A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at ‘quantized’ stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, β-SiC nanorods, α-Si3N4 whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agre...