# Volcanic Eruption Calculation?

I was trying to find the amount of energy created during a volcanic explosion, I have been looking around, There was one formula I found where I could use the Kinetic Energy, which is $$KE=\frac{1}{2}mv^2$$, but I feel that there is something more.

I am looking at Volcanic Explosivity Index for Krakatoa, which says that it is class 6, and it has a TNT equivalence to 200 megatons.

I was hoping if someone can give me the correct calculation to find the means of measuring a volcanic explosion in joules, tonnes or higher.

Or if there are other means or formula like finding the result in newtons, go ahead with that as well

Here is information about the Volcanic Explosivity Index

https://geology.com/stories/13/volcanic-explosivity-index/

It says you can measure it by volume of volcanic material, height of eruption column and duration of explosion.

• One ton of TNT is 4.184 gigajoules. (en.m.wikipedia.org/wiki/TNT_equivalent) Multiply this by 200 million. – G. Smith Jan 6 '19 at 3:07
• Could the calculation be based on the work that goes into lifting the eruptive material a certain distance ($mgh$) rather than the kinetic energy afterward? – Anders Sandberg Jan 6 '19 at 9:03
• @Anders Sandberg if you are referring to Newton’s then that would work too, if you know of a formula, go ahead and type it – C. Jordan Jan 6 '19 at 14:06

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).
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).