# Cartesian to Spherical coordinates Calculator

## Converts from Cartesian (x,y,z) to Spherical (r,θ,φ) coordinates in 3-dimensions.

 Cartesian coordinate P: (x ,y,z) [angle unitdegreeradian] 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit Spherical coordinate P: (r ,θ ,φ )
Cartesian to Spherical coordinates
 [1-10] /43 Disp-Num5103050100200
[1]  2018/12/13 23:42   Male / 20 years old level / Self-employed people / Very /
Purpose of use
Writing computer graphics software.
[2]  2018/08/29 00:07   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Check work
[3]  2018/05/07 19:40   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
homework
Comment/Request
explanation
[4]  2018/03/13 12:30   Male / 40 years old level / An office worker / A public employee / Very /
Purpose of use
for mapping
[5]  2018/03/09 01:56   Male / 50 years old level / An engineer / Useful /
Purpose of use
Seventeenth source to verify equations derived from first-principles.
Comment/Request
Comment 14 had a point on the calculation of phi, though he was incorrect in claiming that your equation is "wrong". Your equation is correct but degenerate in that it suffers from gimbal-lock. Your solution for theta has a similar issue. For a solution free of both of these issues, use:

theta = atan2(y, x) % <- ***
% *** - Check implementation in whatever language you are using, most are
% denominator then numerator. Some are not.

phi = acos(z/r)

With this formulation the only degenerate case is a zero length radius, for which the angles are undefined. As such the input is degenerate and the output being degenerate follows.

[6]  2018/02/01 07:30   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
hohmeworke
Comment/Request
how do you find theta when x = 0
[7]  2017/12/20 23:22   Female / - / High-school/ University/ Grad student / Very /
Purpose of use
to Lerner
Comment/Request
i will like to you for ---
[8]  2017/09/08 03:45   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Checking my own hand calculations.
Comment/Request
Would be nice if you could factor pi out of radians and give answer in fractions when applicable.
[9]  2017/08/24 22:18   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
testing a conversion algorithm I''m using in a programming project
[10]  2017/08/02 22:41   Male / 30 years old level / A teacher / A researcher / Useful /
Purpose of use
To check if my fortran routine performed correct rotation (it did!).

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