A new thermodynamic model is presented for calculating phase relations in peridotite, from 0 001 to 60 kbar and from 800 C to liquidus temperatures, in the system NCFMASOCr. This model system is large enough to simulate phase relations and melting of natural peridotite and basaltic liquids. Calculations in the program THERMOCALC illustrate mantle phase relationships and melting conditions, specifically for the peridotite composition KLB-1. The garnet–spinel transition zone intersects the solidus at 21 4–21 7 kbar, where both Fe3þ and Cr increase spinel stability, expanding the width of the transition. Orthopyroxene is lost at the solidus at 42 kbar in KLB-1, although this pressure is very sensitive to bulk composition. Calculated oxidation states are in excellent agreement with measured log fO2 for xenolith suites with mantle Fe2O3 contents in the range 0 1–0 3wt %. It appears that mantle oxidation state is not just a simple function of P and T, but depends on phase assemblage, and may vary in a complex way within a single assemblage. The liquid model performs well, such that calculated solidus, melt productivity and liquid compositions compare favourably with those of experimental studies, permitting its use in interpolating between, and extrapolating from, experimental P–T conditions. Experimentally challenging but geologically useful regimes can be explored, such as subsolidus samples and very low melt fractions, with application to both mantle xenoliths and the origin of basalt.