Using high-resolution synchrotron powder x-ray diffraction, we have investigated the stability and equation of state ͑EOS͒ of hafnia HfO 2 phases under high pressures before and after laser heating to high temperatures. We observe three phases with increasing pressure: baddeleyite ͑monoclinic, MI͒, orthorhombic I ͑OI͒, and cotunnite ͑orthorhombic, OII͒. The OII phase is stable up to a pressure of at least 105 GPa before and after laser heating to ϳ1800 ͑Ϯ200͒ K. We provide experimental EOSs for the observed phases. The present results for MI-HfO 2 EOS are distinct from previous measurements yielding an ambient-pressure volume ͑V 0 ͒ of 34.50 ͑Ϯ0.04͒ Å 3 / f.u. and an ambient-pressure bulk modulus K 0 of 185 ͑Ϯ23͒ GPa, assuming K 0 Ј=4. In contrast, the experimental EOSs of OI and OII are in good agreement with previous studies. The measured EOSs are consistent with our density-functional theory calculations. The large volume decrease across the OI→ OII phase transition as obtained from both our experiments and calculations is ϳ9%. Despite the large increase in density and high bulk modulus of OII-HfO 2 , we find, using scaling relations, that all HfO 2 phases show similar mechanical hardness ͑H͒ of ϳ10-12 GPa, too low for HfO 2 to be considered a superhard material.