Based on the second order differential equation which describes the radial and azimuthal electric field components, the characteristics of eigen mode field of simple cylindrical polarized beam are analyzed. According to the formulae of coordinate transformation, the Rayleigh-Sommerfeld scalar diffraction integral formula is converted into a calculation formula for the radial and azimuthal electric field components of far field diffraction of the simple cylindrical polarized beam. As the relationship between the spatial frequency spectrum and electric field distribution of the diffraction source is employed, a calculation formula for the spot radius and spatial frequency radius by the differential operator method is suggested. It can be used to calculate the beam propagation factor of the cylindrical polarized beam. Then, the practical applicability of the above formulae is clearly shown through the beam parameters calculation of the LG10 mode cylindrical polarized Laguerre-Gaussian beam.