# International System of Units (SI)

The International System of Units universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement, used prevalently in science and international commerce.

There are seven base units and symbols for the seven base quantities, which are assumed to be independent. These seven base units are essential for the construction of derived units. See: Physical quantity (definition) for base and derived units.

## How to write unit symbols and names, expressing the values of quantities

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter. It is not permissible to use abbreviations for unit symbols or unit names.

A multiple or sub-multiple prefix, if used, is part of the unit and precedes the unit symbol without a separator. A prefix is never used in isolation, and compound prefixes are never used.

Unit symbols are mathematical entities and not abbreviations. Therefore, they are not followed by a period except at the end of a sentence, and one must neither use the plural nor mix unit symbols and unit names within one expression since names are not mathematical entities.

Forming products and quotients of unit symbols the normal rules of algebraic multiplication or division apply. Multiplication must be indicated by one space or a half-high (centered) dot “

” since otherwise some prefixes could be misinterpreted as a unit symbol. The division is indicated by a horizontal line, by a solidus (oblique stroke, /) or by negative exponents. When several unit symbols are combined, care should be taken to avoid ambiguities, for example by using brackets or negative exponents. A solidus must not be used more than once in a given expression without brackets to remove ambiguities.

Unit names are normally printed in roman (upright) type, and they are treated like ordinary nouns. In English, the names of units start with a lower-case letter (even when the symbol for the unit begins with a capital letter), except at the beginning of a sentence or in capitalized material such as a title. In keeping with this rule, the correct spelling of the name of the unit with the symbol °C is “degree Celsius” (the unit degree begins with a lower-case d and the modifier Celsius begins with an upper-case C because it is a proper name).

Although the values of quantities are normally expressed using symbols for numbers and symbols for units, if for some reason the unit name is more appropriate than the unit symbol, the unit name should be spelled out in full.

When the name of a unit is combined with the name of a multiple or sub-multiple prefix, no space or hyphen is used between the prefix name and the unit name. The combination of prefix name plus the unit name is a single word.

In both English and in French, however, when the name of a derived unit is formed from the names of individual units by multiplication, then either a space or a hyphen is used to separate the names of the individual units.

In both English and in French modifiers such as “squared” or “cubed” are used in the names of units raised to powers, and they are placed after the unit name. However, in the case of area or volume, as an alternative, the modifiers “square” or “cubic” may be used, and these modifiers are placed before the unit name, but this applies only in English.

## Rules and style conventions for expressing values of quantities

The value of a quantity is expressed as the product of a number and a unit, and the number multiplying the unit is the numerical value of the quantity expressed in that unit. The numerical value of a quantity depends on the choice of unit. Thus the value of a particular quantity is independent of the choice of unit, although the numerical value will be different for different units.

Symbols for quantities are generally single letters set in italic font, although they may be qualified by further information in subscripts or superscripts or in brackets.

Symbols for units are treated as mathematical entities. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra. This procedure is described as the use of quantity calculus or the algebra of quantities.

Just as the quantity symbol should not imply any particular choice of unit, the unit symbol should not be used to provide specific information about the quantity, and should never be the sole source of information on the quantity. Units are never qualified by further information about the nature of the quantity; any extra information on the nature of the quantity should be attached to the quantity symbol and not to the unit symbol.

The numerical value always precedes the unit, and a space is always used to separate the unit from the number. Thus the value of the quantity is the product of the number and the unit, the space being regarded as a multiplication sign (just as a space between units implies multiplication). The only exceptions to this rule are for the unit symbols for degree, minute, and second, for plane angle, °, ′, and ′′, respectively, for which no space is left between the numerical value and the unit symbol.

Even when the value of a quantity is used as an adjective, a space is left between the numerical value and the unit symbol. Only when the name of the unit is spelled out would the ordinary rules of grammar apply, so that in English a hyphen would be used to separate the number from the unit.

The symbol used to separate the integral part of a number from its decimal part is called the decimal marker.

## Decimal multiples and submultiples of SI units

These SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (for example, one kilobit represents 1000 bits and not 1024 bits).

Prefix symbols are printed in roman (upright) type, as are unit symbols, regardless of the type used in the surrounding text, and are attached to unit symbols without a space between the prefix symbol and the unit symbol. With the exception of da (deka), h (hecto), and k (kilo), all multiple prefix symbols are capital (upper case) letters, and all submultiple prefix symbols are lower case letters. All prefix names are printed in lower case letters, except at the beginning of a sentence.

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to positive or negative power and that can be combined with other unit symbols to form compound unit symbols.

## Historical notes

The forerunner of the SI system of measurement is the metric system developed by a commission chaired by Lagrange since 1791. This system spreads slowly in Europe.

Units, terminology and recommendations of the SI are fixed by the Conférence générale des poids et mesures (CGPM), “General Conference of Weights and Measures”, a body linked with the Bureau international des poids et mesures (BIPM), “International Bureau of Weights and Measures”, bodies created at the Metre Convention of 1875.

The system was born in 1889 in France with the 1st CGPM: at that time it was called “MKS System” because it included only the fundamental units of length (meter), mass (kilogram) and time (second).

In 1935, at the proposal of physicist Giovanni Giorgi, the system was expanded to include units for electrical quantities. The first attempt was the “MKS-Ω System”, adopted by the International Electrotechnical Commission, in which was initially chosen as the basic quantity the electrical resistance, with unit of measure constituted by ohm. After the war, in 1946, always on proposal of Giorgi, CGPM approved the passage from the choice of electrical resistance as basic quantity to the electric current, defining secondly as its basic unit the ampere. So the “MKSA System”, also called “Giorgi System” was born.

In 1954 the 10th CGPM added absolute temperature (and the associated unit of measure: kelvin) and luminous intensity (defining then as its unit of measure the candle) as fifth and sixth fundamental quantities.

In 1961, the 11th CGPM finally established the birth of the International System (SI).

In 1971 the 14th CGPM adds the quantity of substance as a fundamental quantity, and defines the mole through Avogadro’s number.

In 2018, the 26th CGPM redefined the fundamental units in terms of physical constants, finally updating with consideration of years of achievements in the discipline of dimensional analysis.

So today the core of the SI consists in logical order in:

• choice of the basic physical quantities according to the fundamental physical laws of the physical theories considered universal.
• choice of the values of the fundamental physical constants that appear in these laws
• definition of the names of the measurement units of the basic quantities, called basic units for the seven fundamental physical quantities, and their definition from the physical constants.

From the nucleus of the International System we can define all other quantities, which are called derived. These are related to the basic quantities by the physical laws considered, and correspondingly so are their units of measurement.

The international system identifies a single unit of measurement for each derived quantity (on which prefixes are applied), which is always a simple product of powers of the base units. This eliminates conversion coefficients and makes it as easy as possible to calculate the ratios between the values of physical quantities in a problem. The International System of Measurement is called a coherent system because the derived units of measurement can be expressed as a simple product and ratio of the basic physical quantities.

Finally, the SI has defined decimal and binary prefixes to be added to units of measure to identify multiples and submultiples.

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