As technology advancing day by day, the data rate of optical network is moving towards Tb/s speed. The minimum capacity utilization and survivability are the crucial requirement in such high speed optical networks. This research work presents a new approach to calculate both working and spare capacity with the help of single mathematical programming model named as joint capacity planning model. The working traffic and restored traffic are routed jointly in proposed joint capacity planning model. Therefore the joint capacity planning model required minimum capacity in as compare to other optimization models. To evaluate our model, three example networks are proposed i.e., network A (6 node), network B (8 node) & National science foundation network (14 node). Results of these networks are analyzed and compared. The capacity utilization is optimized by increasing the backup paths of the optical networks. It has also been proved in this manuscript that capacity requirement is dependent on the backup path. The proposed joint capacity model provides fast restoration speed and guaranteed protection for optical network.