International System of Units

Cover of brochure The International System of Units.

The International System of Units (abbreviated SI from the French language name [Le Système international d'unités] Error: {{Lang}}: text has italic markup (help)) 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.

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 recognise non-SI units (e.g. the U.S. and U.K.) have redefined their traditional non-SI units in terms of SI units.

History

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

The metric system was conceived by a group of scientists (among them, Antoine-Laurant Lavoisier, who is known as the "father of modern chemistry") 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.^[1] 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: [Le Système international d'unités] Error: {{Lang}}: text has italic markup (help). 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.

Standard prefixes for the metric units of measure (multiples)
v
t
e
Prefix name	N/A	deca	hecto	kilo	mega	giga	tera	peta	exa	zetta	yotta	ronna	quetta
Prefix symbol		da	h	k	M	G	T	P	E	Z	Y	R	Q
Factor	10⁰	10¹	10²	10³	10⁶	10⁹	10¹²	10¹⁵	10¹⁸	10²¹	10²⁴	10²⁷	10³⁰

Standard prefixes for the metric units of measure (submultiples)
v
t
e
Prefix name	N/A	deci	centi	milli	micro	nano	pico	femto	atto	zepto	yocto	ronto	quecto
Prefix symbol		d	c	m	μ	n	p	f	a	z	y	r	q
Factor	10⁰	10⁻¹	10⁻²	10⁻³	10⁻⁶	10⁻⁹	10⁻¹²	10⁻¹⁵	10⁻¹⁸	10⁻²¹	10⁻²⁴	10⁻²⁷	10⁻³⁰

SI writing style

Symbols for units 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" or the uppercase letter "i" (depending on the typographic font used), 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, Australia, and New Zealand (but not elsewhere). This has been accepted as an alternative by the CGPM in 1979. The cursive "ℓ" is occasionally seen, especially in Japan and Hellas, but this is not currently recommended by any standards body. For more information, see Litre.

The SI rule for pluralising units is that symbols of units are not pluralised^[2], for example "25 kg" (not "25 kgs").
- The American National Institute of Standards and Technology has defined guidelines for using the SI units in its own publications and for other users of the SI^[3]. These guidelines give guidance on pluralizing unit names: the plural is formed by using normal English grammar rules, for example, "henries" is the plural of "henry". The units lux, hertz, and siemens are exceptions from this rule: they remain the same in singular and plural. Note that this rule only applies to the full names of units, not to their symbols.

Symbols do not have an appended period/full stop (.) unless at the end of a sentence.

Symbols are written 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 separates 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 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 $\textstyle {\frac {\mathrm {m} }{\mathrm {s} }}.$ 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 (§ 6.1.6) specifically calls for the use of a solidus.^[3] 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 of 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, which also corresponds to the official spelling used in several other languages, such as German, Dutch, Swedish, etc. In addition, the official U.S. spelling for the SI prefix "deca" is "deka".[2]

In some English-speaking countries, 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.^[3]

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 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. 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; kelvins are 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, in a few countries, often given in litres per 100 km (L/100 km).
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.
In the U.S., blood glucose measurements are recorded in milligrams per decilitre (mg/dl); in Canada and Europe, the standard is millimole per 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^[4] 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.

References

^ "The name "kilogram"". Retrieved 2006-07-25.
^ Bureau International des Poids et Mesures (2006). "The International System of Units (SI)" (PDF). 8th ed. Retrieved 2006-07-14. {{cite journal}}: Cite journal requires |journal= (help)
^ ^a ^b ^c Taylor, B.N. (1995). "NIST Special Publication 811: Guide for the Use of the International System of Units (SI)". National Institute of Standards and Technology. Retrieved 2006-06-09. {{cite journal}}: Cite journal requires |journal= (help)
^ Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC, as amended with Directive 89/617/EEC (which changed the cutoff date in article 3.2 to 31 December 1999) and Directive 1999/103/EC (which further changed the date to 31 December 2009). Retrieved on 2006-07-24.

External links

Official

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
Online metric conversions
Online metric conversions Conversion factors based on the Guide for the Use of the International System of Units, B. N. Taylor, NIST, 1995

Pro-metric pressure groups

Pro-customary measures pressure groups

The British Weights and Measures Association

Proposed adjustment to the International system

Dimensional Analysis of the current SI system - Blaze Labs Research