Pressure needed to compress iron to double the density? What is the pressure needed to compress iron to twice its density? (with "its density" meaning solid iron at room temperature and atmospheric pressure, reference 7.874 g/cm³ from Google. )
 A: According to PRL, v.88 (2002), 235502-1, the required pressure is 10-20Mbar (see their Fig. 4). They used laser-driven shock waves. 
A: It is difficult to calculate such properties accurately.  The standard technique is density functional theory, which is as much an art of approximation as science.  I am not qualified to speak to experimental techniques involving sudden compression, but they are of obvious interest to designers of nuclear weapons.
Geophysical models are informative because they can to some extent be validated by seismology.  Even the huge pressure at the center of the Earth is not quite enough to double the density.  The density there is estimated at 13.1 g/cm³, the pressure 364 GPa, and the bulk modulus 1425 GPa.  
A fit to data over the limited range of densities (only 2.5%) and pressures (10%) in the inner core suggests that the bulk modulus varies as $K\propto {{P}^{0.60}}$.   Using $dP=K\ d(\ln \rho )$ to extrapolate 20% in density, you might estimate P = 810 GPa when $\rho $ = 15.75 g/cm3.  
Caveat:  The extrapolation is clearly far out on a limb and shouldn't be trusted.  Naive power-law extrapolations are shaky.  $P\sim {{\rho }^{x}}$ would obviously break down at low pressure.  
