如果一个矢量场是某个标量势的梯度，那幺便称为保守矢量场。有两个密切相关的概念：路径无关和无旋矢量场。任何一个保守矢量场的旋度都是零（因此是无旋的），也具有路径无关的性质。

一个矢量场称为保守的，如果存在一个标量场，使得：

在这里，表示的梯度。当以上的等式成立时，就称为的一个标量势。

矢量分析基本定理表明，任何一个矢量场都可以表示为一个保守矢量场和一个螺线矢量场的和。

In vector calculus a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential. Conservative vector fields have the property that the line integral is path independent, i.e. the choice of integration path between any point and another does not change the result. Path independence of a line integral is equivalent to the vector field being conservative. A conservative vector field is also irrotational; in three dimensions this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected.