We present a new method for estimating the composition of water-bearing primary arc basalt and its source mantle conditions. The PRIMACALC2 model uses a thermodynamic fractional crystallization model COMAGMAT3.72 and runs with an Excel macro to examine the mantle equilibrium and trace element calculations of a primary basalt. COMAGMAT3.72 calculates magma fractionation in 0–10 kb at various compositions, pressure, oxygen fugacity, and water content, but is only applicable for forward calculations. PRIMACALC2 first calculates the provisional composition of a primary basalt from an observed magma. The basalt composition is then calculated by COMAGMAT3.72 for crystallization. Differences in elemental concentrations between observed and the closest-match calculated magmas are then adjusted in the primary basalt. Further iteration continues until the calculated magma composition converges with the observed magma, resulting in the primary basalt composition. Once the fitting is satisfied, back calculations of trace elements are made using stepwise addition of fractionated minerals. Mantle equilibrium of the primary basalt is tested using the Fo-NiO relationship of olivine in equilibrium with the primary basalt, and thus with the source mantle. Source mantle pressure, temperature, and degree of melting are estimated using petrogenetic grids based on experimental data obtained in anhydrous systems. Mantle melting temperature in a hydrous system is computed by adjusting T with a parameterization for a water-bearing system. PRIMACALC2 can be used either in dry or water-bearing arc magmas and is also applicable to mid-ocean ridge basalts and nonalkalic ocean island basalts.