The geometric link between the spherical (r, ϑ, φ) and Cartesian (x, y, z) coordinate systems is shown.

In spherical coordinates, a point in space is defined by the radius r (black), the polar angle ϑ (blue) and the azimuth angle φ (red). The volume element dV=dx⋅dy⋅dz thus becomes dV=r²⋅sin(ϑ) dr⋅dϑ⋅dφ in polar coordinates.