This paper presents a method for probabilistic plane fitting and an application to robotic 3D mapping. The plane is fitted in an orthogonal least-square sense and the output complies with the conventions of the Symmetries and Perturbation model (SPmodel). In the second part of the paper, the presented plane fitting method is used within a 3D mapping application. It is shown that by using probabilistic information, high precision 3D maps can be generated