From spherical coordinates So for the volume element: From cylindrical coordinates So for the volume element: To spherical coordinates From Cartesian coordinates See also the article on atan2 for how to elegantly handle some edge cases. So for the element: From cylindrical coordinates To cylindrical coordinates From Cartesian coordinates From spherical coordinates Arc-length, curvature and torsion from Cartesian coordinates See also Geographic coordinate conversion Transformation matrix References Coordinate transformations Coordinate systems Hamiltonian mechanics