Climate sensitivity to doubled CO2 is a widely used metric for the large-scale response to external forcing. Climate models predict a wide range for two commonly used definitions: the transient climate response (TCR: the warming after 70 years of CO2 concentrations that rise at 1% per year), and the equilibrium climate sensitivity (ECS: the equilibrium temperature change following a doubling of CO2 concentrations). Many observational data sets have been used to constrain these values, including temperature trends over the recent past, inferences from palaeoclimate and process-based constraints from the modern satellite era. However, as the IPCC recently reported, different classes of observational constraints produce somewhat incongruent ranges. Here we show that climate sensitivity estimates derived from recent observations must account for the efficacy of each forcing active during the historical period. When we use single-forcing experiments to estimate these efficacies and calculate climate sensitivity from the observed twentieth-century warming, our estimates of both TCR and ECS are revised upwards compared to previous studies, improving the consistency with independent constraints.