Spherical coordinate system

A three-dimensional coordinate system that locates points by their distance from an origin and two angles. Its angle conventions vary across mathematical and scientific disciplines.

Cartesian coordinate system: A coordinate system that locates points using signed distances along mutually perpendicular axes. Its three linear coordinates provide the standard comparison for spherical coordinates.
Spherical-to-Cartesian coordinate conversion: The formulas that express spherical coordinates as Cartesian coordinates, or convert between the two systems. These equations turn a radius and two angles into three axis positions.
Spherical symmetry: Invariance under rotations about a common center, so physical properties depend only on distance from that center. This symmetry can reduce three-dimensional equations to dependence on radius alone.
Geographic coordinate system: A system that locates positions on Earth using latitude, longitude, and usually altitude. Its latitude convention differs from the common mathematical polar angle measured down from the positive axis.
Polar coordinate system: A two-dimensional coordinate system that locates points by distance from an origin and an angle. Spherical coordinates extend this distance-and-angle framework into three dimensions.
Spherical coordinate Jacobian: The determinant factor that accounts for volume scaling when variables are changed to spherical coordinates. Its radius-squared sine factor explains how coordinate cells grow with distance and angle.
Central force: A force directed toward or away from a fixed center whose magnitude depends only on distance from it. Its radial geometry makes spherical coordinates natural for describing motion.
Cylindrical coordinate system: A three-dimensional coordinate system using distance from an axis, an angle around it, and height along it. It is often preferable when a problem has rotational symmetry about an axis rather than a center.
Euclidean space: A geometric space with flat geometry and the usual rules for distances and angles. The standard spherical system describes positions in three-dimensional Euclidean space.
Spherical harmonics: Angular functions on a sphere that form an orthogonal basis for representing fields and wave solutions. They separate the angular dependence of many equations written in spherical coordinates.

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