The relative stability with respect to pressure of four structural polymorphs of Fe 2 O 3 has been studied using the B3LYP hybrid exchange density functional theory, and for each polymorph a range of charge, spin, and magnetic states were examined. It was found that the B3LYP functional computed charge, magnetic ordering, structural, and elastic properties of corundum structure Fe 2 O 3 are in good agreement with experiment. Magnetic ordering was found to be important for all the polymorphs, and for each polymorph antiferromagnetic ordering was found to be lower in energy than ferromagnetic ordering. The Rh 2 O 3 -II structure was calculated to be metastable, with the transition pressure from the corundum structure and the pressure at which magnetic collapse of Fe 3+ cations occur in good agreement with experiment. At high pressures the lowest-energy configuration for the orthorhombic perovskite structure was computed to occur with mixed high-spin/low-spin Fe 3+ cations. The CaIrO 3 -type structure was also computed to be stable with a mixed high-spin/low-spin Fe 3+ configuration at high pressures, and is computed to be the most stable polymorph at pressures above 46 GPa at 0 K. Overall we predict a number of phase-transition pressures which have been experimentally observed and give some insight into the mechanisms underlying the structural transformations.