differential operator describing the rotation at a point in a 3D vector field

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space. At every point in the field, the curl of that point is represented by a vector. Curl is an extension of torque.

Given a vector field , the curl of can be written as or , where is the gradient and is the cross product operation.[1][2]



  1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-10-14.
  2. "Calculus III - Curl and Divergence". Retrieved 2020-10-14.