In vector calculus, the** curl** is a vector operator that describes the insignificant rotation of a 3-dimensional vector field. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. The curl measures the degree to which the fluid is rotating about a given point, with whirlpools and tornadoes being extreme examples.

In three dimensional space, if the appropriate vector function of a point is V^{→} (x, y, z) = **(v _{1} î + v_{2} ĵ + v_{3} ƙ)**, then a vector along the rotational axis is obtained by the cross product of the operator ∆ and V. This type of product is called curl.

**Physical properties of Curl**

- If f (x, y, z) has continuous second order partial derivatives then curl (∆f = 0
^{→}). This is easy enough to check by plugging into the definition of the derivative. - If F
^{→}is a conservative vector field then Curl, F^{→}= 0^{→}. This is a direct result of what it means to be a conservative vector field and the previous fact. - If F
^{→}is defined on all of Ɍ^{3}whose components have continuous first-order partial derivative and Curl F^{→}= 0^{→}then F^{→}is a conservative vector field.