English: Diagram illustrating the definition of the divergence of a vector field F at a point x . It shows a sequence of concentric closed surfaces S _i with volume V _i enclosing x . The red arrows represent the flux of the vector field ${\displaystyle \iint _{S_{i}}\mathbf {F} \cdot \mathbf {\hat {n}} \,dS,}$ through ${\displaystyle S_{i}}$ . The divergence is the limit of the ratio ${\displaystyle S_{i}/V_{i}}$ as the volume shrinks to zero.