International System of Units

The International System of Units, abbreviated SI from its French language name, Système international d'unités, is a comprehensive set of units of measurement. The SI is based on the original metric system developed in France in the 1790s. In October 1960 the 11th international "General Conference on Weights and Measures" met in Paris and renamed the Metric System (MKSA) of units (based on the six base units: meter, kilogram, second, ampere, kelvin and candela&mdash;in 1971 mole was added as seventh base unit) to the "International System of Units." The 11th Conference also established the abbreviation "SI" as the official abbreviation, to be used in all languages. Adoption of the abbreviation SI, especially outside scientific circles, is slow. The terms "metric system" or "MKSA units" are still frequently being used.

Base units
The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent:

Prefixes
To allow for ease of discussion of quantities orders of magnitude different from the base units, prefixes may be used to form decimal multiples and submultiples of units. The SI prefixes with their meanings and symbols are:

It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.

Derived units
Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units.

Dimensionless derived units
There are two dimensionless derived units, for plane angle and solid angle:

Named derived units
Twenty other derived units have specific names; most are named after pioneering researchers in the fields in which they are used. These are:

Other derived units
Some derived units are named after the basic units from which they are derived, sometimes including the dimension. Other derived units have names which are a mix of base unit names and derived unit names. Some are listed below:

Non-SI units accepted for use
The 2006 edition of the International System of Units, published by the International Bureau of Weights and Measures (BIPM) includes non-SI units that are accepted for use with the International System because they are widely used in everyday life. Their use is expected to continue indefinitely, and each has an exact definition in terms of an SI unit. The values in the table below were extracted from Tables 6 and 8 of the 2006 Edition:

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 since 1979. The cursive "ℓ" is occasionally seen, especially in Japan and Greece, 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, 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 . 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&times;102 m2", "22 °C" . 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 many countries while others use a period. 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&minus;1", "m·s&minus;1" or $$\textstyle\frac{\mathrm{m}}{\mathrm{s}}.$$ A solidus should not be used if the result is ambiguous, i.e. "kg·m&minus;1·s&minus;2" is preferable to "kg/m·s2". (Taylor (§ 6.1.6) 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 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".


 * In some English-speaking countries, the unit "ampere" is often shortened to "amp" (singular) or "amps" (plural).