In this paper, we propose a new framework for the study of cellular networks called the fluid model and we derive from this model analytical formulas for interference, outage probability, and spatial outage probability. The key idea of the fluid model is to consider the discrete base stations (BS) entities as a continuum of transmitters which are spatially distributed in the network. This allows us to obtain simple analytical expressions of the main characteristics of the network. In this paper, we focus on the downlink other-cell interference factor, f, which is defined here as the ratio of outer cell received power to the inner cell received power. Although this factor has been firstly defined for CDMA networks (in particular UMTS and HSDPA), the analysis presented hereafter is still valid for other systems using frequency reuse 1, like OFDMA (WiMAX), TDMA (GSM with frequency hopping), or even ad hoc networks. A closed- form formula of f is provided in this paper. From f, we are able to derive the global outage probability and the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call. All results are compared to Monte Carlo simulations performed in a traditional hexagonal network.