Uncertainty estimates on earthquake focal mechanism (FM) data are often simplified to a single, standard error angle or to a qualitative metric because a straightforward way to describe the full, rotational uncertainty in 3D has not existed. We introduce the rotation vector distribution matrix (RVDM), a 3x3 matrix description of FM uncertainty. The RVDM is a multivariate normal probability distribution of rotation vectors that can easily be computed from a representation of the FM posterior probability distribution (PPD), usually obtained via a grid-search or Monte Carlo method. We then investigate how precisely the RVDM describes synthetic FM PPDs, relying only on P-wave first-motion data in this study, and find that it provides significantly better fits compared to those based on simplified metrics. We further examine the impact of propagating the RVDM into synthetic tectonic stress inversions by comparing to inversions that incorporate only a standard (uniform) rotational uncertainty for each FM, as well as inversions that incorporate the full FM PPDs. Finally, we fit RVDMs to Monte Carlo samples of FM PPDs from the Yakutat microplate (Yukon and northeast British Columbia), derived from P-wave first-motions, and invert for tectonic stress, again comparing to uniform and full-PPD FM uncertainty models. The results from both synthetic and real data suggest that using the RVDM model (or retaining the full PPD) in tectonic stress inversions can greatly reduce stress tensor uncertainties when the FMs are poorly constrained, with lessening importance as overall FM uncertainties decrease.