# Definition(s) > [!NOTE] Definition 1 (Spherical Metric) > Let $n\in \mathbb{N},r\geq 0$ and $S_{r}^n$ denote the [[n-Sphere|n-dimensional sphere]] of radius $r.$ The spherical distance between two points $P,Q\in S_{r}^n$ is the length of the shortest arc of the [[Spherical Line|great circle]] joining them which is given by $d_{S_{r}^n}(P,Q)= r \arccos\left( \frac{\langle P, Q\rangle}{r^2} \right).$ > [!Example] Example > Contents # Properties(s) # Application(s) **More examples**: # Bibliography