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Spherical Coordinates

Illustration

Illustration

Alternate names

spherical coordinate system | spherical polar coordinates

Basic definition

Spherical coordinates are a coordinate system in which points in three-dimensional space are given by two angles and a distance from the origin.

Detailed definition

Spherical coordinates, also called spherical polar coordinates, are a system of curvilinear coordinates that are natural for describing positions on a sphere or spheroid. Define θ to be the azimuthal angle in the x y-plane from the x-axis with 0<=θ<2π (denoted λ when referred to as the longitude), ϕ to be the polar angle (also known as the zenith angle and colatitude, with ϕ = 90° - δ where δ is the latitude) from the positive z-axis with 0<=ϕ<=π, and r to be distance (radius) from a point to the origin. This is the convention commonly used in mathematics.

Related terms

azimuth | colatitude | great circle | Helmholtz differential equation--spherical coordinates | latitude | longitude | oblate spheroidal coordinates | polar angle | polar coordinates | polar plot | polar vector | prolate spheroidal coordinates | zenith angle

Related Wolfram Language symbol

SphericalPlot3D

Educational grade level

high school level

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