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# 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.

Mathematically,

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.