Fluxon-antifluxon annihilation in the perturbed sine-Gordon equation with loss and driving terms is investigated. For the infinite line we find a simple analytic expression for the threshold driving term corresponding to annihilation. With the application of the results to a Josephson junction of finite length an expression for the current voltage characteristic of a zero-field step is derived. The analytical results are in good agreement with numerical simulations. The method is extendable to other systems.