We have transformed the Stokes equation to equations written in the polarization ellipse parameters. Since the transformed Stokes equations directly describe change in each polarization ellipse parameter, they enable us to easily and comprehensively understand change in the polarization ellipse in a plasma. We have obtained highly accurate approximate solutions of the transformed Stokes equation in order to connect the measured polarization state to the plasma parameters (the electron density and the magnetic field) in a short CPU time. We have compared our solutions and the other approximate solutions proposed by previous studies. Only our solutions have shown good agreement between the polarization parameters and the line-integrated plasma parameters. The errors of our solutions are less than 2% of the domain of each polarization parameter up to the high electron density (∼7 × 1020 m−3) and the long laser wavelength (∼170 µm). The CPU time of our solutions is 10 times shorter than that of the Stokes equation.