The bulk properties of iron at the pressure and temperature conditions of Earth's core were determined by a method that combines first-principles and classical molecular dynamic simulations. The theory indicates that (i) the iron melting temperature at inner-core boundary (ICB) pressure (330 gigapascals) is 5400 (+/-400) kelvin; (ii) liquid iron at ICB conditions is about 6% denser than Earth's outer core; and (iii) the shear modulus of solid iron close to its melting line is 140 gigapascals, consistent with the seismic value for the inner core. These results reconcile melting temperature estimates based on sound velocity shock wave data with those based on diamond anvil cell experiments.