Between 14 April and 25 May, 2010, Eyjafjallajökull volcano in Iceland erupted a large amount of fine grained ash. Dispersion models and satellite data were used to identify the location of the ash cloud, but accurate quantitative forecasts of the concentrations could not be made. By using multispectral satellite measurements from the Spin Enhanced Visible and Infrared Imager (SEVIRI), it is shown that quantitative estimates of the mass loadings (g m−2) can be made with a detection limit ∼0.2 g m−2, every 15 minutes. These data represent the most comprehensive coverage, in space and time, of the Eyjafjallajökull ash and its movement. A new ash concentration chart is proposed that removes the ambiguity inherent in assigning high concentrations to highly negative brightness temperature differences. Validation of satellite ash retrievals against measurements from aircraft, ground‐based lidars, and air quality data is presented. The results show a mean bias of −47 μg m−3 and standard deviation of ±154 μg m−3. The satellite ash retrievals are sufficiently accurate for use with dispersion models to constrain ash concentration forecasts. Concentrations in the dense parts of the dispersing ash cloud occasionally exceeded 4 mg m−3 (∼3% of ash‐affected pixels), and ash clouds with concentrations >2 mg m−3 covered large parts of European airspace on several occasions (∼50% of ash‐affected pixels). The statistical analysis leads naturally to a logarithmic scale for assigning ash concentration limits. We suggest that a better approach is to utilize a dosage and illustrate this using a simple model of ash deposition on jet engines. Key Points Quantitative satellite retrievals for volcanic ash are presented and validated A new ash concentration chart is presented A new concept for ash thresholds based on dosages is introduced