Computation of combustion, in particular of emissions over crank angle, relies on chemical oriented models. In some cases, chemical equilibrium can be assumed, as chemical reaction time scales tend to be fast compared to the crank rotation, so the rather complex reaction kinetics can be neglected. For engine process calculation based on the measured cylinder pressure chemical equilibrium concentrations are needed for every crank angle or calculation time step. On the one hand the equilibrium concentrations are necessary for estimating the thermodynamic properties of the working gas (internal energy and specific gas constant) which are needed for deriving the energy release (burn rate) and on the other hand the obtained concentrations are inputs for crank angle based soot and nitric oxygen emission models which depends also on the engine process calculation results. For a common accurate 11 component equilibrium calculation a nonlinear equation system must be solved with an iterative method. To reduce calculation complexity a new explicit method is described in the paper which is especially designed for the typical range of a common Diesel. The main benefit is that it does not need initial values and iteration. Additionally new explicit descriptions for the thermodynamic properties are presented. The development process for both approaches was supported by data based identification methods. Several validation examples are shown to estimate the deviation of the new approaches for chemical equilibrium species and the gas properties compared to the more complicated standard methods in a practical use. In particular the importance of the achieved species accuracy on soot dynamics and nitric oxygen calculation based on published 1- and 2-zone models is presented in detail.