ISO 31-0

ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It is intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of ISO 80000.

Scope

ISO 31 covers only physical quantities used for the quantitative description of physical phenomena. It does not cover conventional scales (e.g., Beaufort scale, Richter scale, colour intensity scales), results of conventional tests, currencies, or information content. The presentation here is only a brief summary of some of the detailed guidelines and examples given in the standard.

Quantities and units

Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all quantities of the same kind. One particular example of such a quantity can be chosen as a reference quantity, called the unit, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the numerical value. For example, if we write

the wavelength is λ = 6.982 × 10⁻⁷ m

then "λ" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10⁻⁷" is the numerical value of the wavelength in metres.

More generally, we can write

A = {A} · [A]

where A is the symbol for the quantity, {A} symbolizes the numerical value of A, and [A] represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 · m = 0.3 · km = ...). This ambiguity makes the {A} and [A] notations useless, unless they are used together.

The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in {λ}_m = 6.982 × 10⁻⁷ or equivalently {λ}_nm = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in

λ/m = 6.982 × 10⁻⁷

or equivalently

λ/nm = 698.2.

This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.

Typographic conventions

Symbols for quantities

Quantities are generally represented by a symbol formed from single letters of the Latin or Greek alphabet.
Symbols for quantities are set in italic type, independent of the type used in the rest of the text.
If in a text different quantities use the same letter symbol, they can be distinguished via subscripts.
A subscript is only set in italic type if it consists of a symbol for a quantity or a variable. Other subscripts are set in upright (roman) type. For example, write V_n for a "nominal volume" (where "n" is just an abbreviation for the word "nominal"), but write V_n if n is a running index number.

Names and symbols for units

If an internationally standardized symbol exists for a unit, then only that symbol should be used. See the SI articles for the list of standard symbols defined by the International System of Units. Note that the distinction between uppercase and lowercase letters is significant for SI unit symbols. For example, "k" is the prefix kilo and "K" stands for the unit kelvin. The symbols of all SI units named after a person or a place start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase; the only exception is litre, where both l and L are allowed. However, it is stated that the CIPM will examine whether one of the two may be suppressed.
Symbols for units should be printed in an upright (roman) typeface.

Numbers

See Sect. 3.3 of the Standard text.

Numbers should be printed in upright (roman) type.
ISO 31-0 (after Amendment 2) specifies that "the decimal sign is either the comma on the line or the point on the line". This follows resolution 10^[1] of the 22nd CGPM, 2003.^[2]
Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. For this reason, ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use as the decimal sign.
For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
The multiplication sign is either a cross or a half-height dot, though the latter should not be used when the dot is the decimal separator.

Expressions

Unit symbols follow the numerical value in the expression of a quantity.
Numerical value and unit symbol are separated by a space. This rule also applies to the symbol "°C" for degrees Celsius, as in "25 °C". The only exception are the symbols for the units of plane angle degree, minute and second, which follow the numerical value without a space in between (for example "30°").
Where quantities are added or subtracted, parenthesis can be used to distribute a unit symbol over several numerical values, as in

T = 25 °C − 3 °C = (25 − 3) °C

P = 100 kW ± 5 kW = (100 ± 5) kW

(but not: 100 ± 5 kW)

d = 12 × (1 ± 10⁻⁴) m

Products can be written as ab, a b, a⋅b, or a×b. The sign for multiplying numbers is a cross (×) or a half-height dot (⋅). The cross should be used adjacent to numbers if a dot on the line is used as the decimal separator, to avoid confusion between a decimal dot and a multiplication dot.
Division can be written as ${\frac {a}{b}}$ , a/b, or by writing the product of a and b⁻¹, for example a⋅b⁻¹. Numerator or denominator can themselves be products or quotients, but in this case, a solidus (/) should not be followed by a multiplication sign or division sign on the same line, unless parentheses are used to avoid ambiguity.

Mathematical signs and symbols

A comprehensive list of internationally standardized mathematical symbols and notations can be found in ISO 31-11.

References

↑ "Resolution 10", 22nd General Conference on Weights and Measures, BIPM .
↑ Brief reference to the history, NIST .

Bibliography

International standard ISO 31-0: Quantities and units — Part 0: General principles. International Organization for Standardization, Geneva, 1992.
SI brochure. Bureau International des Poids et Mesures.
Cvitas, T (February 2002), Quantity calculus, Interdivisional Committee on Terminology, Nomenclature and Symbols (IUPAC) .
I. M. Mills and W. V. Metanomski: On the use of italic and roman fonts for symbols in scientific text. Interdivisional Committee on Nomenclature and Symbols, IUPAC, December 1999.
B. N. Taylor and A. Thompson: The International System of Units (SI). NIST Special Publication 330. US National Institute for Standards and Technology, 2008.
A. Thompson and B. N. Taylor: Guide for the use of the International System of Units (SI). NIST Special Publication 811. US National Institute for Standards and Technology, 2008.
Unit rules and style conventions – Check list for reviewing manuscripts. US National Institute for Standards and Technology, 1998.

ISO standards by standard number
List of ISO standards / ISO romanizations / IEC standards
1–9999	1 2 3 4 5 6 7 9 16 31 -0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 128 216 217 226 228 233 259 269 302 306 428 518 519 639 -1 -2 -3 -5 -6 646 690 732 764 843 898 965 1000 1004 1007 1073-1 1413 1538 1745 1989 2014 2015 2022 2047 2108 2145 2146 2240 2281 2709 2711 2788 2848 2852 3029 3103 3166 -1 -2 -3 3297 3307 3602 3864 3901 3977 4031 4157 4217 4909 5218 5428 5775 5776 5800 5964 6166 6344 6346 6385 6425 6429 6438 6523 6709 7001 7002 7098 7185 7200 7498 7736 7810 7811 7812 7813 7816 8000 8178 8217 8571 8583 8601 8632 8652 8691 8807 8820-5 8859 -1 -2 -3 -4 -5 -6 -7 -8 -8-I -9 -10 -11 -12 -13 -14 -15 -16 8879 9000/9001 9075 9126 9293 9241 9362 9407 9506 9529 9564 9594 9660 9897 9899 9945 9984 9985 9995
10000–19999	10005 10006 10007 10116 10118-3 10160 10161 10165 10179 10206 10218 10303 -11 -21 -22 -28 -238 10383 10487 10585 10589 10646 10664 10746 10861 10957 10962 10967 11073 11170 11179 11404 11544 11783 11784 11785 11801 11898 11940 (-2) 11941 11941 (TR) 11992 12006 12182 12207 12234-2 13211 -1 -2 13216 13250 13399 13406-2 13450 13485 13490 13567 13568 13584 13616 14000 14031 14224 14289 14396 14443 14496 -2 -3 -6 -10 -11 -12 -14 -17 -20 14644 14649 14651 14698 14750 14764 14882 14971 15022 15189 15288 15291 15292 15398 15408 15444 -3 15445 15438 15504 15511 15686 15693 15706 -2 15707 15897 15919 15924 15926 15926 WIP 15930 16023 16262 16612-2 16750 16949 (TS) 17024 17025 17100 17203 17369 17442 17799 18000 18004 18014 18245 18629 18916 19005 19011 19092 (-1 -2) 19114 19115 19125 19136 19439 19500 19501 19502 19503 19505 19506 19507 19508 19509 19510 19600:2014 19752 19757 19770 19775-1 19794-5 19831
20000+	20000 20022 20121 20400 21000 21047 21500 21827:2002 22000 23270 23271 23360 24517 24613 24617 24707 25178 25964 26000 26300 26324 27000 series 27000 27001:2005 27001:2013 27002 27006 27729 28000 29110 29148 29199-2 29500 30170 31000 32000 38500 40500 42010 55000 80000 -1 -2 -3
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