We correlate the experimentally measured fracture toughness of 24 metals and ceramics to their quantum mechanically calculated brittleness parameter. The brittleness parameter is defined as the ratio of the elastic energy density needed to spontaneously break bonds in shear versus in tension, and is a primitive-cell property. Under 300 GPa hydrostatic pressure, the model predicts that diamond has smaller brittleness than molybdenum at zero pressure, and thus should deform plastically without cracking at room temperature.