# Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

@article{Leonard2021ProposalFT, title={Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)}, author={B. P. Leonard}, journal={Metrologia}, year={2021}, volume={58} }

Because of continued confusion caused by the SI’s interpretation of angle and solid angle as dimensionless quantities (and the radian and steradian as dimensionless derived units), it is time for the SI to treat these dimensional physical quantities correctly. Building on previous authors’ foundations, starting from Euclid’s Elements, I argue that angle should be recognized as a base quantity with an independent dimension: angle, A. A dimensionally consistent analysis of rotational geometry and…

## 4 Citations

Comment on ‘Angles in the SI: a detailed proposal for solving the problem’

- PhysicsMetrologia
- 2022

Paul Quincey makes a compelling argument for recognizing angle as a base quantity with the radian as the base unit. Solid angle is then a derived quantity with the steradian a coherent derived unit…

Angles in the SI: a detailed proposal for solving the problem

- PhysicsMetrologia
- 2021

A recent letter [1] proposed changing the dimensionless status of the radian and steradian within the SI, while allowing the continued use of the convention to set the angle 1 radian equal to the…

On the dimension of angles and their units

- MathematicsMetrologia
- 2022

We show the implications of angles having their own dimension, which facilitates a consistent use of units as is done for lengths, masses, and other physical quantities. We do this by examining the…

Angular frequency in the International System of Units. Physicist’s view

- PhysicsMetrologia
- 2021

Currently, in the International System of Units (SI), reciprocal second (s−1) and radian per second (rad s−1) are the units of frequency ν and angular frequency ω, respectively. At the same time,…

## References

SHOWING 1-10 OF 52 REFERENCES

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

- PhysicsMetrologia
- 2019

The article analyzes the arguments that have become the basis for the 1980 CIPM recommendations declaring plane and solid angles as dimensionless derived quantities. This decision was the result of…

Comment on ‘On the units radian and cycle for the quantity plane angle’

- Physics
- 2016

In the referenced paper, Ian Mills addresses the confusion caused by the treatment of plane angle in the International System of Units (SI). As he points out, what the SI calls an ‘angle’ is not a…

A Viewpoint on the Quantity "Plane Angle"

- Mathematics
- 1982

Properties of the quantity "plane angle" are explored under the hypothesis that it is a dimensional quantity. The exploration proceeds especially with respect to the physical concept, its…

Differing angles on angle

- Physics
- 2005

Values of plane angles are expressed with a choice of several units. Historically the quantity needed a unit because it was, and still is, used as a base quantity. ISO/TC 12 defines it as a derived,…

Implications of adopting plane angle as a base quantity in the SI

- Physics
- 2016

The treatment of angles within the SI is anomalous compared with other quantities, and there is a case for removing this anomaly by declaring plane angle to be an additional base quantity within the…

Angles-Let's treat them squarely

- Physics
- 1997

We suggest a self-consistent treatment of the dimensions and units of the geometric quantity “angle.” The method regards “angle” as a fundamental dimensional physical quantity, on a par with length,…

On Angles and Angular Quantities

- Physics
- 1986

It is argued that angles are geometric quantities and have a dimension. The equation giving the length s of the arc cut out by an angle on a circle of radius R is written as s = ? R , where ? is a…

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

- Physics
- 2016

The purpose of this paper is to provide a framework for putting suggestion that angles could be handled in two different ways within the SI into context, outlining the range of options that is available, together with the advantages and disadvantages of these options.

Comment on ‘Dimensionless units in the SI’

- Education
- 2015

In their paper, Mohr and Phillips demonstrate that the SI’s representation of ‘plane angle’ as dimensionless rather than as an independent dimensional quantity continues to create confusion. The…

A New Approach to the Plane Angle

- Education
- 1988

In distinguishing between `category of quantities' and `dimension' the author intends to reach a new understanding of the quantity plane angle. One basis is tensor algebra. Accordingly, the common…