To predict the amount of different phases in gray cast iron by a finite difference model(FDM) on the basis of cooling rate(R),the volume fractions of total γ phase,graphite,and cementite were calculated.The results of phase composition were evaluated to find a proper correlation with cooling rate.More trials were carried out to find a good correlation between the hardness and phase composition.New proposed formulas show that the hardness of gray cast iron decreases as the amount of graphite phase increases,and increases as the amount of cementite increases.These formulas are developed to correlate the phase volume fraction to hardness.The results are compared with experimental data and show reasonable agreement. To predict the amount of different phases in gray cast iron by a finite difference model (FDM) on the basis of cooling rate (R), the volume fractions of total γ phase, graphite, and cementite were calculated. The results of phase composition were evaluated to find a proper correlation with cooling rate. More trials between carried out to find a good correlation between the hardness and phase composition. New proposed formulas show that the hardness of gray cast iron decreases as the amount of graphite phase increases, and increases as the amount of cementite increases.These formulas are developed to correlate the phase volume fraction to hardness. The results are compared with experimental data and show reasonable agreement.