Abstract：The currently used 13 limit equilibrium methods of slices are classified into four types based on the equilibrium conditions. These are type M with only considering moment equilibrium condition about specified center，type VM with considering vertical force equilibrium condition and moment equilibrium condition about specified center，type HV with considering both horizontal and vertical force equilibrium condition，and type HVM with considering horizontal and vertical force equilibrium condition as well as moment equilibrium condition about specified center. Type M, Sweden method，has explicit solution. Type VM, simplified Bishop method, has inexplicit expression for the safety factor whose iteration is not difficult. For the first time，the assumptions regarding the inter-slice force associated with the existing limit equilibrium methods of slices are expressed in the unified formulation. The simple and clear recurrent equations of the inter-slice forces and inter-slice moments are derived based on force equilibrium and moment equilibrium. The unified calculation formulation for the safety factor based on force equilibrium (type HV) in the context of conventional methods of slices is developed based on the recurrent equation of the inter-slice forces which keeps the equilibrium conditions and the assumptions regarding the inter-slice force and unknowns. Based on the recurrent equations of the inter-slice forces and inter-slice moments，the unified calculation formulation for the safety factor based on rigorous equilibrium (type HVM) in the context of conventional methods of slices is developed by Newton-Raphson method. Unified calculation formulation facilitates the development of programming and the comparison among the advantages and disadvantages of different methods.
