Two distinct theories of the strength of porous solids may be found in the literature, one claiming that the volume of pores dictates strength, the other that the longest pores are crucial because they initiate cracks. Various empirical attempts have previously been made to reconcile these apparently conflicting arguments. This paper shows from first principles, using an energy balance method, that strength must depend on both pore volume and on maximum pore length. The theory was verified by measurements on an ideal porous glass, and was also shown to be useful in describing the behaviour of complex porous materials such as hydraulic cement.