Plain carbon steels and alloy steels have a great application in the manufacturing process especially due to their characteristic of high machinability and low cost. The machining of these materials, the study of the cutting forces, and the power required for the cutting process is one of the most important parameters to be evaluated. The relationship between this parameter and the other cutting variables process is crucial for the optimization of the machining process. The results of this research are empirical expressions, obtained from the cutting parameters (tool nose radius, feed rate and depth of cut) and the influence of these parameters on the cutting forces for each carbon steel studied (AISI 1020, AISI 1045 and AISI 4340), as well as a general expression which includes the mechanical properties of these carbon steels. These results enable the user to predict cutting forces when using a turning process.