Cartesian to Spherical Coordinates Calculator

Spherical Coordinates System

Cartesian (Rectangular) to Spherical Coordinates System Diagram

Rectangular to spherical coordinates

Spherical coordinates formula from rectangular/cartesian coordinates


This spherical coordinates converter/calculator converts the rectangular (or cartesian) coordinates of a unit to its equivalent value in spherical coordinates, according to the formulas shown above.

Rectangular coordinates are depicted by 3 values, (X, Y, Z). When converted into spherical coordinates, the new values will be depicted as (r, θ, φ).

To use this calculator, a user just enters in the (X, Y, Z) values of the rectangular coordinates and then clicks the 'Calculate' button, and the spherical coordinates will be automatically computed and shown below.

This calculator can be used to convert 2-dimensional (2D) or 3-dimensional rectangular coordinates to its equivalent spherical coordinates. If desired to convert a 2D rectangular coordinate, then the user just enters values into the X and Y form fields and leaves the 3rd field, the Z field, blank. If desired to convert a 3D rectangular coordinate, then the user enters values into all 3 form fields, X, Y, and Z.

By default, the calculator will compute the result in degrees. However, by using the drop-down menu, the option can changed to radians, so that the result will be computed in radians.

Example Calculations

Example With Rectangular (Cartesian) Coordinates

Convert the rectangular coordinates (2, 3, 8) into its equivalent spherical coordinates.

Spherical coordinates example calculation

This answer is calculated in degrees.

Related Resources

Cartesian (Rectangular) to Cylindrical Coordinates Calculator

Cylindrical to Cartesian Coordinates Calculator

Cylindrical to Spherical Coordinates Calculator

Spherical to Cartesian Coordinate Calculator

Spherical to Cylindrical Coordinate Calculator