New search facility:
BIPM Home | KCDB | JCTLM-DB | Site map | Disclaimer | Contact us
 > You are here: SI > derived units > special names
 Units with special names and symbols; units that incorporate special names and symbols Version française
 Summary Derived units expressed in terms of base units Units with special names and symbols; units that incorporate special names and symbols Units for dimensionless quantities, also called quantities of dimension one
 Related articles Table 3: Coherent derived units in the SI with special names and symbols Table 4: Examples of SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols
 Direct access

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 2 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. Table 3 Table 4 The CIPM, recognizing the particular importance of the health-related units, adopted a detailed text on the sievert for the 5th edition of this Brochure: see Recommendation 1 (CI-1984), and Recommendation 2 (CI-2002).

 Related articles Table 3: Coherent derived units in the SI with special names and symbols Table 4: Examples of SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols