In wireless sensor networks

to extend the network lifetime by reducing energy consumption is one of the most challenging problems.Through network clustering and cluster head cycling

LEACH routing protocol can balance network energy’s load to reduce energy consumption.The key of this protocol is the selection of the number of cluster head.The optimal value of the number of cluster head can minimize the network energy consumption.On the basis of in-depth study of LEACH protocol and its energy model

an estimation algorithm of the optimal number of cluster heads is presented

and the correctness of this algorithm is verified through Monte Carlo simulation.The conclusions can be used to guide the design of the architecture and the routing protocol for wireless sensor networks.