# 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.

 $\rho =$ 1 $\theta =$ 45 degrees radians $\phi =$ 45 degrees radians Number of Decimal Places = 5 $x =$ $y =$ $z =$