The divergence theorem, also known as Gauss's theorem is a result that relates the flow of a tensor field through a surface to the behavior of the tensor field inside the surface.
The divergence theorem states that the outward flux of a tensor field through a closed surface is equal to the volume integral of the divergence over the region inside the surface.
In one dimension, it is equivalent to the fundamental theorem of calculus. In two dimensions, it is equivalent to Green's theorem.
The theorem is a special case of the more general Stokes' theorem