The unit sphere  in three-dimensional space  is the set of points  such that . Let  be the "north pole", and let  be the rest of the sphere. The plane  runs through the center of the sphere; the "equator" is the intersection of the sphere with this plane.
For any point  on , there is a unique line through  and , and this line intersects the plane  in exactly one point , known as the stereographic projection of  onto the plane.
In Cartesian coordinates  on the sphere and  on the plane, the projection and its inverse are given by the formulas
In spherical coordinates  on the sphere (with  the zenith angle, , and  the azimuth, ) and polar coordinates  on the plane, the projection and its inverse are
Here,  is understood to have value  when  = 0. Also, there are many ways to rewrite these formulas using trigonometric identities. In cylindrical coordinates  on the sphere and polar coordinates  on the plane, the projection and its inverse are