  This study entails the third part of a global flare energetics project, in
which Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) data of 191 M and
X-class flare events from the first 3.5 yrs of the Solar Dynamics Observatory
(SDO) mission are analyzed. We fit a thermal and a nonthermal component to
RHESSI spectra, yielding the temperature of the differential emission measure
(DEM) tail, the nonthermal power law slope and flux, and the thermal/nonthermal
cross-over energy $e_{\mathrm{co}}$. From these parameters we calculate the
total nonthermal energy $E_{\mathrm{nt}}$ in electrons with two different
methods: (i) using the observed cross-over energy $e_{\mathrm{co}}$ as
low-energy cutoff, and (ii) using the low-energy cutoff $e_{\mathrm{wt}}$
predicted by the warm thick-target bremsstrahlung model of Kontar et al. {\bf
Based on a mean temperature of $T_e=8.6$ MK in active regions we find
low-energy cutoff energies of $e_{\mathrm{wt}} =6.2\pm 1.6$ keV for the
warm-target model, which is significantly lower than the cross-over energies
$e_{\mathrm{co}}=21 \pm 6$ keV. Comparing with the statistics of magnetically
dissipated energies $E_{\mathrm{mag}}$ and thermal energies $E_{\mathrm{th}}$
from the two previous studies, we find the following mean (logarithmic) energy
ratios with the warm-target model: $E_{\mathrm{nt}} = 0.41 \ E_{\mathrm{mag}}$,
$E_{\mathrm{th}} = 0.08 \ E_{\mathrm{mag}}$, and $E_{\mathrm{th}} = 0.15 \
E_{\mathrm{nt}}$. The total dissipated magnetic energy exceeds the thermal
energy in 95% and the nonthermal energy in 71% of the flare events, which
confirms that magnetic reconnection processes are sufficient to explain flare
energies. The nonthermal energy exceeds the thermal energy in 85\% of the
events, which largely confirms the warm thick-target model.
