What are the prospects for using population policy as tool to reduce carbon emissions? In this paper, we review evidence from population science, in order to inform debates in population ethics that, so far, have largely taken place within the academic philosophy literature. In particular, we ask whether fertility policy is likely to have a large effect on carbon emissions, and therefore on temperature change. Our answer is no. Prospects for a policy of fertility-reduction-as-climate-mitigation are limited by population momentum, a demographic factor that limits possible variation in the size of the population, even if fertility rates change very quickly. In particular, a hypothetical policy that instantaneously changed fertility and mortality rates to replacement levels would nevertheless result in a population of over 9 billion people in 2060. We use a leading climate-economy model to project the consequence of such a hypothetical policy for climate change. As a standalone mitigation policy, such a hypothetical change in the size of the future population - much too large to be implementable by any foreseeable government program - would reduce peak temperature change only to 6.4°C, relative to 7.1°C under the most likely population path. Therefore, fertility reduction is unlikely to be an adequate core approach to climate mitigation.