We propose a P wave based procedure for the rapid estimation of the radiated seismic energy, and a novel relationship for obtaining an energy‐based local magnitude (MLe) measure of the earthquake size. We apply the new procedure to the seismic sequence that struck Central Italy in 2016. Scaling relationships involving seismic moment and radiated energy are discussed for the Mw 6.0 Amatrice, Mw 5.9 Ussita, and Mw 6.5 Norcia earthquakes, including 35 ML > 4 aftershocks. The Mw 6.0 Amatrice earthquake shows the highest apparent stress, and the observed differences among the three main events highlight the dynamic heterogeneity with which large earthquakes can occur in Central Italy. Differences between estimates of MLe and Mw allows identification of events which are characterized by a higher proportion of energy being transferred to seismic waves, providing important real‐time indications of earthquakes shaking potential.