Fracture toughness and fracture energy are two key, interrelated, parameters characterising the material resistance-to-failure. Predicting these values from the solid structure at the atomistic scale remains elusive, even in the simplest situations of ideal brittle fracture. By using numerical simulations on scalar lattice models of fracture, we demonstrate that fracture toughness cannot be deduced from Griffith’s specific surface energy, as is generally believed. Rather, it finds its origin in the matching between the continuum displacement field at the engineering scale and the discrete lattice of solids at the atomic scale. The generic asymptotic form taken by this field near crack tip provides a solution for this matching, and subsequently a way to predict toughness from the atomistic parameters. This method is extended to true vectorial elasticity and is used to revisit the fracture toughness/fracture energy values observed in bidimensional crystalline materials like graphene.