Pile-up and dead-time are two main causes of nonlinearity in the response of a PET scanner as a function of activity in the field of view (FOV). For a given scanner and acquisition system, pile-up effects depend on the material and size of the object being imaged and on the distribution of activity inside and outside the FOV, because these factors change the singles-to-coincidences ratio (SCR). Thus, it is difficult to devise an accurate correction that would be valid for any acquisition. In this work, we demonstrate a linear relationship between SCR and effective dead-time, which measures the effects of both dead-time (losses) and pile-up (gains and losses). This relationship allows us to propose a simple method to accurately estimate dead-time and pile-up corrections using only two calibration acquisitions with, respectively, a high and low SCR. The method has been tested with simulations and experimental data for two different scanner geometries: a scanner with large area detectors and no pile-up rejection, and a scanner composed of two full rings of smaller detectors. Our results show that the SCR correction method is accurate within 7%, even for high activities in the FOV, and avoids the bias of the standard single-parameter method.