A vector field satisfying any of the following conditions is called a conservative vector field.

Each of the following conditions implies the other conditions, meaning that if one is true, then all are true.

Let **F** be a continuously differentiable vector field defined on R^{3} except possibly for a finite number of points:

- For any oriented simple closed curve, the line integral of the vector field along the curve is equal to zero.
- For any two oriented curves C
_{1} and C_{2} which have the same endpoints, the line integral of the vector field along each path is equal to the other.
**F** is the gradient of some scalar field ƒ.
- The curl of
**F** is equal to zero