If  is a vector field and  is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is :
Here,  is the angle between the vectors  and .
The circulation  of a vector field  around a closed curve  is the line integral:
In a conservative vector field this integral evaluates to zero for every closed curve. That means that a line integral between any two points in the field is independent of the path taken. It also implies that the vector field can be expressed as the gradient of a scalar function, which is called a potential.