# Stokesâ€™ Theorem

Stokesâ€™ theorem combines the ideas of Greenâ€™s theorem with the curl of a vector field. Greenâ€™s theorem applies only to two-dimensional vector fields and to regions in the two-dimensional plane. Stokesâ€™ theorem generalises Greenâ€™s theorem to three dimensions.**Statement**

This theorem states that the line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over the surface bounded by the path.

where

*S*is the surface enclosed by the path*L*. The positive direction of is related to the positive sense of defining*L*according to the right-hand rule.