A new Lambert w representation for the surface potential from the PSP MOS model point of view is proposed. The resultant of this methodology is to benefit from merging of PSP model accuracy as a compact model and iterative simplicity of the Lambert W function. This increases the speed and accuracy of the circuit simulators specially for both cases of weak as well as moderate inversion. The suggested approach leans on reformatting the implicit equation of the surface potential in the form of Lambert W representation via a proper mathematical curve fitting. The fitting parameters has been tolerated for wide temperature range of about 350C for each range. This is done through making use of the dominant dependency of the normalized body effect coefficient. The proposed algorithm is validated for a typical 0.18um technology by means of MATLAB 2016 and proves an accuracy of ± 5% to the original PSP model for a temperature range of [-18 o C, 100 o C].