Abstract. It is known that the ionospheric cross polar cap potential (CPCP) saturates when the interplanetary magnetic field (IMF) B_z becomes very large. Few studies have offered physical explanations as to why the polar cap potential saturates. We present 13 events in which the reconnection electric field (REF) goes above 12mV/m at some time. When these events are examined as typically done in previous studies, all of them show some signs of saturation (i.e., over-prediction of the CPCP based on a linear relationship between the IMF and the CPCP). We show that by taking into account the size of the magnetosphere and the fact that the post-shock magnetic field strength is strongly dependent upon the solar wind Mach number, we can better specify the ionospheric CPCP. The CPCP (Φ) can be expressed as Φ=(10^-4v²+11.7B(1-e^-M_a/3)sin³(θ/2)) {r_ms/9 (where v is the solar wind velocity, B is the combined Y and Z components of the interplanetary magnetic field, M_a is the solar wind Mach number, θ=acos(B_z/B), and r_ms is the stand-off distance to the magnetopause, assuming pressure-balance between the solar wind and the magnetosphere). This is a simple modification of the original Boyle et al. (1997) formulation.