We derive the optimal differential privacy (DP) parameters of a mechanism\nthat satisfies a given level of R\\'enyi differential privacy (RDP). Our result\nis based on the joint range of two $f$-divergences that underlie the\napproximate and the R\\'enyi variations of differential privacy. We apply our\nresult to the moments accountant framework for characterizing privacy\nguarantees of stochastic gradient descent. When compared to the\nstate-of-the-art, our bounds may lead to about 100 more stochastic gradient\ndescent iterations for training deep learning models for the same privacy\nbudget.\n