# Convert Cylindrical to Spherical Coordinates - Calculator

## Cylindrical and Spherical Coordinates

Convert rectangular to spherical coordinates using a calculator.
Using trigonometric ratios, it can be shown that the cylindrical coordinates $(r,\theta,z)$ and spherical coordinates $(\rho,\theta,\phi)$ in Fig.1 are related as follows:
$\rho = \sqrt{r^2+z^2}$ , $\theta = \theta$ , $\tan \phi = \dfrac{r}{z}$       (I)
$r = \rho \sin \phi$ , $\theta = \theta$ , $z = \rho \cos \phi$       (II) The calculator calculates the spherical coordinates $\rho$ , $\theta$ and $\phi$ given the cylindrical coordinates $r$ , $\theta$ and $z$ using the formulas in I above.

## Use Calculator to Convert Cylindrical to Spherical Coordinates

1 - Enter $r$, $\theta$ 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.
Angle $\theta$ may be entered in radians and degrees.

 $r =$ 2 $\theta =$ 45 degrees radians $z =$ 5 Number of Decimal Places = 5 $\rho =$ $\theta =$   Radians $\theta =$   Degrees $\phi =$   Radians $\phi =$   Degrees