The authors use FUND 3.9 to estimate the social cost of four greenhouse gases—carbon dioxide, methane, nitrous oxide, and sulphur hexafluoride—with sensitivity tests for carbon dioxide fertilization, terrestrial feedbacks, climate sensitivity, discounting, equity weighting, and socioeconomic and emissions assumptions. They also estimate the global damage potential for each gas—the ratio of the social cost of the non-carbon dioxide greenhouse gas to the social cost of carbon dioxide. For all gases, they find the social costs and damage potentials sensitive to alternative assumptions. The global damage potentials are compared to global warming potentials (GWPs), a key metric used to compare gases. The authors find that global damage potentials are higher than GWPs in nearly all sensitivities. This finding suggests that previous papers using GWPs may be underestimating the relative importance of reducing non-carbon dioxide greenhouse gas emissions from a climate damage perspective. Of particular interest is the sensitivity of results to carbon dioxide fertilization, which notably reduces the social cost of carbon dioxide, but only has a small effect on the other gases. As a result, the global damage potentials for methane and nitrous oxide are much higher with carbon dioxide fertilization included, and higher than many previous estimates.