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

 $$\rho =$$ 1 $$\theta =$$ 45 degrees radians $$\phi =$$ 45 degrees radians Number of Decimal Places = 5 $$r =$$ $$\theta =$$ (radians) $$\theta =$$ (degrees) $$z =$$