Fractal theory is usually used to investigate the topography of machined surfaces, but the relationship between fractal dimensions and wear rate is less studied. A contribution in this field is proposed with wear tests performed on the AISI 1046 steel after the grinding by use of the P80, P180 and P320 abrasive sheets. A 3D fractal study of the worn surfaces is carried out by using power spectral density (PSD) in order to examine the relationship between rate of wear and its 3D fractal dimension. The 3D fractal analysis of the worn surfaces showed that higher values of fractal dimensions indicate a larger real contact area and therefore a better wear resistance of the AISI 1046 steel.