Spherical coordinate system

In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are

  • the radial distance r along the line connecting the point to a fixed point called the origin;
  • the polar angle θ between this radial line and a given polar axis; and
  • the azimuthal angle φ, which is the angle of rotation of the radial line around the polar axis.

(See graphic regarding the "physics convention".)

Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle) is called the reference plane (sometimes fundamental plane).

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