Abstract: "Wireless Sensor Networks (WSNs)" represent a set of sensors spatially deployed assisted by other to sense, monitor or track certain zone. Sensors can communicate with base station either directly or through other nodes. Each sensor has an ability to cover certain area usually represented by a circle. This circle radius is equal to the sensor sensing range and its center is the location (coordinates) of the sensor node. In most WSN applications there are many regions are covered by more than one circle (sensor). Such regions are called overlapping regions. In other words such region will be sense and monitor by more than one sensor. In such case same (redundant) data will be delivered to the base station. But in other application it is required and important to increase the system reliability in preventing intruders. Overlapping has many significant effects on the network behavior metrics. It is so important to estimate and optimize the overlapping regions in the process of planning and deploying any new WSN. These overlapping represent the intersection areas (lens) surrounded by arcs resulted from circles intersections. In this study, a new developed Monte Carlo approach is utilized to estimate all the intersection areas among many circles. A computer simulation technique in Net Logo Software is developed to perform this task. The developed approach is found to be useful in estimating all the not uniform regions in any WSN coverage area in a simple manner. Such calculations represent a challenge in mathematics it shows very near exact calculations.