# Dictionary:Divergence theorem

The flux ${\displaystyle \phi }$ through a surface (or the integral of the vector flux density g over a closed surface) equals the divergence of the flux density integrated over the volume contained by the surface:
${\displaystyle \phi =\iint {\textbf {g}}\cdot d{\textbf {s}}=\iiint \nabla \cdot {\textbf {g}}\;dxdydz}$.