Estimating the cost to society from a ton of CO2-termed the social cost of carbon (SCC)-requires connecting a model of the climate system with a representation of the economic and social effects of changes in climate, and the aggregation of diverse, uncertain impacts across both time and space. A growing literature has examined the effect of fundamental structural elements of the models supporting SCC calculations. This work has accumulated in a piecemeal fashion, leaving their relative importance unclear. Here, we perform a comprehensive synthesis of the evidence on the SCC, combining 1,823 estimates of the SCC from 147 studies with a survey of authors of these studies. The distribution of published 2020 SCC values is wide and substantially right-skewed, showing evidence of a heavy right tail (truncated mean of $132). ANOVA reveals important roles for the inclusion of persistent damages, the representation of the Earth system, and distributional weighting. However, our survey reveals that experts believe the literature underestimates the SCC due to an undersampling of model structures, incomplete characterization of damages, and high discount rates. To address this imbalance, we train a random forest model on variation in the literature and use it to generate a synthetic SCC distribution that more closely matches expert assessments of appropriate model structure and discounting. This synthetic distribution has a mean of $283 per ton CO2 for a 2020 pulse year (5% to 95% range: $32 to $874), higher than most official government estimates, including a 2023 update from the U.S. EPA.