Curl

In vector calculus, the curl of a vector field $\vec{F}$ is defined as:

$$\nabla \times \vec{F}$$

where $\nabla$ is the gradient operator taken with the cross product of the vector field. The curl is distributive (over addition/subtraction terms).

Geometrically, it represents how much a vector field rotates at a given point $\vec{P}$. The direction of the curl is the axis of minimum rotation, and the magnitude is the speed of rotation. If the curl is 0, then the field won’t rotate.

See also

• Divergence, the dot product equivalent
• Stokes’ theorem, sometimes referred to as the curl theorem