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SI Brochure: The International System of Units (SI) [8th edition, 2006; updated in 2014]
Units with special names and symbols; units that incorporate special names and symbols
SI Brochure, Section 2.2.2

    For convenience, certain coherent derived units have been given special names and symbols. There are 22 such units, as listed in Table 3. These special names and symbols may themselves be used in combination with the names and symbols for base units and for other derived units to express the units of other derived quantities. Some examples are given in Table 4. The special names and symbols are simply a compact form for the expression of combinations of base units that are used frequently, but in many cases they also serve to remind the reader of the quantity involved. The SI prefixes may be used with any of the special names and symbols, but when this is done the resulting unit will no longer be coherent.

    Among these names and symbols the last four entries in Table 3 are of particular note since they were adopted by the 15th CGPM (1975, Resolutions 8 and 9), the 16th CGPM (1979, Resolution 5) and the 21st CGPM (1999, Resolution 12) specifically with a view to safeguarding human health.

    In both Tables 3 and 4 the final column shows how the SI units concerned may be expressed in terms of SI base units. In this column factors such as m0, kg0, etc., which are all equal to 1, are not shown explicitly.

    The values of several different quantities may be expressed using the same name and symbol for the SI unit. Thus for the quantity heat capacity as well as the quantity entropy, the SI unit is the joule per kelvin. Similarly for the base quantity electric current as well as the derived quantity magnetomotive force, the SI unit is the ampere. It is therefore important not to use the unit alone to specify the quantity. This applies not only to scientific and technical texts, but also, for example, to measuring instruments (i.e. an instrument read-out should indicate both the unit and the quantity measured).

    A derived unit can often be expressed in different ways by combining base units with derived units having special names. Joule, for example, may formally be written newton metre, or kilogram metre squared per second squared. This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others.

    In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension. When using this freedom, one may recall the process by which the quantity is defined. For example, the quantity torque may be thought of as the cross product of force and distance, suggesting the unit newton metre, or it may be thought of as energy per angle, suggesting the unit joule per radian. The SI unit of frequency is given as the hertz, implying the unit cycles per second; the SI unit of angular velocity is given as the radian per second; and the SI unit of activity is designated the becquerel, implying the unit counts per second. Although it would be formally correct to write all three of these units as the reciprocal second, the use of the different names emphasises the different nature of the quantities concerned. Using the unit radian per second for angular velocity, and hertz for frequency, also emphasizes that the numerical value of the angular velocity in radian per second is 2pi times the numerical value of the corresponding frequency in hertz.

    In the field of ionizing radiation, the SI unit of activity is designated the becquerel rather than the reciprocal second, and the SI units of absorbed dose and dose equivalent are designated the gray and the sievert, respectively, rather than the joule per kilogram. The special names becquerel, gray, and sievert were specifically introduced because of the dangers to human health that might arise from mistakes involving the units reciprocal second and joule per kilogram, in case the latter units were incorrectly taken to identify the different quantities involved.

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We are pleased to present the updated (2014) 8th edition of the SI Brochure, which defines and presents the Système International d'Unités, the SI (known in English as the International System of Units).

Chapter 1: Introduction

Chapter 2: SI units

Chapter 3: Decimal multiples and submultiples of SI units

  • SI prefixes
  • Factor Name Symbol Factor Name Symbol
    101 deca da 10–1 deci d
    102 hecto h 10–2 centi c
    103 kilo k 10–3 milli m
    106 mega M 10–6 micro µ
    109 giga G 10–9 nano n
    1012 tera T 10–12 pico p
    1015 peta P 10–15 femto f
    1018 exa E 10–18 atto a
    1021 zetta Z 10–21 zepto z
    1024 yotta Y 10–24 yocto y
  • The kilogram

Chapter 4: Units outside the SI

Chapter 5: Writing unit symbols and names, and expressing the values of quantities

General principles for the writing of unit symbols and numbers were first given by the 9th CGPM (1948, Resolution 7). These were subsequently elaborated by ISO, IEC, and other international bodies. As a consequence, there now exists a general consensus on how unit symbols and names, including prefix symbols and names, as well as quantity symbols should be written and used, and how the values of quantities should be expressed. Compliance with these rules and style conventions, the most important of which are presented in this chapter, supports the readability of scientific and technical papers.

Appendix 1: Decisions of the CGPM and the CIPM

This appendix lists those decisions of the CGPM and the CIPM that bear directly upon definitions of the units of the SI, prefixes defined for use as part of the SI, and conventions for the writing of unit symbols and numbers. It is not a complete list of CGPM and CIPM decisions. For a complete list, reference must be made to the BIPM website, successive volumes of the Comptes Rendus des Séances de la Conférence Générale des Poids et Mesures (CR) and Procès-Verbaux des Séances du Comité International des Poids et Mesures (PV) or, for recent decisions, to Metrologia.

Since the SI is not a static convention, but evolves following developments in the science of measurement, some decisions have been abrogated or modified; others have been clarified by additions. In the SI Brochure, a number of notes have been added by the BIPM to make the text more understandable; they do not form part of the original text.

In the printed brochure, the decisions of the CGPM and CIPM are listed in strict chronological order in order to preserve the continuity with which they were taken. However in order to make it easy to locate decisions related to particular topics a table of contents is also provided, ordered by subject:

Appendix 2: Practical realization of the definitions of some important units

Appendix 3: Units for photochemical and photobiological quantities

Optical radiation is able to cause chemical changes in certain living or non-living materials: this property is called actinism, and radiation capable of causing such changes is referred to as actinic radiation. Actinic radiation has the fundamental characteristic that, at the molecular level, one photon interacts with one molecule to alter or break the molecule into new molecular species. It is therefore possible to define specific photochemical or photobiological quantities in terms of the result of optical radiation on the associated chemical or biological receptors.

In the field of metrology, the only photobiological quantity which has been formally defined for measurement in the SI is for the interaction of light with the human eye in vision. An SI base unit, the candela, has been defined for this important photobiological quantity. Several other photometric quantities with units derived from the candela have also been defined (such as the lumen and the lux, see Table 3 in Chapter 2).