Abstract: The computing of the area covered by N circles placed randomly on a plane is called the computing of the area of the union of circular arcs. It is not only practical but also an important algorithm in Computational geometry, CAD/CAM and Computer graphics. Giving the formula for the computing of polygon area and central angle with constrain arc, based on the computing of intersection of arcs and polygon area and sector area, this paper proposed a new algorithm for computing the area of the union of circular arcs dynamically. This algorithm is characterized by its high speed and high accuracy. The computational time is not affected by the accuracy required and the size of the circle. It can be applied to all the cases for the computing of the area of the union of circular arcs and can be used widely with its user friendly interface.