A numerical technique was proposed to plot the Abbott curve and to compute its associated parameters defined by the DIN 4776 and ISO 13565 norms. These parameters were then extended and applied to non-sigmoid Abbott curves. By studying the discretisation errors, we show that a minimum of 200 intercepts, with parabolic interpolations between discretised data profiles, have to be taken into consideration to calculate the parameters as accurately as possible. Experimental profiles were eroded by means of a numerical wear model, and it was shown that the Abbott parameters correlate well with the wear model parameters. Our numerical estimations of Abbott parameters were performed for electro-eroded, tool machined, polished, worn and sandblasted surfaces. Manual measures were compared with our algorithmic method and it was shown that the difference is lower than 1% for Mr1 and Mr2 Abbott parameters, but the numerical technique leads to a lower dispersion.