We have developed a general semiempirical total reaction cross section formula for proton-nucleus reactions. It is applicable for all materials with nuclear charge Z greater than 5, and all proton kinetic energies from the lowest measured energies up to \ensuremath{\approxeq}20 GeV. While the regime of applicability is greatly enlarged, agreement between the calculated cross sections and the experimental data is comparable to or better than all earlier published results in their regime of applicability. \textcopyright{} 1996 The American Physical Society.