# Cylindrical Coordinates

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Related to Cylindrical coordinate system: Polar coordinates, Spherical coordinate system

## cylindrical coordinates

[sə′lin·drə·kəl ‚kō′ȯrd·ən·əts] (mathematics)

A system of curvilinear coordinates in which the position of a point in space is determined by its perpendicular distance from a given line, its distance from a selected reference plane perpendicular to this line, and its angular distance from a selected reference line when projected onto this plane.

## Cylindrical Coordinates

The cylindrical coordinates of a point *M* are the three numbers *r*, θ, and *z* characterizing the position of *M* in space (see Figure 1). The coordinates are called cylindrical because the coordinate surface *r* = const is a cylinder

whose elements are parallel to the *z*-axis. The relation between the cylindrical coordinates and the rectangular coordinates *x*, *y*, and *z* of *M* is given by the equations *x* = *r* cos θ, *y* = *r* sin θ, and *z* = *z*.