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Convert Cylindrical to Spherical Coordinates - Calculator



Cylindrical and Spherical Coordinates

Convert rectangular to spherical coordinates using a calculator.
Using trigonometric ratios, it can be shown that the cylindrical coordinates \( (r,\theta,z) \) and spherical coordinates \( (\rho,\theta,\phi) \) in Fig.1 are related as follows:
\( \rho = \sqrt{r^2+z^2} \) , \( \theta = \theta \) , \( \tan \phi = \dfrac{r}{z} \)       (I)
\( r = \rho \sin \phi \) , \( \theta = \theta \) , \( z = \rho \cos \phi \)       (II)
cylindrical and spherical coordinates.
Fig.1 - Cylindrical and spherical coordinates
The calculator calculates the spherical coordinates \( \rho \) , \( \theta \) and \( \phi \) given the cylindrical coordinates \( r \) , \( \theta \) and \( z \) using the formulas in I above.


Use Calculator to Convert Cylindrical to Spherical Coordinates

1 - Enter \( r \), \( \theta \) and \( z \) and press the button "Convert". You may also change the number of decimal places as needed; it has to be a positive integer.
Angle \( \theta \) may be entered in radians and degrees.


\( r = \)
\( \theta = \)
\( z = \)
Number of Decimal Places =


\( \rho = \)
\( \theta = \)   Radians
\( \theta = \)   Degrees
\( \phi = \)   Radians
\( \phi = \)   Degrees


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