Spherical Coordinates

Spherical coordinates are a way to describe the location of a point in three-dimensional space based on , the distance from the origin (where ); , the angle between the point and the x-z plane (in the positive x direction); and , the angle between the point and the z axis (in the positive z direction). Thus, each point is described by: .

In a sense, spherical coordinates are coordinates on a sphere just like polar coordinates are coordinates on a circle.

The equations converting the parameters are as follows:

The Jacobian in spherical polar coordinates is so that .