# Convert Spherical to Rectangular Coordinates - Calculator

## Spherical and Rectangular Coordinates

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

## Use Calculator to Convert Spherical to Rectangular 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 $$x =$$ $$y =$$ $$z =$$