In his thesis, Kevin Walker extends the invariant defined by A. Casson for homology $3$-spheres to rational homology spheres ($3$-manifolds with the same rational homology as $S^3$). The modification of Walker's invariant after a surgery on a single knot which transforms a rational homology sphere to another rational homology sphere is given by a Surgery Formula (see paragraph 0). In this paper, we describe a simple and programmable process to calculate Walker's invariant of a rational homology sphere given by one of its surgery diagrams. (We call a surgery diagram a regular projection of a link, each component of which is framed by a rational number ; we use Rolfsen's conventions to define the manifold presented by such a diagram (see [R], p. 259–260)). The first section shows how to modify the diagram in a simple way so that the computation reduces to a finite sequence of applications of the Surgery Formula. The second section is devoted to describe elementary methods to do it. Section 0 states a few results of Walker.