Spherical volume element
= Spherical volume element
{title2=$dV=r^2\sin\theta\,dr\,d\theta\,d\phi$}
With polar <angle> $\theta$ measured from positive $z$ and azimuth $\phi$, the Cartesian formulas $x=r\sin\theta\cos\phi$, $y=r\sin\theta\sin\phi$, $z=r\cos\theta$ have <Jacobian determinant> $r^2\sin\theta$. For $r\geq0$ and $0\leq\theta\leq\pi$ this gives the unsigned <volume element> shown. The inverse determinant is $1/(r^2\sin\theta)$ off the origin and polar axis.