Cylindrical coordinate system

The cylindrical coordinate system is a three-dimensional system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted ) which measures the height of a point above the plane.

A point P is given as . In terms of the Cartesian coordinate system:

• is the distance from O to P', the orthogonal projection of the point P onto the XY plane. This is the same as the distance of P to the z-axis.
• is the angle between the positive x-axis and the line OP', measured anti-clockwise.
• is the same as .

Cylindrical coordinates are useful in analyzing surfaces that are symmetrical about an axis, with the z-axis chosen as the axis of symmetry. For example, the infinitely long circular cylinder that has the Cartesian equation x² + y² = c² has the very simple equation r = c in cylindrical coordinates. Hence the name "cylindrical" coordinates.

Conversion from Cartesian to cylindrical coordinates