# 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 $0 \le \phi \le \pi$ 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.

 $(x , y , z )$ = (1 , 1 , 1) Number of Decimal Places = 5 $\rho =$ $\theta =$   Radians $\theta =$   Degrees $\phi =$   Radians $\phi =$   Degrees