# Review of Content Standard

# Quantities and Units (ISO 31:1992)

# September, 2005

1.  This review is intended to assess the potential utility of content
    standards for use and potentially for inclusion in an ISO
    11179-based metadata registry. The review is directed primarily
    toward the utility of the standard itself, rather than to matching
    the standard with specific agency programs. The review covers issues
    such as the subject area, currency, quality, authority, and
    acceptance of the standards. These are factors that need to be taken
    into account no matter what the programmatic application of the
    standard may be.

## 1. Summary

**International Standard ISO 31**
([Quantities](http://en.wikipedia.org/wiki/Physical_quantity) and
[units](http://en.wikipedia.org/wiki/Physical_unit), [International
Organization for
Standardization](http://en.wikipedia.org/wiki/International_Organization_for_Standardization),
1992) is the most widely respected style guide for the use of units of
[measurement](http://en.wikipedia.org/wiki/Measurement), and formulas
involving them, in scientific and educational documents worldwide. In
most countries, the notations used in mathematics and science textbooks
at schools and universities follow exactly the guidelines given by ISO
31.

This standard gives general information about principles concerning
physical quantities, equations, quantity and unit symbols, and coherent
unit systems, especially the International System of Units, SI,
including recommendations for printing symbols and numbers. Annex A
includes a guide to terms used in names for physical quantities, Annex B
a guide to the rounding of numbers, Annex C international organizations
in the field of quantities and units.

## 2. Identification of Standard {#identification-of-standard .unnumbered}

### 2.1. Title

Quantities and units

### 2.2. Acronym

ISO 31:1992

### 2.3. Web page(s), Identifier, or Contact Information:

### 2.3.1 Web page(s)

http://www.iso.ch/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=3621&ICS1=1&ICS2=60&ICS3=&scopelist=

### 2.3.2 Identifier

ISO 31:1992

### 2.3.3 Contact Information

International Organization for Standardization (ISO)

http://www.iso.org/iso/en/ISOOnline.frontpage

### 

### 2.4 Authority

**2.4.1 Creator**

International Organization for Standardization (ISO)

TC 12, Quantities, units, symbols, conversion factors

Secretariat:
[SIS](http://www.iso.org/iso/en/stdsdevelopment/tc/tclist/TechnicalCommitteeContactPage.TechnicalCommitteeContact?COMMID=542&ACRONYM=SIS)

Secretary: Mr. Anders J. Thor

Chair: Mr. Gunnar Petersson (Sweden) until end 2006

**2.4.2. Acceptance as authoritative**

The **International System of Units** (abbreviated **SI** from the
[French](http://en.wikipedia.org/wiki/French_language) phrase, *Système
International d\'Unités*) is the most widely used [system of
units](http://en.wikipedia.org/wiki/System_of_units). It is the most
common system for everyday
[commerce](http://en.wikipedia.org/wiki/Commerce) in the world, and is
almost universally used in the realm of
[science](http://en.wikipedia.org/wiki/Science).

In [1960](http://en.wikipedia.org/wiki/1960), SI was selected as a
specific subset of the existing
[Metre](http://en.wikipedia.org/wiki/Metre)-[Kilogram](http://en.wikipedia.org/wiki/Kilogram)-[Second](http://en.wikipedia.org/wiki/Second)
systems of units (MKS), rather than the older
[Centimetre-Gram-Second](http://en.wikipedia.org/wiki/Centimetre_gram_second_system_of_units)
system (CGS). Various new units were added with the introduction of the
SI and at later times. SI is sometimes referred to as the [**metric
system**](http://en.wikipedia.org/wiki/Metric_system), especially [in
the United
States](http://en.wikipedia.org/wiki/Metric_system_in_the_United_States),
which has not widely adopted it, and in the [United
Kingdom](http://en.wikipedia.org/wiki/United_Kingdom), where conversion
is only partial. SI is a specific canon of measurements derived and
extended from the *Metric system*; however, not all metric units of
measurement are accepted as SI units.

### 2.5 Publisher

International Organization for Standardization (ISO)

Much of the material in ISO 31 comes originally from Document IUPAP-25
of the *Commission for Symbols, Units and Nomenclature* (SUN Commission)
[\[3\]](http://www.physics.umanitoba.ca/IUPAP/C2.html) of the
*International Union of Pure and Applied Physics*

Some of the material in ISO 31 originates from the *Interdivisional
Committee on Terminology, Nomenclature and Symbols*
[\[4\]](http://www.iupac.org/standing/ictns.html) of the *International
Union of Pure and Applied Chemistry*

### 2.6 Language(s)

### This standard is available in both French and English. {#this-standard-is-available-in-both-french-and-english. .unnumbered}

###  3. Content description {#content-description .unnumbered}

### 3.1 Subject area of content and area of application

ISO 31 covers only [physical
quantities](http://en.wikipedia.org/wiki/Physical_quantities) used for
the quantitative description of physical phenomena. It does not cover
conventional scales (e.g., [Beaufort
scale](http://en.wikipedia.org/wiki/Beaufort_scale), [Richter
scale](http://en.wikipedia.org/wiki/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.

Physical quantities can be grouped into mutually comparable categories.
For example, length, width, diameter and wavelength are all in the same
category, which 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 and {*A*} symbolizes the
numerical value of *A* if it is expressed using the unit \[*A*\]. Both
the numerical value and the unit symbol are factors and their product is
the quantity.

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 labeling the
axes of graphs or for the headings of table columns, where repeating the
unit after each numerical value can be typographically inconvenient.

> **3.2 Kind of content**

## Typographic conventions

### Symbols for quantities {#symbols-for-quantities .unnumbered}

-   Quantities are generally represented by a symbol formed from single
    letters of the Latin or Greek alphabet.

```{=html}
<!-- -->
```
-   Symbols for quantities are set in [italic
    type](http://en.wikipedia.org/wiki/Italic_type), independent of the
    type used in the rest of the text.

```{=html}
<!-- -->
```
-   If in a text different quantities use the same letter symbol, they
    can be distinguished via subscripts.

```{=html}
<!-- -->
```
-   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](http://en.wikipedia.org/wiki/Roman_type)) 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](http://en.wikipedia.org/wiki/SI) article 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 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](http://en.wikipedia.org/wiki/Litre), where both l and L are
    allowed.

```{=html}
<!-- -->
```
-   Symbols for units should be printed in an upright
    ([roman](http://en.wikipedia.org/wiki/Roman_type)) typeface.

### Numbers

-   Numbers should be printed in upright
    ([roman](http://en.wikipedia.org/wiki/Roman_type)) type.

```{=html}
<!-- -->
```
-   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. 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.

```{=html}
<!-- -->
```
-   ISO 31-0 specifies that the decimal sign is the comma on the
    baseline, but recognizes that in English documents a dot on the line
    is also commonly used.

```{=html}
<!-- -->
```
-   For numbers whose magnitude is less than 1, the decimal sign should
    be preceded by a zero.

### Expressions

-   Unit symbols follow the numerical value in the expression of a
    quantity.

```{=html}
<!-- -->
```
-   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 exceptions 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°\").

```{=html}
<!-- -->
```
-   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-heigh 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.

```{=html}
<!-- -->
```
-   Division can be written as
    ![](media/image1.png){width="0.17708333333333334in"
    height="0.3958333333333333in"}, *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](http://en.wikipedia.org/w/index.php?title=ISO_31-11&action=edit).

### 3.3 Audience(s) {#audiences .unnumbered}

Scientists and researchers worldwide. In most countries, the notations
used in mathematics and science textbooks at schools and universities
follow exactly the guidelines given by ISO 31.

### 3.4 Related Standards/3.5 Standards Dependencies

See CMAP "Relationships of Standards and Guidance Documents for SI
Units"

### 

**3.6 Content Quality**

High.

### 4. Currency of Content

### 4.1 Date

1992

### 4.2 Versions, Updates

The last published version was published in 1992. The current revision
has reached the decision review stage (90.92) as of 1999-12-22.

### 4.3 Currency

The wikipedia states: "A second, older and today less widely known
international standard on quantities and units is [IEC
27](http://en.wikipedia.org/wiki/IEC_27). There are plans to merge these
two standards in the next edition of ISO 31." ref:
http://en.wikipedia.org/wiki/ISO_31

**5. Acceptance**

**International Standard ISO 31**
([Quantities](http://en.wikipedia.org/wiki/Physical_quantity) and
[units](http://en.wikipedia.org/wiki/Physical_unit), [International
Organization for
Standardization](http://en.wikipedia.org/wiki/International_Organization_for_Standardization),
1992) is the most widely respected style guide for the use of units of
[measurement](http://en.wikipedia.org/wiki/Measurement), and formulas
involving them, in scientific and educational documents worldwide. In
most countries, the notations used in mathematics and science textbooks
at schools and universities follow exactly the guidelines given by ISO
31.

### 

### 6. Content details

### 6.1 Size statistics (estimated)

The standard comes in 14 parts:

> [ISO 31-0](http://en.wikipedia.org/wiki/ISO_31-0): General principles
>
> [ISO 31-1](http://en.wikipedia.org/wiki/ISO_31-1):
> [Space](http://en.wikipedia.org/wiki/Space) and
> [time](http://en.wikipedia.org/wiki/Time)
>
> [ISO
> 31-2](http://en.wikipedia.org/w/index.php?title=ISO_31-2&action=edit):
> Periodic and related
> [phenomena](http://en.wikipedia.org/wiki/Phenomena)
>
> [ISO
> 31-3](http://en.wikipedia.org/w/index.php?title=ISO_31-3&action=edit):
> Mechanics
>
> [ISO
> 31-4](http://en.wikipedia.org/w/index.php?title=ISO_31-4&action=edit):
> [Heat](http://en.wikipedia.org/wiki/Heat)
>
> [ISO
> 31-5](http://en.wikipedia.org/w/index.php?title=ISO_31-5&action=edit):
> [Electricity](http://en.wikipedia.org/wiki/Electricity) and
> [magnetism](http://en.wikipedia.org/wiki/Magnetism)
>
> [ISO
> 31-6](http://en.wikipedia.org/w/index.php?title=ISO_31-6&action=edit):
> [Light](http://en.wikipedia.org/wiki/Light) and related
> [electromagnetic
> radiations](http://en.wikipedia.org/wiki/Electromagnetic_radiation)
>
> [ISO
> 31-7](http://en.wikipedia.org/w/index.php?title=ISO_31-7&action=edit):
> [Acoustics](http://en.wikipedia.org/wiki/Acoustics)
>
> [ISO
> 31-8](http://en.wikipedia.org/w/index.php?title=ISO_31-8&action=edit):
> Physical [chemistry](http://en.wikipedia.org/wiki/Chemistry) and
> [molecular physics](http://en.wikipedia.org/wiki/Molecular_physics)
>
> [ISO
> 31-9](http://en.wikipedia.org/w/index.php?title=ISO_31-9&action=edit):
> Atomic and [nuclear
> physics](http://en.wikipedia.org/wiki/Nuclear_physics)
>
> [ISO
> 31-10](http://en.wikipedia.org/w/index.php?title=ISO_31-10&action=edit):
> [Nuclear reactions](http://en.wikipedia.org/wiki/Nuclear_reaction) and
> [ionizing radiations](http://en.wikipedia.org/wiki/Ionizing_radiation)
>
> [ISO
> 31-11](http://en.wikipedia.org/w/index.php?title=ISO_31-11&action=edit):
> Mathematical signs and [symbols](http://en.wikipedia.org/wiki/Symbol)
> for use in the physical sciences and
> [technology](http://en.wikipedia.org/wiki/Technology)
>
> [ISO
> 31-12](http://en.wikipedia.org/w/index.php?title=ISO_31-12&action=edit):
> Characteristic [numbers](http://en.wikipedia.org/wiki/Number)
>
> [ISO
> 31-13](http://en.wikipedia.org/w/index.php?title=ISO_31-13&action=edit):
> [Solid state
> physics](http://en.wikipedia.org/wiki/Solid_state_physics)

Numbers of pages varies.

### 6.2 Format / Schemas(s)

Paper and pdf versions are available.

### 6.3 Media / Download

Available as a pdf file from
http://www.iso.ch/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=3621&ICS1=1&ICS2=60&ICS3=&scopelist=

### 6.4 Licensing Issues/6.5 Documentation

ISO standards are available for purchase online. ISO 1000 along with all
parts of [ISO 31](http://en.wikipedia.org/wiki/ISO_31) are available in
book form as

> ISO Standards Handbook: Quantities and units. 3rd ed., International
> Organization for Standardization, Geneva, 1993, 345 p., [ISBN
> 92-67-10185-4](http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=9267101854),
> 182.00 CHF.
> <http://www.iso.ch/iso/en/prods-services/otherpubs/Handbooks.PublicationList?CLASSIFICATION=HANDBOOKS>

+-------------------------------------------------------------------+---+---+
|   -------------------------------------- ----------               | ! | ! |
| ----------------------------------------------------------------- | [ | [ |
| ----------------------------------------------------------------- | ] | ] |
|   Quantities and units \-- Part 0:                                | ( | ( |
|   General principles                                              | m | m |
|                                                                   | e | e |
|                                                                   | d | d |
|                                                                   | i | i |
|   Edition:                               3 (Monolingual)          | a | a |
|                                                                   | / | / |
|   Number of pages:                       21                       | i | i |
|                                                                   | m | m |
|   Technical committee / subcommittee:    [TC                      | a | a |
|                                          12](http                 | g | g |
| ://www.iso.org/iso/en/stdsdevelopment/tc/tclist/TechnicalCommitte | e | e |
| eDetailPage.TechnicalCommitteeDetail?COMMID=542&scopelist=); [ISO | 4 | 4 |
|                                                                   | . | . |
|                                        Standards](http://www.iso. | p | p |
| org/iso/en/CatalogueListPage.CatalogueList?COMMID=542&scopelist=) | n | n |
|                                                                   | g | g |
|   ICS:                                                            | ) | ) |
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| /CatalogueListPage.CatalogueList?ICS1=1&ICS2=60&ICS3=&scopelist=) | w | w |
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|                             ![](media/image2.png){width="0.166666 | t | t |
| 66666666666in" height="0.16666666666666666in"} Published standard | h | h |
|                                                                   | = | = |
|   Current stage:                                                  | " | " |
|   [90.92](http://www.iso.org/iso/en/widepages/stagetable.html#90) | 0 | 2 |
|                                                                   | . | . |
|   Stage date:                            1999-12-22               | 1 | 0 |
|                                                                   | 0 | 8 |
|                                                                   | 4 | 3 |
|                                                                   | 1 | 3 |
|                                                                   | 6 | 3 |
|   -------------------------------------- ----------               | 6 | 3 |
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|                                                                   | i | - |
|                                                                   | n | 2 |
|                                                                   | " | i |
|                                               Size          Price | h | n |
|                                                                   | e | " |
|   ![](me                                                          | i | h |
| dia/image3.png){width="0.2916666666666667in"   [ISO 31-0:1992 PDF | g | e |
|  version                                                          | h | i |
|                                                                   | t | g |
|                                                                   | = | h |
|                                           4738 KB       CHF 99,00 | " | t |
|   height="0.22916666666666666in"}                      (en)](jav  | 1 | = |
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|   ![](me                                                          | 6 | 1 |
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|  version                                                          | 6 | 6 |
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|   ![](me                                                          | e | 6 |
| dia/image3.png){width="0.2916666666666667in"   [ISO 31-0:1992 pap | - | 6 |
| er version                                                        | 2 | e |
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|   ![](me                                                          |   |   |
| dia/image3.png){width="0.2916666666666667in"   [ISO 31-0:1992 pap |   |   |
| er version                                                        |   |   |
|                                                                   |   |   |
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|   height="0.22916666666666666in"}                      (fr)](jav  |   |   |
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|   --------                                                        |   |   |
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| --------------------------------------- --------- --- ----------- |   |   |
+-------------------------------------------------------------------+---+---+

+---+---+------------------------------------------------------------------+
| ! | ! |   -------------------------------------------------------------  |
| [ | [ |   ![](media/image5.png){width="0.3125in" height="0.25in"}        |
| ] | ] |                                                                  |
| ( | ( |   -------------------------------------------------------------  |
| m | m |                                                                  |
| e | e |                                                                  |
| d | d |                                                                  |
| i | i |                                                                  |
| a | a |                                                                  |
| / | / |                                                                  |
| i | i |                                                                  |
| m | m |                                                                  |
| a | a |                                                                  |
| g | g |                                                                  |
| e | e |                                                                  |
| 4 | 4 |                                                                  |
| . | . |                                                                  |
| p | p |                                                                  |
| n | n |                                                                  |
| g | g |                                                                  |
| ) | ) |                                                                  |
| { | { |                                                                  |
| w | w |                                                                  |
| i | i |                                                                  |
| d | d |                                                                  |
| t | t |                                                                  |
| h | h |                                                                  |
| = | = |                                                                  |
| " | " |                                                                  |
| 2 | 0 |                                                                  |
| . | . |                                                                  |
| 0 | 1 |                                                                  |
| 8 | 8 |                                                                  |
| 3 | 7 |                                                                  |
| 3 | 5 |                                                                  |
| 3 | i |                                                                  |
| 3 | n |                                                                  |
| 3 | " |                                                                  |
| 3 | h |                                                                  |
| 3 | e |                                                                  |
| 3 | i |                                                                  |
| 3 | g |                                                                  |
| 3 | h |                                                                  |
| 3 | t |                                                                  |
| 3 | = |                                                                  |
| 3 | " |                                                                  |
| 2 | 1 |                                                                  |
| e | . |                                                                  |
| - | 0 |                                                                  |
| 2 | 4 |                                                                  |
| i | 1 |                                                                  |
| n | 6 |                                                                  |
| " | 6 |                                                                  |
| h | 6 |                                                                  |
| e | 6 |                                                                  |
| i | 6 |                                                                  |
| g | 6 |                                                                  |
| h | 6 |                                                                  |
| t | 6 |                                                                  |
| = | 6 |                                                                  |
| " | 6 |                                                                  |
| 1 | 6 |                                                                  |
| . | 6 |                                                                  |
| 0 | 6 |                                                                  |
| 4 | e |                                                                  |
| 1 | - |                                                                  |
| 6 | 2 |                                                                  |
| 6 | i |                                                                  |
| 6 | n |                                                                  |
| 6 | " |                                                                  |
| 6 | } |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| 6 |   |                                                                  |
| e |   |                                                                  |
| - |   |                                                                  |
| 2 |   |                                                                  |
| i |   |                                                                  |
| n |   |                                                                  |
| " |   |                                                                  |
| } |   |                                                                  |
+---+---+------------------------------------------------------------------+