Changing Coordinate Systems: Spherical and Cylindrical

Spherical Coordinates	Cylindrical Coordinates

Since the θ coordinate is the same in both coordinate systems, we just need to relate ρ and φ to r and z. We have the following triangles:

Spherical Coordinates	Cylindrical Coordinates

Comparing these we see that

• r = ρ sin φ
• z = ρ cos φ
• ρ = sqrt(r² + z²)
• φ = tan^-1(r/z)