We define the concept of the moral cost of carbon (MCC): the internal carbon price individuals implicitly apply to their consumption decisions. We argue that the MCC is a key metric for policy design. It reveals how much consumers are willing to sacrifice to address the carbon externality. We propose an artefactual experimental design to measure the distribution of the MCC among a target population. We find that the MCC is highly heterogeneous. It follows a bi-modal distribution where it is effectively zero for almost half of the sample. It is also malleable with respect to extrinsic incentives—carbon pricing crowds out the MCC, but only for consumers that are the least morally motivated.