
Spherical and Rectangular CoordinatesConvert 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 \( 0 \le \phi \le \pi \) 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 Coordinates1  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.More References and linksMaths Calculators and Solvers. 