A Lambertian surface is a kind of very important assumption in shape from shading (SFS), which is widely used in many measurement cases. In this paper, a novel scaled SFS method is developed to measure the shape of a Lambertian surface with dimensions. In which, a more accurate light source model is investigated under the illumination of a simple point light source, the relationship between surface depth map and the recorded image grayscale is established by introducing the camera matrix into the model. Together with the constraints of brightness, smoothness and integrability, the surface shape with dimensions can be obtained by analyzing only one image using the scaled SFS method. The algorithm simulations show a perfect matching between the simulated structures and the results, the rebuilding root mean square error (RMSE) is below 0.6mm. Further experiment is performed by measuring a PVC tube internal surface, the overall measurement error lies below 2%.