Concise Formulas for the Area and Volume of a Hyperspherical Cap

Spherical caps in hyperspace have found applications in stochastic optimizations and software engineering. However, there is a need for concise formulas for surface area and volume that are easy to express and compute. In this note, concise formulas are given in closed-forms. These formulas are obtained by integrating the area/volume of an (n-1)-sphere over a great circle arc in hyperspherical coordinates.