The diopter power and magnification matrices characterize the first-order properties of ophthalmic lenses for different gaze directions. Therefore an efficient method to compute them is highly valuable in ophthalmic lens design and optical performance simulations. I present a novel method to numerically compute these matrices in ophthalmic lenses comprising any set of arbitrary surfaces. The method is based on computing one base ray, along the gaze direction, and two rays close to it. These two rays are obtained varying a small parameter that indicates their separation from the base ray. The method was validated comparing the results with a single refractive surface where exact solutions are directly obtained.