Earthquake impacts are widely studied across numerous disciplines. However, no systematic approach to quantify the "size" of an earthquake for impact research exists. This work provides the first comprehensive discussion and empirical study on how to measure the natural hazard of an earthquake for application in the social sciences. A data set consisting of all relevant global ground shaking from 1973 to 2015 combined with population exposure data and impact data is constructed based on 14,608 ShakeMaps. The empirical work shows that magnitude is not a good proxy for shaking and that measures of total earthquake size based on ground motion parameters perform better in explaining impacts than magnitude. In particular peak ground acceleration (PGA) performs well and is applied for two separate impact analyses. First, the relationship between earthquake ground shaking and public health related variables in California is investigated. Second, the global impact of earthquake ground shaking on long-run economic growth is studied. Furthermore, this work introduces the concept of a shaking center as well as a shaking centroid and provides the first global statistics on the area exposed to strong ground shaking for a given earthquake.