The frictional force F-f was determined on different materials as a function of the loading force F-n by means of friction force spectroscopy. Specially prepared tips with spherical tip ends and a variety of tip radii between approximate to 10-100 nm were employed. For this type of tip, a mathematical description of F-f(F-n) can be found. Comparison of theory and experiment at the example of amorphous carbon shows good agreement.