Functions describing simple models for solid-state reaction kinetics under isothermal conditions were transformed in order to obtain new functions with improved properties suitable for kinetic analysis. The transformations were performed trough multiplying well known functions as Johnson-Mehl-Avrami or Jander's with assisting functions. In such manner, new functions, Phi, were obtained enabling calculation of kinetic parameters in a simple way. The relationships between the values of the extremes of Phi functions and various kinetic parameters have been established. The calculation of kinetic parameters by application of new equations have been demonstrated on six model systems. Very good agreement between preset and calculated parameters for each model system has been observed. Using the same approach, the rate-determining step, i.e. the reaction model, and proper kinetic equation could also be determined.