Emerging applications such as connected farms, wildness monitoring, smart cities, and Factory of the Future leverage emerging Low Power Wide Area Networks (LPWAN), allowing a good trade-off between radio range, data rate, and energy consumption. However, only few theoretical studies of these recent technologies are available to help network designers to optimize real field deployments or even achieve real-time adaptation of transmission parameters. A new approach based on Marcum function is proposed in this paper to estimate-in a fast and accurate manner-the performance in terms of Bit Error Rate of LoRa, one of the most used LPWAN technologies. The method is proposed for Gaussian channels, over challenging propagation environments, i.e., Ricean and Nakagami fadings. Simulation results show that our proposed approximation reduces the approximation error about one order of magnitude compared to existing ones and can be computed by classical software. INDEX TERMS Accurate approximation, fading channels, Internet of Things, LoRa performance, low-power wide area networks, Marcum function.