The **cylindrical coordinate system** is similar to that of the spherical coordinate system, but is an alternate extension to the polar coordinate system. Its elements, however, are something of a cross between the polar and Cartesian coordinates systems.

The coordinate system uses the standard polar coordinate system in the x-y plane, utilizing a distance from the origin (**r**) and an angle (**θ**) of extension from the positive x-axis (or pole). However, the third coordinate is a simple z-axis distance from above the x-y plane, just as any standard Cartesian system would utilize.

The coordinate represents the coordinate that exists at height **h** above the x-y plane (the z-coordinate). While, looking down from above, onto the x-y plane, the coordinate would appear to be at the polar coordinate **(r, θ)**

## Conversion

Given the coordinates:

- Spherical:
- Cylindrical:
- Cartesian:

Spherical coordinates may be converted to cylindrical coordinates by:

Cylindrical coordinates may be converted to spherical coordinates by:

Cartesian coordinates may be converted into cylindrical by:

Cylindrical coordinates may be converted into Cartesian by: