Differential expression analysis of RNA sequencing (RNA-seq) data can identify changes in cellular RNA levels, but provides limited information about the kinetic mechanisms underlying such changes. Nucleotide-recoding RNA-seq methods (NR-seq; e.g., TimeLapse-seq, SLAM-seq, etc.) address this shortcoming and are widely used approaches to identify changes in RNA synthesis and degradation kinetics. While advanced statistical models implemented in user-friendly software (e.g., DESeq2) have ensured the statistical rigor of differential expression analyses, no such tools that facilitate differential kinetic analysis with NR-seq exist. Here we report the development of Bayesian analysis of the kinetics of RNA (bakR), an R package to address this need. bakR relies on Bayesian hierarchical modeling of NR-seq data to increase statistical power by sharing information across transcripts. Analyses of simulated data confirmed that bakR implementations of the hierarchical model outperform attempts to analyze differential kinetics with existing models. bakR also uncovers biological signals in real NR-seq datasets and provides improved analyses of existing datasets. This work establishes bakR as an important tool for identifying differential RNA synthesis and degradation kinetics.