International System of Units

For other uses, see International System of Units (disambiguation).

The International System of Units (abbreviated SI from the French phrase, Système International d'Unités) is the most widely used system of units. It is the most common system for everyday commerce in the world, and is almost universally used in the realm of science.

In 1960, SI was selected as a specific subset of the existing Metre-Kilogram-Second systems of units (MKS), rather than the older Centimetre-Gram-Second system (CGS). Various new units were added with the introduction of the SI and at later times. SI is sometimes referred to as the metric system, especially in the United States, which has not widely adopted it, although it has been used more commonly in recent years, and in the United Kingdom and the Republic of Ireland, where conversion is only partial. SI is a specific canon of measurements derived and extended from the Metric system; however, not all metric units of measurement are accepted as SI units.

History

Scientists, chiefly in France, had been advocating and discussing a decimal system of measurement based on natural units at least since 1640, but the first official adoption of such a system was after the French Revolution of 1789. The metric system tried to choose units which were non-arbitrary and practical, merging well with the revolution's official ideology of "pure reason"; it was proposed as a considerable improvement over the inconsistent customary units which existed before, whose value often depended on the region.

The most important unit is that of length: one metre was originally defined to be equal to 1/10 000 000^th of the distance from the pole to the equator along the meridian through Paris. (Prior discussions had often suggested the length of a seconds pendulum in some standard gravity, which would have been only slightly shorter, and perhaps easier to determine.) This is approximately 10% longer than one yard. Later on, a platinum rod with a rigid, X-shaped cross section was produced to serve as the easy-to-check standard for one metre's length. Due to the difficulty of actually measuring the length of a meridian quadrant in the 18th century, the first platinum prototype was short by 0.2 millimetres. More recently, the metre was redefined as a certain multiple of a specific radiation wavelength, and currently it is defined as the distance travelled by light in a vacuum in a specific period of time. Attempts to relate an integer multiple of the metre to any meridian have been abandoned.

The original base unit of mass in the metric system was the gram, chosen to match the mass of one cubic centimetre of water. For practical reasons, the reference standard that was deposited at the Archives de la république on June 22, 1799 was a kilogram (a cylinder of platinum). One kilogram is about 2.2 pounds. In 1889, the first CGPM sanctioned a replacement prototype, a cylinder of a 90% platinum, 10% iridium alloy; this has served as the standard ever since, and is stored in a Paris vault. The kilogram became the base unit in 1901.

Also in 1901, a kilogram of distilled pure water at its densest (+3.98 degrees Celsius) under a standard atmosphere of pressure was used to define the litre, a more convenient unit than the very large cubic metre. Because this litre turned out to be different from the cubic decimetre by about 28 millionths, this definition was abandoned in 1964 in favour of the cubic decimetre.

The kilogram is the only base unit not to have been redefined in terms of an unchanging natural phenomenon. Such a definition, said to be in terms of an artefact (the cylinder in Paris), is particularly inconvenient, because, in principle, it can be used only by travelling to Paris and, with permission, comparing one's own candidate standard to the reference one. For this reason, as well as the effort required to protect the standard from absorbtion or dispersion of gases and vapours, at a meeting of the Royal Society in London on 15 February, 2005, scientists called for the mass of the standard kilogramme in Paris to be replaced by a standard based on "an invariable property of nature"; but no decision on redefinition can be taken before 2007.

The unit of temperature became the centigrade or inverted Celsius grade, which means the mercury scale is divided into 100 equal-length parts between the water-ice mixture at 0 °C and the boiling point of pure, distilled water at 100 °C (under a standard atmosphere). This is the metric unit of temperature in everyday use. A hundred years later, the discovery of absolute zero prompted the establishment of a new temperature scale which relocates the zero point at absolute zero, with the difference between freezing and boiling water close to 100 K.

The metric unit of time became the second, originally defined as 1/86 400^th of a mean solar day. The formal definition of the second has been changed several times as more accurate definitions became possible, based first on astronomic observations, then the tuning fork clock, quartz clock, and today the caesium atomic clock.

The SI was first given its name in 1960, and last added to in 1971. It is administered by the standards organization: the Bureau International des Poids et Mesures (International Bureau of Weights and Measures).

Cultural issues

The swift worldwide adoption of the metric system as a tool of economy and everyday commerce was based mainly 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.

Cultural differences can be represented in the local everyday uses of metric units. For example, bread is sold in one-half, one or two kilogram sizes in many countries, but you buy them by multiples of one hundred grams in the former USSR. 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. A profound cultural difference between physicists and engineers, especially radio engineers, existed prior to the adoption of the MKS system and hence its descendent, SI. Engineers work with volts, amperes, ohms, farads, and coulombs, which are of great practical utility, while the CGS units, which are fine for theoretical physics (because of the absence of fabricated "constants" like the "permittivity of the vacuum") are quite inconvenient for engineering usage and totally unfamiliar to householders using appliances rates in volts and watts.

Non-scientific people should not be put off by the fine-tuning that has happened to the metric base units over the past 200 years, as experts have tried frequently to refine the metric system to fit the best scientific researcher (e.g. CGS to MKS to SI system changes or the invention of the Kelvin scale). These changes do not affect the everyday use of metric units. The presence of these adjustments has been one reason advocates of the U.S. customary units have used against metrication; these customary units, however, are nowadays defined in terms of SI units, thus any difference in the definition of the SI units results in a difference of the definition of the customary units.

Basis

SI consists of seven base units and several derived units, together with a set of prefixes.

The seven SI base units are the kilogram (mass), metre (distance), second (time), ampere, kelvin (temperature), mole (amount), and candela.

SI also defines a number of SI prefixes to be used with the units: these combine with any unit name to give subdivisions and multiples. For example, the prefix kilo denotes a multiple of a thousand, so the kilometre is 1000 metres, the kilogram 1000 grams, and so on. The prefixes are never combined; a millionth of a kilogram is a milligram, and not a 'microkilogram'.

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 offical abbreviation is "L". "l" is commonly used, but is deprecated for being too similar to "1". The handwriting-style "ℓ" is also often used to solve this problem where the particular character is available, especially in Japan. For more on this exception for the litre, see Litre.
• Symbols are written in singular form: i.e. "25 kg", not "25 kgs". Pluralization would be language dependent; "s" plurals (as in French and English) are particularly undesirable since "s" is the symbol of the second.
• Symbols do not have an appended period (.).
• 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", "7.3×10² 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 should 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).
• In English, the decimal point should be written as the full stop, i.e. the number "twenty four point five one" would be written as "24.51". (This was introduced by the CIPM in 1997). In all other languages, the comma is used instead, (i.e. "24,51").
• 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 ${\frac {\mbox{m}}{\mbox{s}}}$. A solidus should not be used if the result is ambiguous, i.e. "kg·m^-1·s^-2" is preferable to "kg/m/s²".

With a few exceptions (such as draught beer sales in the United Kingdom) the system can legally be used in every country in the world and many countries do not maintain definitions of other units. Those countries that still give official recognition to non-SI units (e.g. the US and UK) have defined many of the modern units in terms of SI units; for example, the common yard is defined to be exactly 0.9144 metres. In the US, survey distances are also defined in terms of metric units, but differently: 1 survey yard = 3600/3937 m. They have, however, not been redefined due to the accumulation of error it would entail and the survey foot and survey mile remain as separate units. (This was not a problem for the United Kingdom, as the Ordnance Survey has been metric since before World War II.) (See weights and measures for a history of the development of units of measurement.)

Units

Base units

The following are the fundamental units from which all others are derived, they are dimensionally independent. The definitions stated below are widely accepted.

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.

Derived units with special names

Base units can be put together to derive units of measurement for other quantities. Some have been given names.

Non-SI units accepted for use with SI

The following units are not SI units but are "accepted for use with the International System."

SI prefixes

The following SI prefixes can be used to prefix any of the above units to produce a multiple or submultiple of the original unit. This includes the degree Celsius (e.g. "1.2 m°C"); however, to avoid confusion, prefixes are not used with the time-related unit symbols min (minute), h (hour), d (day). They are not recommended for use with the angle-related symbols ° (degree), ' (minute of arc), and " (second of arc) [2], but for astronomical usage, they are sometimes used with seconds of arc.

SI prefixes

Prefix		Base 10	Decimal	Adoption
Name	Symbol
quetta	Q	1030	1000000000000000000000000000000	2022
ronna	R	1027	1000000000000000000000000000
yotta	Y	1024	1000000000000000000000000	1991
zetta	Z	1021	1000000000000000000000
exa	E	1018	1000000000000000000	1975
peta	P	1015	1000000000000000
tera	T	1012	1000000000000	1960
giga	G	109	1000000000
mega	M	106	1000000	1873
kilo	k	103	1000	1795
hecto	h	102	100
deca	da	101	10
—	—	100	1	—
deci	d	10−1	0.1	1795
centi	c	10−2	0.01
milli	m	10−3	0.001
micro	μ	10−6	0.000001	1873
nano	n	10−9	0.000000001	1960
pico	p	10−12	0.000000000001
femto	f	10−15	0.000000000000001	1964
atto	a	10−18	0.000000000000000001
zepto	z	10−21	0.000000000000000000001	1991
yocto	y	10−24	0.000000000000000000000001
ronto	r	10−27	0.000000000000000000000000001	2022
quecto	q	10−30	0.000000000000000000000000000001
Notes

Obsolete metric prefixes

The following metric prefixes are no longer in use: myria-, myrio-, and any double prefixes such as those formerly used in micromicrofarads, hectokilometres, millimicrons.

See: Obsolete metric prefixes

Spelling variations

Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre'. This is in keeping with standard American English spelling (for example, Americans also use 'center' rather than 'centre,' using the latter only rarely for its stylistic implications; see also American and British English differences). In addition, the official US spelling for the SI prefix 'deca' is 'deka'.

The US government has approved these spellings for official use, but the BIPM only recognizes the British English spellings as official names for the units. In scientific contexts only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.

The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and use is declining.

See also

• Weights and measures
• Mesures usuelles
• Metrified Imperial system
• Other measurement systems:
  • Imperial units
  • U.S. customary units
  • Metre-tonne-second system of units
  • Chinese system of units
  • Planck units
  • Atomic units
  • Geometrized units
  • Ancient weights and measures
  • Medieval weights and measures
• CODATA
• Metrication
• Metric system in the United States
• Metrology
• UTC (Coordinated Universal Time)
• Binary Prefixes - used to quantify large amounts of computer data
• Orders of magnitude
• ISO 31

External links

Official

• BIPM (SI maintenance agency) (home page)
• BIPM brochure (SI reference)
• ISO 1000:1992 SI units and recommendations for the use of their multiples and of certain other units, with its price tag of 99 Swiss francs for a 22 page, coverless pamphlet showing why the public is sometimes a little slow to pick up on their recommendations.

Information

• US NIST reference on SI
  • chart
• SI - Its history and use in science and industry
• A Dictionary of Units of Measurement
• Cyrillic transcription of SI symbols
• Judson, Lewis B., Weights and Measures Standards of the United States: A brief history, NBS Special Publication 447, orig. iss. October 1963, updated March 1976 (46 page PDF file)
• Metric system and conversion tables (courtesy French property advice)
• metre-info - an encyclopaedia of all metric units

Pro-metric pressure groups

• The UK Metric Association
• The US Metric Association

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 0632035838.