Size (displacement) frequencies of 10 fault populations follow a power-law associated with cut-off in the range smaller than a characteristic size. They are depicted by five geometrical parameters of fault population; cut-off size, sharpness of cut-off, fault number density, fault displacement density and the power-law exponent. The former three are rock properties related to dissipative energy density and constitute the similarity law of the size frequency. The fault displacement density is a measure of total input energy density. The power-law exponent decreases as the -1/4 power of total input energy density normalized by dissipative energy density. ¿ 1998 American Geophysical Union