The question of material stability is of fundamental importance to any analysis of system properties in condensed matter physics and materials science. The ability to evaluate chemical stability, i.e., whether a stoichiometry will persist in some chemical environment, and structure selection, i.e. what crystal structure a stoichiometry will adopt, is critical to the prediction of materials synthesis, reactivity and properties. Here, we demonstrate that density functional theory, with the recently developed strongly constrained and appropriately normed (SCAN) functional, has advanced to a point where both facets of the stability problem can be reliably and efficiently predicted for main group compounds, while transition metal compounds are improved but remain a challenge. SCAN therefore offers a robust model for a significant portion of the periodic table, presenting an opportunity for the development of novel materials and the study of fine phase transformations even in largely unexplored systems with little to no experimental data.