The quality of the surfaces is an important characteristic pursued when processing the parts used in the construction of machines. There is a constant search for new, original processing schemes and tools, which lead to the best possible results. For this, the authors have designed an original lathe tool, with inclined tangential cutting edge with adjustable inclination, for which a patent application has been submitted. By using this tool, a large number of tests with representative processing parameters were performed on 42CrMo4QT steel specimens, considering a complete research plan. All tests were performed with the same depth of cut, but different speeds, feed rates and inclination of the cutting edge of the tool. The roughness of the obtained surfaces was measured using a high-performance electronic roughness meter. For comparison, processing under similar conditions was performed using a normal turning tool. The present paper presents a mathematical model for the theoretical roughness in turning with an inclined tangential edge, analyses the influence of the working parameters on the roughness and compares the ideal values with values obtained experimentally.