A new concept, the strength of bond, and a new form expressing the hardness of covalent and ionic crystals are presented. Hardness is expressed by means of quantities inherently coupled to the atomistic structure of matter, and, therefore, hardness can be determined by first-principles calculations. Good agreement between theory and experiment is observed in the range of 2 orders of magnitude. It is shown that a lower coordination number of atoms results in higher hardness, contrary to common opinion presented in general literature.