Spherical Coordinates


Spherical coordinate system is a coordinate system in three dimensional space. 3 dimensional objects can be described using spherical coordinates. Three parameters are used to describe these objects and these three parameters are radial distance, inclination angle and azimuth angle.

In spherical coordinate system we need to select two orthogonal directions, zenith reference and origin point. Origin is always perpendicular to zenith reference. Let us see three coordinates of spherical coordinate system:

Radial distance: This radial distance is the distance from origin O to a particular point say 'p'. We will denote radial distance by symbol (r).

Inclination angle: We also call this angle as polar angle or zenith angle. This is an angle between zenith reference and segment of line 'op'. We represent polar angle by symbol (θ).

Azimuth angle: This angle between azimuth reference and orthogonal segment line 'op'. This angle is a signed angle. We represent this azimuth angle by symbol (ф).

So three coordinates will be denoted as (r, θ, ф). These three points mark a single point in three dimensional space. Every point has many equivalent points in three dimensional space. There is range decided for all three coordinates.

Radial distance must be greater than zero, it can never be a negative value, so r > 0.

Inclination angle of spherical coordinate can lie from zero degree to 180 degrees. So we can denote it as 00 ≤ θ ≤ 1800.

And azimuth angle will be defined in the range zero degree to 360 degrees.

00 ≤ ф ≤ 3600

This coordinate system is useful for objects like sphere and it is used in geographic coordinate system widely.

Topics Covered in Spherical Coordinates

Spherical Coordinates conversions

Coordinate system is defined as system in which one or more than one parameters are used to describe the location of particle in space. These parameters are called as coordinates and space in which point of particle is located is known as coordinate plane. Various types of coordinate systems are Cartesian coordinate system, spherical coordinate system, cy...Read More

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