In geography, the latitude is the elevation.Įven with these restrictions, if φ is 0° or 180° (elevation is 90° or −90°) then the azimuth angle is arbitrary and if r is zero, both azimuth and inclination/elevation are arbitrary. This is the standard convention for geographic longitude.įor the polar angle φ, the range for inclination is equivalent to for elevation.

However, the azimuth θ is often restricted to the interval (−180°, +180°], or (− π, + π] in radians, instead of [0, 360°). If it is necessary to define a unique set of spherical coordinates for each point, one must restrict their ranges. This article will use the ISO convention frequently encountered in physics: ( r, θ, φ ). The use of symbols and the order of the coordinates differs among sources and disciplines. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The polar angle may be called colatitude, zenith angle, normal angle, or inclination angle. The radial distance is also called the radius or radial coordinate. It can be seen as the three-dimensional version of the polar coordinate system. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. In this image, r equals 4/6, θ equals 90°, and φ equals 30°.

A globe showing the radial distance, polar angle and azimuthal angle of a point P with respect to a unit sphere, in the mathematics convention.

Spherical geometry khan academy