Global climate models are susceptible to drift, causing spurious trends in output variables. Drift is often corrected using data from a control simulation. However, internal climate variability within the control simulation introduces uncertainty to the drift correction process. To quantify this drift uncertainty, we develop a probabilistic technique: Monte Carlo drift correction (MCDC). MCDC samples the standard error associated with drift in the control time series. We apply MCDC to an ensemble of global climate models from the Coupled Model Intercomparison Project Phase 6 (CMIP6). We find that drift correction partially addresses a problem related to drift: energy leakage. Nevertheless, the energy balance of several models remains suspect. We quantify the drift uncertainty of global quantities associated with the Earth's energy balance and thermal expansion of the ocean. When correcting drift in a cumulatively integrated energy flux, we find that it is preferable to integrate the flux before correcting the drift: An alternative method would be to correct the bias before integrating the flux, but this alternative method amplifies the drift uncertainty. Assuming that drift is linear likely leads to an underestimation of drift uncertainty. Time series with weak trends may be especially susceptible to drift uncertainty: for historical thermosteric sea level rise since the 1850s, the drift uncertainty can range from 3 to 24 mm, which is of comparable magnitude to the impact of omitting volcanic forcing in control simulations. Derived coefficients-such as the ocean's expansion efficiency of heat-can also be susceptible to drift uncertainty. When evaluating and analysing global climate model data that are susceptible to drift, researchers should consider drift uncertainty.@en