${\displaystyle \underset{\text{S}}{\iint }\mathrm{rot}}U\cdot e_{\text{n}}dA={\displaystyle \underset{\text{C}}{\oint }U\cdot dr}$

where e_ndA is the vector surface element and dr is the vector line element

Note 1 to entry: The orientation of the surface S with respect to the curve C is chosen such that, at any point of C, the vector line element, the unit vector normal to S and defining its orientation, and the unit vector normal to these two vectors and oriented towards the exterior of the curve, form a right-handed or a left-handed trihedron according to space orientation.

Note 2 to entry: The Stokes theorem can be generalized to the n-dimensional Euclidean space.

Note 3 to entry: In magnetostatics, the Stokes theorem is applied to express that the magnetic flux through the surface S is equal to the circulation over C of the magnetic vector potential.