Estimation methods for the longest Rouse relaxation time (tau (R)) of an entangled polymer in a semidilute solution were examined. We evaluated tau (R) by fitting the dynamic modulus (G') with the Rouse model theory in the power law range, where G' was proportional to the square root of the angular frequency (omega). The tau (R) values thus obtained for polystyrene (PS) solutions in tricresyl phosphate (TCP) were employed to derive an empirical formula for the evaluation of tau (R) from the viscosity (eta): tau (R eta) = 6M eta/pi (2)cRT(1.5M(e)/M)(2.4). M is the molecular weight, and c is the mass of polymer per unit volume; M-e = cRT/G(N) is the entanglement molecular weight, where G(N) is the G' value at the inflection point of the graph of log G' versus log omega. The subscript eta indicates that tau (R) is derived from eta data. The proposed equation was also applicable to bulk PS and bulk polyisoprene. Discrepancies among reported tau (R) values in semidilute solutions seem to be mostly due to discrepancies in M, values. For PS solutions in dioctyl phthalate, a Theta solvent, the tau (R) value derived from eta was much larger than that from the G' curve. Apart from the evaluation method of tau (R), we observed for PS that M-e was independent of temperature for good solvent systems and melts, that M-e for solutions in TCP agreed with that for solutions in another good solvent, and that M-e for a Theta -solvent system was equal to that for good solvent systems with the same M and c values.