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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 mathematics the curl is noted by:

where is the vector differential operator del, and F is the vector field the curl is being applied to, and is composed of [Fx, Fy, Fz].

Expanded, is

A simple way to remember the expanded form of the curl is to think of it as:

or as the determinant of the following matrix:

where 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: