  In this article, we study the Calabi invariant on the unit disk usually
defined on compactly supported Hamiltonian diffeomorphisms of the open disk. In
particular we extend the Calabi invariant to the group of $C^1$ diffeomorphisms
of the closed disk which preserves the standard symplectic form. We also
compute the Calabi invariant for some diffeomorphisms of the disk which
satisfies some rigidity hypothesis.
