Carbonate melts are important active metasomatic agents and efficient transport agents; their thermodynamic properties at high temperatures and pressures are therefore of considerable interest for various geochemica applications. However, due to the extreme challenges in relevant experiments, current knowledge of even the density of carbonate melts is limited. In this study, we provide high quality volumetric data of Ca CO3-melt from firs principles at high temperatures and pressures(up to3,500 K and 60 GPa). The accuracy of these data is demonstrated through comprehensive comparison with available experimental data and a thorough discussion of the predictability of the re-scaling method proposed in this study. Based on the simulations, an equation of state has been established that is critical to relevant highly disputed questions such as the decomposition and solidification boundaries of Ca CO3 melts, the latter of which is briefly discussed in this study with a newly derived ab initio melting curve to high pressures.