The Southern Ocean is the largest sink of anthropogenic carbon in the present-day climate. Here, Southern Ocean š¯‘¯CO2 and its dependence on wind forcing are investigated using an equilibrium mixed layer carbon budget. This budget is used to derive an expression for Southern Ocean š¯‘¯CO2 sensitivity to wind stress. Southern Ocean š¯‘¯CO2 is found to vary as the square root of area-mean wind stress, arising from the dominance of vertical mixing over other processes such as lateral Ekman transport. The expression for p\hbox {CO}_{2} is validated using idealised coarse-resolution ocean numerical experiments. Additionally, we show that increased (decreased) stratification through surface warming reduces (increases) the sensitivity of the Southern Ocean š¯‘¯CO2 to wind stress. The scaling is then used to estimate the wind-stress induced changes of atmospheric š¯‘¯CO2 in CMIP5 models using only a handful of parameters. The scaling is further used to model the anthropogenic carbon sink, showing a long-term reversal of the Southern Ocean sink for large wind stress strength.