Volcanic Eruption Calculation?
There are apparently several ways of estimating total energy release in volcanic eruptions, all of them approximate. Energy is released as heat, vibrations, deformation of rock, kinetic energy of ejected material etc. Calculating an exact energy budget is hard.

The  Volcanic Explosivity Index (VEI) indicates how much volume the ejecta of the eruption takes up. One can estimate the energy release as a function of VEI class $M$ as $E=10^{aM+c}$ Joule where $a\approx 0.79$ and $c = 14$ (based on de La Cruz-Reyna 1991). That was in turn based on estimates from Yokoyama (1957).

Another way of estimating is to look at seismic signals and calculate how much energy the eruption must have had to produce the measured waveforms. Seismologists have fairly decent models of the scaling of energy with shaking intensity, and one can estimate how much it attenuates with distance.

A third way is to consider how much the pressure in the magma chamber is reduced times the reduction in volume, $E=\Delta P\cdot V$. A pressure drop of 5 MPa is apparently typical, and the volume reduction is proportional to the ejected volume (with some scaling factor from packed rock to ejecta).