High Quality Content by WIKIPEDIA articles! The Kelvin–Stokes theorem, also known as the curl theorem, is a theorem in vector calculus on R3. Given a vector field, the theorem relates the the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The Kelvin-Stokes theorem is a special case of the “generalized Stokes` theorem.” In particular, the vector field on R3 can be considered as a 1-form in which case curl is the exterior derivative.