The goal of this work is to understand how the phase diagram (PHAD) of the platinum-palladium (Pt-Pd) alloy changes with size and shape and how it correlates with catalytic properties. By using nano-thermodynamics, the size and shape effects on the PHAD of Pt-Pd nanoparticles were determined theoretically. The PHAD of some nanoparticles (sphere, tetrahedron, octahedron, decahedron, cube, cuboctahedron and rhombic dodecahedron) exhibits a congruent melting point that becomes more and more pronounced when the size decreases. At the right of the congruent melting point i.e. close to the Pt-rich side, the coexistence region exhibits a contraction while an expansion is noticed at larger palladium concentrations. From the Gibbs free energy analysis, the stability of all the considered shapes has been determined versus temperature and composition. Furthermore, the surface segregation was also calculated and it is shown that the surface segregation is reversed at very small sizes. Indeed, below a critical size, Pd does not segregate anymore at the surface like it normally does for larger nanoparticles; but Pt does. The critical size range has been determined for each considered shape; and within this range Pt and Pd co-exist at the surface. Finally, the most catalytically active shapes are predicted to be the tetrahedron and the cube in agreement with the available experimental data and other theoretical results.