${\displaystyle \underset{\text{V}}{\iiint }\mathrm{div}U}dV={\displaystyle \underset{\text{S}}{∯}U}\cdot e_{\text{n}}dA$

where dV is the volume element and e_ndA is the vector surface element

Note 1 to entry: The divergence theorem can be generalized to the n-dimensional Euclidean space.

Note 2 to entry: In electrostatics, the divergence theorem is applied to express that the electric flux through a closed surface is equal to the total electric charge in the domain enclosed by the surface. It is then called "Gauss law".