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 unit degree radian ] 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit Spherical coordinate P: (r ,θ ,φ )
 $\normal Transformation\ coordinates\\\hspace{10} Cartesian\ (x,y,z)\ \right\ Spherical\ (r,\theta,\phi)\\\vspace{5}\hspace{10} r=\sqrt{x^2+y^2+z^2}\\\hspace{10} \theta=tan^{\tiny -1}{\large\frac{y}{x}}\\\hspace{10} \phi=tan^{\tiny -1}{\large\frac{\sqrt{x^2+y^2}}{z}}\\$
Cartesian to Spherical coordinates
 [1-10] /42 Disp-Num5103050100200
[1]  2018/08/29 00:07   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Check work
[2]  2018/05/07 19:40   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
homework
Comment/Request
explanation
[3]  2018/03/13 12:30   Male / 40 years old level / An office worker / A public employee / Very /
Purpose of use
for mapping
[4]  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.

[5]  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
[6]  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 ---
[7]  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.
[8]  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
[9]  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!).
[10]  2017/06/12 20:57   Male / 20 years old level / High-school/ University/ Grad student / A little /
Purpose of use
it is partially used in Electromagnetic field theoryin my 3rd year of electrical engineering

Sending completion

To improve this 'Cartesian to Spherical coordinates Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired person Others
Useful?
Very Useful A little Not at All
Purpose of use?