On the status of plane and solid angles in the International System of Units (SI)

2018/10/31 by M. I. Kalinin, M I Kalinin · 3 citations
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Calibration and Measurement Techniques #Scientific Measurement and Uncertainty Evaluation #Statistical and numerical algorithms #physics.class-ph

paper · pdf · doi:10.1088/1681-7575/ab3fbf

Correction of error in the calculation of the ratio between the steradian and the radian. 13 pages, 3 figures

openalex created_date 2018/11/02 · arxiv created 2018/11/08 · openalex publication_date 2019/08/30 · arxiv updated 2020/01/08 · openalex updated_date 2026/07/28

Abstract

The article analyzes the arguments that became the basis for declaring in 1995, at the 20th General Conference on Weights and Measures that the plane and solid angles are dimensionless derived quantities in the International System of Units. The inconsistency of these arguments is shown. It is found that a plane angle is not a derived quantity in the SI, and its unit, the radian, is not a derived unit. A solid angle is the derived quantity of a plane angle, but not a length. Its unit, the steradian, is a coherent derived unit of the radian.

Citations

• Dimensionless units in the SI
• On Angles and Angular Quantities
• Definitions of the units radian, neper, bel and decibel
• Angles—Let’s treat them squarely
• A Viewpoint on the Quantity "Plane Angle"
• Implications of adopting plane angle as a base quantity in the SI
• The range of options for handling plane angle and solid angle within a system of units
• A clearer approach for defining unit systems

Cited by

• Angles in the SI: a detailed proposal for solving the problem
• On the dual nature of a plane angle
• Radian [wikipedia]

Related

• The range of options for handling plane angle and solid angle within a system of units
• Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)
• On the dual nature of a plane angle
• Implications of adopting plane angle as a base quantity in the SI
• The term `angle' in the international system of units