Wireless sensor networks play an important role in several industries. Ad-hoc networks with multi-hop transmissions are considered suitable for wireless sensor networks because of their high scalability and low construction cost. However, a lack of centralized control makes it difficult to respond to congestion when system capacity is exceeded. Therefore, the analysis of system capacity is a critical issue for system design. In this paper, we propose a novel zone division model to analyze the capacity of multi-hop wireless sensor networks using carrier sense multiple access with collision avoidance protocols. We divide the one-hop area to a gateway (GW) into two zones: an outer zone, where access nodes (ANs) can relay packets from multi-hop ANs, and an inner zone where ANs cannot relay packets. Using this approach, we calculate the packet loss for each zone to estimate the capacity, considering the difference in the communication range of the GW and ANs, as well as the collision with hidden nodes. Comparisons with simulation results and the conventional method show that our model achieves higher estimation accuracy.