Convert Spherical to Cylindrical Coordinates - Calculator
Spherical and Rectangular Coordinates
Convert spherical to cylindrical coordinates using a calculator.
Using Fig.1 below, the trigonometric ratios and Pythagorean theorem, it can be shown that the relationships between spherical coordinates \( (\rho,\theta,\phi) \) and cylindrical coordinates \( (r,\theta,z) \) are as follows:
\( r = \rho \sin \phi \) , \( \theta = \theta \) , \( z = \rho \cos \phi \) (I)
\( \rho = \sqrt {r^2 + z^2} \) , \( \theta = \theta \) , \( \tan \phi = \dfrac{r}{z} \) (II)
with \( 0 \le \theta \lt 2\pi \) and \( 0 \le \phi \le \pi \)
Fig.1 - Cylindrical and spherical coordinates
The calculator calculates the cylindrical coordinates \( r \), \( \theta \) and \( z \) given the spherical coordinates \( \rho \) , \( \theta \) and \( \phi \) using the three formulas in I.
Use Calculator to Convert Spherical to Cylindrical 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.
