  Strongly interacting Fermi gases are of great current interest. Not only are
fermions the most common particles in the universe, but they are also thought
to have a universal thermodynamic behavior for strong interactions
\cite{heiselberg,carlson,ho}. Recent experiments on ultra-cold Fermi gases
provide an unprecedented opportunity to test universality in the laboratory
\cite{hara,thomas,partridge,stewart,luo}. In principle this allows - for
example - the interior properties of hot, dense neutron stars to be
investigated on earth. Here we carry out a detailed test of this prediction. We
analyze results from three ultra-cold fermion experiments involving two
completely distinct atomic species in different kinds of atomic trap
environments \cite{partridge,stewart,luo}. The data is compared with the
predictions of a recent strong interaction theory \cite{hldepl,hldpra}.
Excellent agreement is obtained, with no adjustable parameters. By
extrapolating to zero temperature, we show that the experimental measurements
yield a many-body parameter} $\mathbf{\beta\simeq-0.59\pm.07}$,
\textbf{describing the universal energy of strongly interacting Fermi gases.
