Circulation can be related to curl of a vector field  and, more specifically, to vorticity if the field is a fluid velocity field,
By Stokes theorem, the flux of curl or vorticity vectors through a surface S' is equal to the circulation around its perimeter,
Here, the closed integration path  is the boundary or perimeter of an open surface , whose infinitesimal element normal  is oriented according to the right-hand rule. Thus curl and vorticity are the circulation per unit area, taken around a local infinitesimal loop.
In potential flow of a fluid with a region of vorticity, all closed curves that enclose the vorticity have the same value for circulation.