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. Key Points An energy‐based local magnitude scale (MLe) for measuring the earthquake size during real‐time operations is proposed In the analysis of the 2016 Central Italy sequence, large values for the apparent stress are observed, extending from about 0.5 to 25 MPa Mw and MLe can be used together for better capturing the shaking potential of earthquakes in real‐time applications