Density-functional theory is used to compute the ferromagnetic moment as a function of lattice constant for bcc and fcc Mn. For bcc Mn, a relatively small moment is found in the lattice-constant range 5.20lal6.025 a.u. and a large moment is found in the region ag5.90 a.u., with a discontinuous low-spin to high-spin transition occurring somewhere in the double-moment region 5.90lal6.025 a.u. For fcc Mn, the moment is found to be zero in the range 6.50lal\ensuremath{\sim}7.275 a.u. and large in the region ag\ensuremath{\sim}7.275 a.u., with a discontinuous zero-moment to high-moment transition occurring near a=7.275 a.u. Information obtained from magnetic susceptibility calculations is used to predict the magnetic order of the ground state in some of the lattice-constant ranges considered. The susceptibility calculations indicate that bcc Mn has a ferromagnetic ground state in the range 5.2lal5.4 a.u. and that fcc Mn has an antiferromagnetic ground state in the region ag6.8 a.u.