abstract: It has been observed in the last years that one dimensional scalar conservation laws enjoy some contraction properties in Monge-Kantorovich (Wasserstein) distances. (See recent papers by Bolley-Brenier-Loeper and Carrillo-Di Francesco-Lattanzio.) We show that this is a general feature of multidimensional scalar conservation laws and introduce a related L2 formulation that completely recover Kruzhkov's entropy solutions.