A model based on a thermodynamic framework for CO2 concentrations and speciation in natural silicate melts at graphite/diamond-saturated to fluid-saturated conditions is presented. The model is simultaneously calibrated with graphite-saturated and fluid-saturated conditions allowing for consistent model predictions across the CCO buffer. The model was calibrated using water-poor (≤1 wt% H2O) silicate melts from graphite- to CO2-fluid-saturation over a range of pressure (P = 0.05–3 GPa), temperature (T = 950–1600 °C), composition (foidite-rhyolite; NBO = 0.02–0.92; wt% SiO2 ~ 39–77, TiO2 ~ 0.1–5.8, Al2O3 ~ 7.5–18, FeO ~ 0.2–24 MgO ~ 0.1–24, CaO ~ 0.3–14, Na2O~1-5, K2O ~ 0–6), and fO2 (~QFM +1.5 to ~QFM −6). The model can predict CO2 concentrations for a wide range of silicate melt compositions from ultramafic to rhyolitic compositions, i.e., melts that dissolve carbon only as carbonate anions CO32– and those that dissolve carbon both as CO32– and as molecular CO2mol as a function of pressure, temperature, and oxygen fugacity. The model also does a reasonable job in capturing CO2 solubility in hydrous silicate melts with ≤2–3 wt% H2O. New CO2 solubility experiments at pressures >3 GPa suggest that the newly developed CO2 solubility model can be satisfactorily extrapolated to ~4–5 GPa. Above 5 GPa the model poorly reproduces experimental data, likely owing to structural change in silicate melt at pressures above 5 GPa. An Excel spreadsheet and a Matlab function are provided as online supplementary materials for implementing the new CO2 solubility model presented here.