The international system of units will be redefined in terms of fundamental constants in 2018, specially the kilogram which is still defined, nowadays, by a material artefact. For many years, two experiments have been carried out to define the kilogram based on an atomic or a fundamental physical constant: the X-ray crystal density (XRCD) methods to determine the Avogadro constant (N_A) and the watt balance to determine the Planck constant (h). Both constants can be compared using other fundamental constants issued from atomic physics. An overview of the determinations of these fundamental constants from atomic physics, since 1998, is given. Their contributions to the accuracy of the comparison between the two methods will be underlined. The consequences of an eventual evolution of their estimates will be also considered.