Dimensions of Plane and Solid Angles and Their Units in the International System of Units (SI)

• Published in: Measurement techniques 2021, Vol.63 (10), p.798-805
• Main Authors: Kalinin, M. I., Isaev, L. K., Bulygin, F. V.
• Format: Article
• Language: English
• Subjects: Analysis; Analytical Chemistry; Characterization and Evaluation of Materials; Circles (geometry); Flying-machines; International System of Units; Measurement Science and Instrumentation; Metric system; Physical Chemistry; Physics; Physics and Astronomy; Series expansion; Trigonometric functions
• ISSN: 0543-1972; 1573-8906
• DOI: 10.1007/s11018-021-01855-y

The situation was analyzed that has been established in the International System of Units (SI) as a result of adoption of the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities. It was shown that such decision was based on a misunderstanding of the mathematical formula, relating the arc length of a circle with its radius and corresponding central angle, as well as series expansions of trigonometric functions. As follows from the conducted analysis, the plane angle value does not depend on any of the SI quantities and should be treated as a base quantity, while its unit (radian) should be added to the population of base SI quantities. Therefore, the value of a solid angle becomes a derived quantity from a plane angle, and its unit (steradian) represents a coherent derived unit equal to a square radian.