Abstract Compressibility factor (z-factor) of gasses is a thermodynamic property used to account for the deviation of real gas deviation from the ideal gas behavior. The best correlations for this factor given by Hall and Yarborough, Dranchuk & Abou-Kassem and Dranchuk, Purvis & Robinson are based on nonlinear equation of state requiring iterative solution. It is not uncommon for nonlinear equations to have multiple roots, hence, Newton-Raphson often fail to converge or converges on the undesired root of these equations. This unstable behavior of iterative procedure requires that the initial guess is set close to the desired root to ensure convergence. Here we examine the residual equations of the reduced densities of these correlations and set the criteria for the determination of the initial guess as function of the reduced temperature (1.05 ≤ Tpr ≤ 3) and pressure (0.2 ≤ Ppr ≤ 15), we retuned the coefficients using 5940 experimental data points from Handbook of Natural Gas Engineering and also derived the reduced compressibility equation based on these three correlations.