One of the major uncertainties in our ability to predict future climate change, and hence its impacts, is our lack of knowledge of the Earth's climate sensitivity. A significant part of this uncertainty is due to different cloud feedbacks between models, although differences in other feedbacks, such as water vapour, also play a role. Recently there have been several efforts to try and narrow this range using a combination of observations and climate model data; however, the large uncertainties in climate sensitivity have, if anything, increased. In particular, it has proved extremely difficult to rule out very high values of climate sensitivity using observations. Here, following on from ideas of Manabe, we combine data from the 1985-1996 Earth Radiation Budget Experiment (ERBE) with surface temperature change information and estimates of radiative forcing to diagnose the climate sensitivity. Importantly our estimate is completely independent of climate model results. We find a climate sensitivity of 2.3+-1.3Wm-2K-1, which corresponds to a 1.0-3.6 K range for the equilibrium warming due to a doubling of carbon dioxide. We present an argument that this value is likely to be representative of longer-term climate change. Further, we are able to use our methodology to: 1) retrieve shortwave and longwave components of climate feedback; and 2) suggest clear-sky and cloud feedback terms. Comparing climate models to these results will provide an important test of their feedback mechanisms.