Cartesian to Spherical coordinates Calculator

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

Cartesian to Spherical coordinates
    1. Cartesian coordinate P:
 (x
    1. ,
    2. y
    3. ,
    4. z
    5. )
    1. [angle unit
    2. ]

    1. Spherical coordinate P:
 (r
    1.  
    2. ,
    3. θ
       
    4. ,
    5. φ
       
    6. )
    Cartesian to Spherical coordinates
    [1-10] /48Disp-Num
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    [1]  2020/05/31 19:57   Male / 20 years old level / High-school/ University/ Grad student / Very /
    Purpose of use
    Computer graphics software usage
    [2]  2019/12/09 23:14   Male / 60 years old level or over / A teacher / A researcher / Very /
    Purpose of use
    Making a key for a calc iii final exam
    [3]  2019/12/04 07:25   Male / 40 years old level / A teacher / A researcher / Useful /
    Purpose of use
    checking answers
    [4]  2019/11/09 14:22   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
    Purpose of use
    Homework
    Comment/Request
    Exact answer in radian conversion is more helpful
    [5]  2019/07/16 08:57   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
    Purpose of use
    Homework
    [6]  2018/12/13 23:42   Male / 20 years old level / Self-employed people / Very /
    Purpose of use
    Writing computer graphics software.
    [7]  2018/08/29 00:07   Male / 20 years old level / High-school/ University/ Grad student / Very /
    Purpose of use
    Check work
    [8]  2018/05/07 19:40   Male / 20 years old level / High-school/ University/ Grad student / Very /
    Purpose of use
    homework
    Comment/Request
    explanation
    [9]  2018/03/13 12:30   Male / 40 years old level / An office worker / A public employee / Very /
    Purpose of use
    for mapping
    [10]  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.


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