A double surface integral operator representing integration over a closed surface in vector calculus and physics.
Examples
Surface integral over a closed surface
\oiint_S \vec{E} \cdot d\vec{S} = \frac{Q_{enc}}{\epsilon_0}
Gauss's divergence theorem
\oiint_S \vec{F} \cdot d\vec{S} = \iiint_V (\nabla \cdot \vec{F})\,dV
Electric flux through a closed surface
\Phi_E = \oiint_S \vec{E} \cdot \hat{n}\,dA