National Physical Laboratory

The range of options for handling plane angle and solid angle within a system of units.

Quincey, P G
Metrologia, 2016, 53, (2), 840-845
NPL Doc. Ref:
PDB: 7923 | DDB: 7555
Document Type:
Periodical article

Note: An asterisk after an author's name indicates a non-NPL author.


The radian and steradian are unusual units within the SI, originally belonging to their own category of 'supplementary units', with this status being changed to dimensionless 'derived units' in 1995. Recent papers have suggested that angles could be handled in two different ways within the SI, both differing from the present system. The purpose of this paper is to provide a framework for putting such suggestions into context, outlining the range of options that is available, together with the advantages and disadvantages of these options.Consideration of the relationship between solid angle and plane angle in simple situations shows that if they are to be considered to have dimensions, these dimensions must be independent; although solid angle can be said to have the dimensions of (plane angle)2 for negligibly small angles, this is not generally true. This, and the desirability of treating the two quantities in the same way, are additional factors influencing the decision on how angles should be handled within a system of units.Although less rigorously logical than some alternatives, the present SI approach is generally supported, but with some changes to the SI brochure to make the position clearer, in particular with regard to the designation of the radian and steradian as derived units.

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