Cylindrical coordinate system
![A cylindrical coordinate system with origin O, polar axis A, and longitudinal axis L. The dot is the point with radial distance ρ = 4, angular coordinate φ = 130°, and height z = 4.](/Images/godic/202501/07/Coord_system_CY_1.svg0124.png")
![The coordinate surfaces of the cylindrical coordinates (ρ, φ, z). The red cylinder shows the points with ρ=2, the blue plane shows the points with z=1, and the yellow half-plane shows the points with φ=−60°. The z-axis is vertical and the x-axis is highlighted in green. The three surfaces intersect at the point P with those coordinates (shown as a black sphere); the Cartesian coordinates of P are roughly (1.0, −1.732, 1.0).](/Images/godic/202501/07/Cylindrical_coordinate_surfaces0124.png")
![Cylindrical coordinate surfaces. The three orthogonal components, ρ (green), φ (red), and z (blue), each increasing at a constant rate. The point is at the intersection between the three colored surfaces.](/Images/godic/202501/07/Cylindrical_coordinate_surfaces0124.gif")
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.