Angular Distance

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DEFINITION

Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere. — https://en.wikipedia.org/wiki/Angular_distance

Since it is the angle between two vectors it can be derived from the Cosine Similarity.

When the vectors may be positive or negative:

$$d_{ang}=\frac{\arccos (d_{cos})}{\pi }$$

if the vector elements are always positive:

$$d_{ang}=\frac{2\arccos (d_{cos})}{\pi }$$