# 9.4 Relations between Cartesian, Cylindrical, and Spherical Coordinates

Consider a cartesian, a cylindrical, and a spherical coordinate system, related as shown in Figure 1. Figure 1: Standard relations between cartesian, cylindrical, and spherical coordinate systems. The origin is the same for all three. The positive z-axes of the cartesian and cylindrical systems coincide with the positive polar axis of the spherical system. The initial rays of the cylindrical and spherical systems coincide with the positive x-axis of the cartesian system, and the rays =90° coincide with the positive y-axis.

Then the cartesian coordinates (x,y,z), the cylindrical coordinates (r, ,z), and the spherical coordinates ( , , ) of a point are related as follows:   Next: 9.5 Homogeneous Coordinates in Space
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Silvio Levy
Wed Oct 4 16:41:25 PDT 1995

This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas (CRC Press). Unauthorized duplication is forbidden.