Laboratory stick-slip friction experiments indicate that peak slip rates increase with the stresses loading the fault to cause rupture. If this applies also to earthquake fault zones, then the analysis of rupture processes is simplified inasmuch as the slip rates depend only on the local yield stress and are independent of factors specific to a particular event, including the distribution of slip in space and time. We test this hypothesis by first using it to develop an expression for radiated energy that depends primarily on the seismic moment and the maximum slip rate. From laboratory results, the maximum slip rate for any crustal earthquake, as well as various stress parameters including the yield stress, can be determined based on its seismic moment and the maximum slip within its rupture zone. After finding that our new equation for radiated energy works well for laboratory stick-slip friction experiments, we used it to estimate radiated energies for five earthquakes with magnitudes near 2 that were induced in a deep gold mine, an M 2.1 repeating earthquake near the San Andreas Fault Observatory at Depth (SAFOD) site and seven major earthquakes in California and found good agreement with energies estimated independently from spectra of local and regional ground-motion data. Estimates of yield stress for the earthquakes in our study range from 12 MPa to 122 MPa with a median of 64 MPa. The lowest value was estimated for the 2004 M 6 Parkfield, California, earthquake whereas the nearby M 2.1 repeating earthquake, as recorded in the SAFOD pilot hole, showed a more typical yield stress of 64 MPa.