Interactions between the carbon cycle, climate and human societies are subject to several major vulnerabilities, broadly defined as factors contributing to the risk of harm from human-induced climate change. We assess five vulnerabilities: (1) effects of increasing CO2 on the partition of anthropogenic carbon between atmospheric, land and ocean reservoirs; (2) effects of climate change (quantified by temperature) on CO2 fluxes; (3) uncertainty in climate sensitivity; (4) non-CO2 radiative forcing and (5) anthropogenic CO2 emissions. Our analysis uses a physically based expression for Tp(Qp), the peak warming Tp associated with a cumulative anthropogenic CO2 emission Qp to the time of peak warming. The approximations in this expression are evaluated using a non-linear box model of the carbon–climate system, forced with capped emissions trajectories described by an analytic form satisfying integral and smoothness constraints. The first four vulnerabilities appear as parameters that influence Tp(Qp), whereas the last appears through the independent variable. In terms of likely implications for Tp(Qp), the decreasing order of the first four vulnerabilities is: uncertainties in climate sensitivity, effects of non-CO2 radiative forcing, effects of climate change on CO2 fluxes and effects of increasing CO2 on the partition of anthropogenic carbon.