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;[a] and
  • the azimuthal angle φ, which is the angle of rotation of the radial line around the polar axis.[b]

(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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