Iron oxide magnetic nanoparticles (NPs) are stimuli-responsive materials at the forefront of nanomedicine. Their realistic finite temperature simulations are a formidable challenge for first-principles methods... Here, we use density functional tight binding to open up the required time and length scales and obtain global minimum structures of Fe3O4 NPs of realistic size (1400 atoms, 2.5 nm) and of different shapes, which we then refine with hybrid density functional theory methods to accomplish proper electronic and magnetic properties, which have never been accurately described in simulations. On this basis, we develop a general empirical formula and prove its predictive power for the evaluation of the total magnetic moment of Fe3O4 NPs. By converting the total magnetic moment into the macroscopic saturation magnetization, we rationalize the experimentally observed dependence with shape. We also reveal interesting reconstruction mechanisms and unexpected patterns of charge ordering. (read more)