CC bond lengths and diameters of armchair single wall carbon nanotubes from (4,4) to (15,15) have been calculated using semi-empirical PM3 and PM5 and density functional PBEPBE and B3LYP methods. The CC bonds are found to be elongated comparatively to those in graphene sheet, 1.421 angstrom. The bonds directed along the nanotube axis and circumference are elongated differently. The smaller the nanotube index, the larger the bond elongation, but it does not exceed 0.008 angstrom (0.6% of the graphene sheet value) even for the (5,5) nanotube. We suggest new theoretical relationship between the nanotube diameter, indices, and bond lengths. (c) 2005 Elsevier B.V. All rights reserved.