Global quantification of total RNA is used to investigate steady state levels of gene expression. However, being able to differentiate pre-existing RNA (that has been synthesized prior to a defined point in time) and newly transcribed RNA can provide invaluable information e.g. to estimate RNA half-lives or identify fast and complex regulatory processes. Recently, new techniques based on metabolic labeling and RNA-seq have emerged that allow to quantify new and old RNA: Nucleoside analogs are incorporated into newly transcribed RNA and are made detectable as point mutations in mapped reads. However, relatively infrequent incorporation events and significant sequencing error rates make the differentiation between old and new RNA a highly challenging task. We developed a statistical approach termed GRAND-SLAM that, for the first time, allows to estimate the proportion of old and new RNA in such an experiment. Uncertainty in the estimates is quantified in a Bayesian framework. Simulation experiments show our approach to be unbiased and highly accurate. Furthermore, we analyze how uncertainty in the proportion translates into uncertainty in estimating RNA half-lives and give guidelines for planning experiments. Finally, we demonstrate that our estimates of RNA half-lives compare favorably to other experimental approaches and that biological processes affecting RNA half-lives can be investigated with greater power than offered by any other method. GRAND-SLAM is freely available for non-commercial use at http://software.erhard-lab.de; R scripts to generate all figures are available at zenodo (doi: 10.5281/zenodo.1162340).