We prepared five pairs of hydrogenous and deuterated ring polystyrene samples over a wide range of molecular weights (10 kg/mol < M-w < 400 kg/mol) and investigated their chain conformations in bulk by small-angle neutron scattering (SANS) measurements. From the SANS profiles obtained, we estimated the radii of gyration R-g of the ring polymers by the Guinier approximation. R-g can be related to the degree of polymerization N as R-g similar to N-0.47. This scaling exponent v = 0.47 +/- 0.01 is evidently smaller than that for the Gaussian chains (v = 0.50) but higher than previous experimental reports (v = 0.42-0.43). Then our data were compared with various simulation and experimental data by introducing the entanglement degree of polymerization Ne for linear polymers as a normalized parameter. R-g of three smaller rings, i.e., R-10, R-30, and R-70, where the numbers denote molecular weights in kg/mol unit, are in good agreement with simulation results, while two larger rings, R-100 and R-400, exhibit higher R-g values than the simulations. Considering that the latter two higher molecular weight samples include maximum 3% of linear contamination, their effects on chain dimension were calculated. As a result, it has been confirmed that 3% of linear contaminations can overestimate R-g of rings as much as 6% for R-100 and 12% for R-400. Thus, R-g for pure large rings should be considerably lower than the present experimental values. We conclude Flory's exponent v in R-g similar to N-v for rings may not be constant but rather show molecular weight dependence due to their topological constraint.