We report the results of the first large-scale international survey of public perception of geoengineering and solar radiation management (SRM). Our sample of 3105 individuals in the United States, Canada and the United Kingdom was recruited by survey firms that administer internet surveys to nationally representative population samples. Measured familiarity was higher than expected, with 8% and 45% of the population correctly defining the terms geoengineering and climate engineering respectively. There was strong support for allowing the study of SRM. Support decreased and uncertainty rose as subjects were asked about their support for using SRM immediately, or to stop a climate emergency. Support for SRM is associated with optimism about scientific research, a valuing of SRM's benefits and a stronger belief that SRM is natural, while opposition is associated with an attitude that nature should not be manipulated in this way. The potential risks of SRM are important drivers of public perception with the most salient being damage to the ozone layer and unknown risks. SRM is a new technology and public opinions are just forming; thus all reported results are sensitive to changes in framing, future information on risks and benefits, and changes to context.