This work studies both limited sensitivity and nonlinearity of far field RF energy harvesting observed in reality and quantifies their effect, attempting to fill a major hole in the simultaneous wireless information and power transfer (SWIPT) literature. RF harvested power is modeled as an arbitrary nonlinear, continuous, and non-decreasing function of received power, taking into account limited sensitivity and saturation effects. RF harvester's sensitivity may be several dBs worse than communications receiver's sensitivity, potentially rendering RF information signals useless for energy harvesting purposes. Given finite number of datapoint pairs of harvested (output) power and corresponding input power, a piecewise linear approximation is applied and the statistics of the harvested power are offered, as a function of the wireless channel fading statistics. Limited number of datapoints are needed and accuracy analysis is also provided. Case studies include duty-cycled (non-continuous), as well as continuous SWIPT, comparing with industry-level, RF harvesting. The proposed approximation, even though simple, offers accurate performance for all studied metrics. On the other hand, linear models or nonlinear-unlimited sensitivity harvesting models deviate from reality, especially in the low input power regime. The proposed methodology can be utilized in current and future SWIPT research.