Let M be a compact Hamiltonian T-space (where T is a compact torus) with isolated fixed points. Let u be a moment map for M. Then the image u(M) is a convex polytope. I will discuss how to obtain geometric data from the image of the moment map using a formula due to L. Jeffrey and F. Kirwan called the Residue Formula. I will present the abelian version of this formula and show how it can be used to distinguish chambers of the moment map polytope (joint work by myself, T. Holm and L. Jeffrey). I will also discuss why these techniques suggest that other questions about the "calculus" of equivariant cohomology for Hamiltonian T- spaces may be addressed using similar methods. Time permitting, I will dicuss how the same methods can be applied to find the volume of the symplectic reduction by a diagonal torus of a product of toric varieties. In fact, I conjecture that these techniques can be used to integrate any cohomology class on the reduction of a product of any compact Hamiltonian T-spaces. This last topic is work in progress.