A new model for the quantitative analysis of Kelvin Probe Force Microscopy (KPFM) measurements of quasi-one-dimensional systems is presented. It is applied to precisely determine the local surface potential (SP) of semiconducting nanofibers of poly (3-hexylthiophene) (P3HT) self-assembled on various flat substrates. To study these quasi-one dimensional objects, the effective area has been defined. This parameter represents the area of sample surface interacting with the KPFM probe and it plays a crucial role in the estimation of the SP of nanofibers having a cross-section comparable to the apical diameter of the tip, i.e., 20 nm. Therefore our model makes it possible to gain quantitative insight into nano-systems smaller than 20 nm. In particular, through the estimation of the effective area, it allows to determine the local surface potential of single nanofiber as well as to simulate the KPFM image of nano-assemblies adsorbed both on electrically insulating and conducting substrates. This versatile model represents a useful tool to study with a high degree of precision the surface potential characteristics of nanowires paving the way towards their use as building blocks for the fabrication of electronic nanodevices with improved performance.