Convert Spherical to Rectangular Coordinates - Calculator
Spherical and Rectangular Coordinates
Convert spherical to rectangular coordinates using a calculator.
It can be shown, using trigonometric ratios, that the spherical coordinates \( (\rho,\theta,\phi) \) and rectangualr coordinates \( (x,y,z) \) in Fig.1 are related as follows:
\( x = \rho \sin \phi \cos \theta \) , \( y = \rho \sin \phi \sin \theta \) , \( z = \rho \cos \phi \) (I)
\( \rho = \sqrt {x^2 + y^2 + z^2} \) , \( \tan \theta = \dfrac{y}{x} \) , \( \cos \phi = \dfrac{z}{\sqrt {x^2 + y^2 + z^2}} \) (II)
Fig.1 - Rectangular and spherical coordinates
The calculator calculates the rectangualr coordinates \( x \), \( y \) and \( z \) given the spherical coordinates \( \rho \) , \( \theta \) and \( \phi \) using the three formulas in I.
Use Calculator to Convert Spherical to Rectangular Coordinates
1 - Enter \( \rho \) , \( \theta \) and \( \phi \), selecting the desired units for the angles, and press the button "Convert". You may also change the number of decimal places as needed; it has to be a positive integer.
