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 mechanics results in the appearance of a constant of Nature equal to the central angle of a plane circular sector whose arc length is equal to that of its radius. This is the common (but not current SI) concept of the radian, rad, appropriately chosen as the base unit for angle. What the SI calls ‘angle’ is actually a nondimensionalized angle: the physical angle (dimension A) divided by one radian. Using a coordinate-system-independent definition of solid angle, I show that this is a derived quantity with dimension A ² and appropriate unit radian-squared. The steradian is retained as a coherent derived unit: sr = rad². Clarification of terminology is needed in distinguishing between ‘geometrical’ and ‘mathematical’ trigonometric functions and in related topics, including the distinction between frequency and angular velocity, and between phase and phase angle, among other things.

由于 SI 将角度和立体角解释为无量纲量（以及弧度和球面度作为无量纲导出单位）所造成的持续混乱，SI 是时候正确处理这些量纲物理量了。建立在以前作者的基础上，从欧几里德的元素开始，我认为角度应该被认为是一个具有独立量纲的基本量：角度，A。旋转几何和力学的量纲一致分析导致自然常数的出现等于平面圆形扇区的中心角弧长等于它的半径。这是弧度的常见（但不是当前的 SI）概念，rad，被适当地选择为角度的基本单位。SI 所说的“角度”实际上是一个无量纲的角度：物理角度（尺寸 A）除以一个弧度。使用与坐标系无关的立体角定义，我表明这是一个导出量，其尺寸为 A ²和适当的单位弧度平方。球面度保留为相干导出单位：sr = rad ². 需要澄清术语以区分“几何”和“数学”三角函数以及相关主题，包括频率和角速度之间的区别，以及相位和相角之间的区别等等。