The distribution of gases such as ozone and water vapour in the stratosphere—which affect surface climate—is influenced by the meridional overturning of mass in the stratosphere, the Brewer–Dobson circulation. However, observation-based estimates of the global strength of this circulation are difficult to obtain. Here we present two calculations of the mean strength of the meridional overturning of the stratosphere. We analyse satellite data that document the global diabatic circulation between 2007–2011, and compare these to three reanalysis data sets and to simulations with a state-of-the-art chemistry–climate model. Using measurements of sulfur hexafluoride (SF6) and nitrous oxide, we calculate the global mean diabatic overturning mass flux throughout the stratosphere. In the lower stratosphere, these two estimates agree, and at a potential temperature level of 460 K (about 20 km or 60 hPa in tropics) the global circulation strength is 6.3–7.6 × 10^9 kg/s. Higher in the atmosphere, only the SF6-based estimate is available, and it diverges from the reanalysis data and simulations. Interpretation of the SF6-data-based estimate is limited because of a mesospheric sink of SF6; however, the reanalyses also differ substantially from each other. We conclude that the uncertainty in the mean meridional overturning circulation strength at upper levels of the stratosphere amounts to at least 100%.