We present a geometric approach to the finite Rational Inattention (RI) model, recasting it as a convex optimization problem with reduced dimensionality that is well suited to numerical methods. We provide an algorithm that outperforms existing RI computation techniques in terms of both speed and accuracy in both static and dynamic RI problems. We further introduce methods to quantify the impact of numerical inaccuracy on the model's outcomes and to produce robust predictions regarding the most frequently implemented actions.