In terms of measuring the fall-off fragments of the built-up edges on the finished surface during orthogonal cutting, it is shown to be capable of estimating the turning surface roughness. The distributions of the over cuts by the built-up edges on the orthogonal cutting consist with the Weibull distribution, and provide information on the mechanism of the formation process of the finished surface during three dimensional cutting. The actual depth of cut is varied by the position at the turning tool edge, therefore, the results indicate that maximum height (Rmax) of surface roughnesses on the turning are assessed from integration of over cuts on the orthogonal cutting.