$\mathrm{div}U=\underset{V\to 0}{\lim }\frac{1}{V}{\displaystyle \underset{\text{S}}{∯}U\cdot e_n\mathrm{d}A}$

where e_ndA is the vector surface element oriented outwards and V is the volume

Note 1 to entry: In orthonormal Cartesian coordinates, the divergence is:

${\displaystyle \mathrm{div}U=\frac{\partial U_x}{\partial x}+\frac{\partial U_y}{\partial y}+\frac{\partial U_z}{\partial z}}$

Note 2 to entry: The divergence of the vector field U is denoted div U or ∇ ⋅ U.