# How do I convert from 3-D Cartesian coordinates to cylindrical coordinates?

Oct 21, 2014

If Cartesian coordinates are $\left(x , y , z\right)$, then its corresponding cylindrical coordinates $\left(r , \theta , z\right)$ can be found by

$r = \sqrt{{x}^{2} + {y}^{2}}$

theta={(tan^{-1}(y/x)" if "x>0),(pi/2" if "x=0 " and " y>0),(-pi/2" if " x=0" and "y<0),(tan^{-1}(y/x)+pi" if "x<0):}

$z = z$

Note: It is probably much easier to find $\theta$ by find the angle between the positive $x$-axis and the vector $\left(x , y\right)$ graphically.

I hope that this was helpful.