Work out zigbee mesh node count instantly with clear inputs, formula shown and shareable results.
Node count is coverage area divided by the effective area each node serves, which is its circular range reduced by the overlap needed for mesh redundancy. Routers must be mains powered since they cannot sleep, so the router-to-end-device split drives the installation cost.
Mesh sizing
coverage per node = pi r^2 x (1 - overlap); nodes = ceil(area / coverage per node)
Mesh routing needs at least two paths from every node, and real coverage is never circular. 25-40% overlap is normal for a reliable mesh.
They must keep their radio on to forward traffic for others. Only end devices can sleep, which is why battery nodes are always leaves in the topology.