Convert Rectangular to Spherical Coordinates - Calculator
Rectangular and Spherical Coordinates
Convert rectangular to spherical coordinates using a calculator.
using simple trigonometry, it can be shown that the rectangular rectangular coordinates \( (x,y,z) \) and spherical coordinates \( (\rho,\theta,\phi) \) 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)
with \( 0 \le \theta \lt 2\pi \) and \( 0 \le \phi \le \pi \)
Fig.1 - Rectangular and spherical coordinates
The calculator calculates the spherical coordinates \( \rho \), \( \theta \) and \( \phi \) given the rectangular coordinates \( x \) , \( y \) and \( z \) using the three formulas in II.
Use Calculator to Convert Rectangular to Spherical Coordinates
1 - Enter \( x \), \( y \) and \( z \) and press the button "Convert". You may also change the number of decimal places as needed; it has to be a positive integer.
The angles \( \theta \) and \( \phi \) are given in radians and degrees.
