The natural parameterization of vacuum oscillations in three neutrino flavors is studied. Compact and exact relations of its three parameters with the ordinary three mixing angles and CP-violating phase are obtained. Its usefulness is illustrated by considering various applications: the study of the flavor ratio and of its uncertainties, the comparison of expectations and observations in the flavor triangle, and the intensity of the signal due to Glashow resonance. The results in the literature are easily reproduced and in particular the recently obtained agreement of the observations of IceCube with the hypothesis of cosmic neutrino oscillations is confirmed. It is argued that a Gaussian treatment of the errors appropriately describes the effects of the uncertainties on the neutrino oscillation parameters.