Spherical Coordinates

Wolfram Article

$(\rho ,\theta ,\varphi )=\left(\sqrt{x^2+y^2+z^2},{\tan }^{-1}\left(\frac{y}{x}\right),{\cos }^{-1}\left(\frac{z}{\rho }\right)\right)$

• Conversion from rectangular coordinates to spherical coordinates
• $\theta$ is the polar angle
• $\varphi$ is the azimuthal angle
• The $\theta$ and $\varphi$ symbols are often swapped in the context of physics

$(x,y,z)=(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )$

• Conversion from spherical to rectangular coordinates

$J_{\text{spherical}}={\rho }^2\sin \varphi$

• Jacobian for conversion from rectangular to spherical coordinates