Stokes' theorem
Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem, or rotor theorem is a theorem in vector calculus on three-dimensional Euclidean space and real coordinate space, R 3 {\displaystyle \mathbb {R} ^{3}} . Given a vector field, the theorem relates 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.