Low-power wide-area network (LPWAN) technologies are gaining momentum for internet-of-things (IoT) applications since they promise wide coverage to a massive number of battery-operated devices using grant-free medium access. LoRaWAN, with its physical (PHY) layer design and regulatory efforts, has emerged as the widely adopted LPWAN solution. By using chirp spread spectrum modulation with qausi-orthogonal spreading factors (SFs), LoRa PHY offers coverage to wide-area applications while supporting high-density of devices. However, thus far its scalability performance has been inadequately modeled and the effect of interference resulting from the imperfect orthogonality of the SFs has not been considered. In this paper, we present an analytical model of a single-cell LoRa system that accounts for the impact of interference among transmissions over the same SF (co-SF) as well as different SFs (inter-SF). By modeling the interference field as Poisson point process under duty-cycled ALOHA, we derive the signal-to-interference ratio (SIR) distributions for several interference conditions. Results show that, for a duty cycle as low as 0.33%, the network performance under co-SF interference alone is considerably optimistic as the inclusion of inter-SF interference unveils a further drop in the success probability and the coverage probability of approximately 10% and 15%, respectively for 1500 devices in a LoRa channel. Finally, we illustrate how our analysis can characterize the critical device density with respect to cell size for a given reliability target.