The social cost of carbon – or marginal damage caused by an additional ton of carbon dioxide emissions – has been estimated by a U.S. government working group at $21/tCO2 in 2010. That calculation, however, omits many of the biggest risks associated with climate change, and downplays the impact of current emissions on future generations. Our reanalysis explores the effects of uncertainty about climate sensitivity, the shape of the damage function, and the discount rate. We show that the social cost of carbon is uncertain across a broad range, and could be much higher than $21/tCO2. In our case combining high climate sensitivity, high damages, and a low discount rate, the social cost of carbon could be almost $900/tCO2 in 2010, rising to $1,500/tCO2 in 2050. The most ambitious scenarios for eliminating carbon dioxide emissions as rapidly as technologically feasible (reaching zero or negative net global emissions by the end of this century) require spending up to $150 to $500 per ton of reductions of carbon dioxide emissions by 2050. Using a reasonable set of alternative assumptions, therefore, the damages from a ton of carbon dioxide emissions in 2050 could exceed the cost of reducing emissions at the maximum technically feasible rate. Once this is the case, the exact value of the social cost of carbon loses importance: the clear policy prescription is to reduce emissions as rapidly as possible, and cost-effectiveness analysis offers better insights for climate policy than cost-benefit analysis.