*This article is about curl in mathematics. You may want Curl programming language.*

In vector calculus, **curl** is a vector operator that shows a vector field's tendency to rotate about a point. Common examples include:

- In a tornado the winds are rotating about the eye, and a vector field showing wind velocities would have a non-zero curl at the eye, and possibly elsewhere (see vorticity).
- In a vector field that describes the linear velocities of each individual part of a rotating disk, the curl will have a constant value on all parts of the disk.
- If a freeway was described with a vector field, and the lanes had different speed limits, the curl on the borders between lanes would be non-zero.

**F**is the vector field the curl is being applied to, and is composed of [F

_{x}, F

_{y}, F

_{z}].

Expanded, is

**i**,

**j**, and

**k**are the unit vectors for the x, y, and z axes, respectively.

Note that the result of the curl operator acting on a vector field is not really a vector, it is a pseudovector. This means that it takes on opposite values in left-handed and right-handed coordinate systems (see Cartesian coordinate system). (Conversely, the curl of a pseudovector is a vector.)

**See also:**