The near-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 standardise the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. For use in science, it simplifies dealing with very large and small quantities, since it lines up so well with the decimal numeral system.
Many units in everyday and scientific use 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. Some examples include:
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 US customary units, are nowadays defined in SI units, any change in the definition of the SI units results in a change of the definition of the older units, as well.
One of the European Union's (EU) objectives is the creation of a single market for trade. In order to achieve this objective, the EU standardised on using SI as the legal units of measure. At the time of writing (2009) it had issued two units of measurement directives which catalogued the units of measure that might be used for, amongst other things, trade: the first was Directive 71/354/EEC issued in 1971 which required member states to standardise on SI rather than use the variety of cgs and mks units then in use. The second was Directive 80/181/EEC issued in 1979 which replaced the first and which gave the United Kingdom and the Republic of Ireland a number of derogations from the original directive.
The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty or which were in universal use in worldwide trade. They also permitted the use of supplementary indicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, supplementary indicators have been allowed indefinitely.
|Standards and conventions|
– CODATA report
In the International System of Units (SI) (BIPM, 2006), the definition of the meter 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.
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The International System of Units is the international standard form of the metric system today. SI is the short name for this from the French language phrase Système International d'unités.
Sometimes we want to talk about larger or smaller measurements. Then we add a prefix. A prefix is adding something to the beginning of a word to make a new word. The prefix kilo- means "1000" and the prefix milli- means "0.001". So one kilometre is 1000 metres and one milligram is a 1000th of a gram. These prefixes are shown in the table on the right side.
These were created in France after the French Revolution. They are now used almost everywhere in the world, except for the United States, Liberia and Myanmar, where the older imperial units are still widely used. Other countries, most of them historically related to the British Empire, are slowly replacing the old imperial system with the metric system.
Even the United Kingdom, which created the old US units of measurement, is now using the metric system and the imperial system at the same time. There is pressure to become more metric, both from UK government plans written before Britain's entry into the European Union and because of EU rules about common systems of measurement.
|yotta-||Y||1 000 000 000 000 000 000 000 000|
|zetta-||Z||1 000 000 000 000 000 000 000|
|exa-||E||1 000 000 000 000 000 000|
|peta-||P||1 000 000 000 000 000|
|tera-||T||1 000 000 000 000|
|giga-||G||1 000 000 000|
|mega-||M||1 000 000|
|milli-||m||1/ 1 000|
|micro-||µ||1/ 1 000 000|
|nano-||n||1/ 1 000 000 000|
|pico-||p||1/ 1 000 000 000 000|
|femto-||f||1/ 1 000 000 000 000 000|
|atto-||a||1/ 1 000 000 000 000 000 000|
|zepto-||z||1/ 1 000 000 000 000 000 000 000|
|yocto-||y||1/ 1 000 000 000 000 000 000 000 000|
The SI base units are measurements used by scientists and other people around the world. All the other units can be written by combining these seven base units in different ways. These other units are called "derived units".
Unit: metre or meter (m)
One metre is defined as the distance light travels in a vacuum in 1/299,792,458 second. It is also 1/10000000 (one ten-millionth) of the distance from the North Pole to the Equator. This standard was adopted in 1983 when the speed of light in vacuum was defined to be precisely 299,792,458 m/s.
Unit: kilogram (kg)
One kilogram is defined to be the mass of a specific cylinder of platinum-iridium alloy. It is kept at the International Bureau of Weights and Measures near Paris. There is an ongoing effort to introduce a definition using other basic or atomic constants.
Unit: second (s)
Unit: ampere (A)
The ampere is that constant electrical current (or flow) which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per metre of length.
The ampere is one of two base units (the other being the candela) that uses derived units in its definition, not just base units. One newton is 1 kg m s-2.
Unit: kelvin (K)
Unit: mole (mol)
Unit: candela (cd)
The candela is the luminous intensity (brightness), 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.
The candela is one of two base units (the other being the ampere) that uses derived units in its definition, not just base units. One hertz is 1 s-1, one watt is 1 J s-1 = 1 kg m2 s-2 and the steradian 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.
Unit: radian (rad)
Unit: steradian (sr)
Unit: hertz (Hz)
Unit: newton (N)
Unit: pascal (Pa)
Unit: joule (J)
Unit: watt (W)
Unit: coulomb (C)
Unit: volt (V)
Unit: farad (F)
Unit: ohm (Ω)
There are also derived units which have special names. Usually these were made to make calculating simpler.
|Name||Symbol||Quantity||Expression in terms of other units||Expression in terms of SI base units|
|joule||J||energy, work, heat||N∙m||m2∙kg∙s−2|
|watt||W||power, radiant flux||J/s||m2∙kg∙s−3|
|coulomb||C||electric charge or electric flux||s∙A||s∙A|
|volt||V||voltage, electrical potential difference, electromotive force||W/A = J/C||m2∙kg∙s−3∙A−1|
|ohm||Ω||electrical resistance, impedance, reactance||V/A||m2∙kg∙s−3∙A−2|
|tesla||T||magnetic field||V∙s/m2 = Wb/m2 = N/A∙m||kg∙s−2∙A−1|
|henry||H||inductance||V∙s/A = Wb/A||m2∙kg∙s−2∙A−2|
|Celsius||°C||Celsius Temperature||T°C = TK − 273.15||K|
|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|