A numerical full wave analysis is used to determine the spatial variation of electromagnetic fields of a radio wave in a stratified ionosphere. It is shown that the Faraday rotation may be accumulated as the analysis proceeds by breaking the electric field into constituent characteristic modes and accumulating phase. This has been achieved for vertical, oblique, reflective, and transionospheric propagation. Comparison of the full wave analysis with simpler methods of calculating the rotation, such as ray tracing and very high frequency approximations, permits the determination of the conditions under which these simpler methods break down. It is found that ray tracing agrees very closely with the full wave analysis in most situations and always so for transionospheric propagation. Some discrepancy between these methods appears when reflecting from severe vertical gradients where the full wave analysis is known to be required in accurately estimating the transmission coefficients. For reflective propagation at oblique incidence, small departures in the methods are also evident. Both methods converge to the high-frequency approximation as the radio frequency increases above the peak plasma frequency.