Although 97% of experts generally agree that modern global warming is largely caused by human activities, some people hold biased, inaccurate beliefs about the causes of climate change and the strength of the scientific consensus. Numeracy skills, which are among the strongest predictors of decision making quality and risk literacy (i.e., the ability to evaluate and understand risk), theoretically should help reduce climate-related biases and polarization. However, some studies suggest that numeracy may ironically be associated with small yet significant increases in belief biases among people who strongly identify with specific cultural worldviews. While suggestive, these studies have not assessed the potential confounds associated with differences in knowledge. Accordingly, this paper presents the first two studies to address previous limits and test a cognitive model of the structural relations among numeracy, worldviews, knowledge, beliefs, and climate risk perceptions. Converging results from Study 1 (i.e., probabilistically representative national sample, n = 305) and Study 2 (i.e., diverse adult U.S. residents, n = 537) revealed that numeracy is generally associated with robust direct and indirect positive predictive links with climate change knowledge, beliefs, and risk attitudes. On average, highly numerate people were about 4 times more likely than less numerate people to have accurate knowledge and beliefs, and about 3 times more likely to express above average relative risk concerns. Numeracy’s protective influence was fully mediated by differences in knowledge, which was by far the strongest predictor of accurate beliefs and risks attitudes (e.g., 5-40 times stronger association with knowledge than cultural worldviews). Biases associated with cultural worldviews were also found to be largely but not entirely mediated by differences in knowledge (e.g., individualists tended to be less knowledgeable than egalitarians). Overall, findings are consistent with mechanisms described in Skilled Decision Theory and highlight the robust link between numeracy skills (e.g., risk literacy) and acquisition of accurate knowledge and beliefs (e.g., representative understanding) that tends to protect against cognitive vulnerability and judgment biases. Discussion also considers implications of the lack of interactions on attitude polarization, and the need for integrated modeling of cognitive skills and knowledge as a routine part of the development of accurate and transparent risk and science communication.