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

TL;DR

This paper critically examines the SI status of plane and solid angles, arguing that a plane angle is not a derived quantity and its unit, the radian, is not derived, challenging the 1995 declaration.

Contribution

It provides a detailed analysis showing that plane angles are not derived quantities in SI and clarifies the status of radians and steradians as units.

Findings

Plane angles are not derived quantities in SI.

Radian is not a derived unit in SI.

Steradian is a coherent derived unit of radian.

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.