– the intergovernmental organization through which Member States act together
     on matters related to measurement science and measurement standards.
Search facility:

| Site map | News | Contact us | [ FR ]
SI Brochure: The International System of Units (SI) [8th edition, 2006; updated in 2014]
Non-SI units accepted for use with the SI, and units based on fundamental constants (contd.)
SI Brochure, from Section 4.1

    Table 7 contains units whose values in SI units have to be determined experimentally, and thus have an associated uncertainty. Except for the astronomical unit, all other units in Table 7 are related to fundamental physical constants. The first three units, the non-SI units electronvolt, symbol eV, dalton or unified atomic mass unit, symbol Da or u, respectively, and the astronomical unit, symbol ua, have been accepted for use with the SI by the CIPM. The units in Table 7 play important roles in a number of specialized fields in which the results of measurements or calculations are most conveniently and usefully expressed in these units. For the electronvolt and the dalton the values depend on the elementary charge e and the Avogadro constant NA, respectively.

    There are many other units of this kind, because there are many fields in which it is most convenient to express the results of experimental observations or of theoretical calculations in terms of fundamental constants of nature. The two most important of such unit systems based on fundamental constants are the natural unit (n.u.) system used in high energy or particle physics, and the atomic unit (a.u.) system used in atomic physics and quantum chemistry. In the n.u. system, the base quantities for mechanics are speed, action, and mass, for which the base units are the speed of light in vacuum c0, the Planck constant h divided by 2pi, called the reduced Planck constant with symbol , and the mass of the electron me, respectively. In general these units are not given any special names or symbols but are simply called the n.u. of speed, symbol c0, the n.u. of action, symbol , and the n.u. of mass, symbol me. In this system, time is a derived quantity and the n.u. of time is a derived unit equal to the combination of base units /mec02. Similarly, in the a.u. system, any four of the five quantities charge, mass, action, length, and energy are taken as base quantities. The corresponding base units are the elementary charge e, electron mass me, action , Bohr radius (or bohr) a0, and Hartree energy (or hartree) Eh, respectively. In this system, time is again a derived quantity and the a.u. of time a derived unit, equal to the combination of units /Eh. Note that a0 = alpha/(4piRinfinity), where alpha is the fine-structure constant and Rinfinity is the Rydberg constant; and Eh = e2/(4piepsilon0a0) = 2Rhc0 = alpha2mec02, where epsilon0 is the electric constant and has an exact value in the SI.

    For information, these ten natural and atomic units and their values in SI units are also listed in Table 7. Because the quantity systems on which these units are based differ so fundamentally from that on which the SI is based, they are not generally used with the SI, and the CIPM has not formally accepted them for use with the International System. To ensure understanding, the final result of a measurement or calculation expressed in natural or atomic units should also always be expressed in the corresponding SI unit. Natural units (n.u.) and atomic units (a.u.) are used only in their own special fields of particle and atomic physics, and quantum chemistry, respectively. Standard uncertainties in the least significant digits are shown in parenthesis after each numerical value.

    Table 7. Non-SI units whose values in SI units must be obtained experimentally

    Quantity Name of unit Symbol for unit Value in SI units (a)
    Units accepted for use with the SI
    energy electronvolt (b) eV 1 eV = 1.602 176 565(35) x 10–19 J
    mass dalton, (c) Da 1 Da = 1.660 538 921(73) x 10–27 kg
    unified atomic mass unit u 1 u = 1 Da
    Natural units (n.u.)
    speed n.u. of speed
    (speed of light in vacuum)
    c0 299 792 458 m/s (exact)
    action n.u. of action
    (reduced Planck constant)
    h bar 1.054 571 726(47) x 10–34 J s
    mass n.u. of mass
    (electron mass)
    me 9.109 382 91(40) x 10–31 kg
    time n.u. of time h bar/(mec02) 1.288 088 668 33(83) x 10–21 s
    Atomic units (a.u.)
    charge a.u. of charge
    (elementary charge)
    e 1.602 176 565(35) x 10–19 C
    mass a.u. of mass
    (electron mass)
    me 9.109 382 91(40) x 10–31 kg
    action a.u. of action
    (reduced Planck constant)
    h bar 1.054 571 726(47) x 10–34 J s
    length a.u. of length, bohr
    (Bohr radius)
    a0 0.529 177 210 92(17) x 10–10 m
    energy a.u. of energy, hartree
    (Hartree energy)
    Eh 4.359 744 34(19) x 10–18 J
    time a.u. of time h bar/Eh 2.418 884 326 502(12) x 10–17 s

    [ updated 2014 ]

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).