Divergence is a vector operator which describes the net "out flow" of a vector field in three-dimensional Euclidean space at a point. The divergence at a point in a field is represented by a vector whose length and direction denote the magnitude and axis of the total "out flow".

The divergence of a field is denoted as or . The divergence of a field is defined as follows

Where .

Physical Interpretation

If we consider a vector field to represent the velocity of some fluid the divergence represents how much fluid is created or destroyed at a point.

Incompressible fluids like liquids will always have a divergence of 0 at every point as the velocity of the fluid into a point must always be equal to the velocity of the fluid flowing out