Positronium-formation cross sections from positron-hydrogen collisions are calculated by solving a set of close-coupled, time-dependent partial differential equations. These cross sections are determined by propagating a time-evolving wave packet on a two-dimensional radial lattice and then projecting the wave function onto the stationary states of the atom. Calculations are performed through Lϭ8 and are extrapolated for Lу9 at energies of 30, 40, and 50 eV. Using distorted-wave calculations to determine ionization cross sections at these higher energies, we are able to extract approximate positronium-formation cross sections from the transfer ionization cross sections. Comparisons are made with experiment.