AbstractWe present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively and are shown to be identical in dimensiond ≥ 2, albeit with pronounced finite size effects at the critical dimension,d = 2. A symmetry of the problem reveals that dimensiondand 4 − dare equivalent, thus the celebrated Airy distribution describing the areal distribution of thed = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimensiondwe find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimensiond = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.