Many works have been devoted to connectivity of wireless sensor networks. This is an important feature for wireless sensor networks (WSNs) to provide the nodes with the capability of communicating with one or several sinks. In most of these works, many theoretical results are based on the perfect geometric disc model are presented, but the numerical simulations only proves the theoretical trend is correct, and a big gap between the theoretical results and numerical simulations exists. To obtain the realistic result, we proposed a modified geometric disc model, which is called the downsizing geometric disc model. In our model, each node is assumed to be connected to each other node in a variable transmission range. Extensive experimental results prove that our method is feasible and leads to a more accurate threshold. In addition, we also can determine the accurate ( )c n in the existing works based on our experimental results.