In the context of the ER=EPR conjecture, some examples for the entanglement between scattering particles are discussed in the AdS/CFT correspondence. This motivates us to ask the following question: What is the entanglement of the final state of two outgoing particles in an elastic scattering process in quantum field theory? One can guess interaction generates the entanglement between these particles. We try to answer this primitive question by the use of S-matrix formalism. Firstly the entanglement entropy is calculated in weak coupling perturbation. Next, exploiting the S-matrix formalism non-perturbativelywith partial wave expansion, we incorporate the contribution of inelastic channels into this entanglement entropy. Finally we show the novel formula that describes the entanglement entropy in terms of physical observables, i.e.,cross sections and a maximal impact parameter.