Smart manufacturing is mainly slanted towards high-quality products with maximum productivity and less expense. Surface roughness is one of the quality traits for a product and hence it is very crucial to evaluate for the product quality assurance. A critical research area, the miniaturized mechanical system finds various applications in the industries. This is highly challenging owing to the overwhelming effect of machining parameters at the micro scale regime. This research propositions a mathematical relation and an AI algorithm for the measurement of surface roughness. A novel mathematical relation has been established for surface roughness measurement using geometrical properties of the tool giving more emphasis on the effect of principal cutting-edge angle. Further, a surface roughness measurement algorithm has also been proposed using machine learning method for high-speed micro turning, having training and validation experiments designed by partial factorial for Nimonic 90 alloy. A Gaussian process regression with 5-fold cross validation ANN model was trained for the surface roughness prediction with input parameters namely extracted surface features, machining parameters, vibrational, and force data. The developed model shows a correlation of 78.55% between the predicted and experimental values of surface roughness.