The work presented in this paper examines the effects of cutting parameters (cutting speed, feed rate and depth of cut) onto the surface roughness through the mathematical model developed by using the data gathered from a series of turning experiments performed. An additional investigation was carried out in order to evaluate the influence of two well-known coating layers onto the surface roughness. For this purpose, the experiments were repeated for two CNMG 120408 (with an ISO designation) carbide inserts having completely the same geometry and substrate but different coating layers, in a manner that identical cutting conditions would be ensured. The workpiece material machined was cold-work tool steel AISI P20. Of the two types of inserts employed; Insert 1 possesses a coating consisting of a TiCN underlayer, an intermediate layer of Al2O3 and a TiN outlayer, all deposited by CVD; whilst Insert 2 is PVD coated with a thin TiAlN layer (3 +/- 1 mu m). The total average error of the model was determined to be 4.2% and 5.2% for Insert 1 and Insert 2, respectively; which proves the reliability of the equations established. (C) 2008 Elsevier B.V. All rights reserved.