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 was 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 ISO 31-0 was withdrawn on 17 November 2009. It is superseded by ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of ISO 80000.


ISO 31 covers physical quantities used for the quantitative description of physical phenomena. The presentation here is a 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

Names and symbols for units

Main articles: SI, SI base unit, SI derived unit, and SI prefix


See Sect. 3.3 of the Standard text.

For example, one divided by two (one half) may be written as 0.5 or 0,5.
For example, one million (1000000) may be written as 1 000 000.


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

Mathematical signs and symbols

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

See also


  1. ^ "Resolution 10", 22nd General Conference on Weights and Measures, BIPM.
  2. ^ Baum, Michael (22 November 2006). " Brief reference to the history | Decimals Score a Point on International Standards ". NIST. Archived from the original on 27 November 2006. Retrieved 17 November 2018. Until recently, the rule at the International Organization for Standardization (ISO—the world's largest developer of standards) and the International Electrotechnical Commission (IEC—the leading global electrical and electronic standards organization) was that all numbers with a decimal part must be written in formal documents with a comma decimal separator, the prevailing fashion in Europe. The constant pi, for example, starts 3,141 592 653.