Volcanic Eruption Energy Calculator

Most of the energy an eruption releases is heat carried in the erupted magma, not blast. The thermal term is mass times specific heat times temperature drop, and with a bulk density near 2500 kg/m3, a specific heat near 1000 J per kg per K, and roughly 1000 degrees C of cooling to ambient, every cubic kilometre of ejecta represents about 2.5e18 J. Kinetic energy is a much smaller share: ejecta leaving the vent at 100 m/s carries only about 0.5% of the thermal figure, which is why explosive and effusive eruptions of similar volume have comparable total energy budgets. The Volcanic Explosivity Index supplies the volume when it is unknown, since VEI n corresponds approximately to 10^(n-4) cubic kilometres of tephra, one order of magnitude per step from under 0.0001 km3 at VEI 0 to over 1000 km3 at VEI 8. Several caveats limit these numbers. VEI is a bulk tephra scale and says nothing about lava volume, so effusive eruptions such as those at Kilauea score low despite large energy release. Bulk tephra volume also overstates magma volume by a factor of two to three because of vesiculation, so dense-rock equivalent should be used for careful work. Column height is only a weak proxy for exit velocity, since plume height scales roughly with the fourth root of mass eruption rate and is strongly influenced by atmospheric stratification. The earthquake-magnitude equivalent shown here is a rough energy comparison, not a seismological measurement.

Volcanologists spent much of the twentieth century trying to put eruptions on a common scale. Early schemes were descriptive, naming eruption styles after type localities such as Strombolian, Vulcanian, and Plinian, the last honouring Pliny the Younger's account of Vesuvius in AD 79. Quantitative approaches followed: George Walker proposed in the early 1970s that eruptions be classified using measurable deposit properties such as dispersal area and fragmentation index rather than eyewitness impressions, which made systematic comparison of prehistoric deposits possible. The Volcanic Explosivity Index itself was introduced by Christopher Newhall of the US Geological Survey and Stephen Self of the University of Hawaii in a 1982 paper in the Journal of Geophysical Research. They combined erupted volume, column height, and qualitative descriptors into a single logarithmic 0 to 8 scale so that historical accounts and geological deposits could be catalogued together. The index was adopted by the Smithsonian Institution Global Volcanism Program, established in 1968, whose database now assigns VEI values to thousands of Holocene eruptions. David Pyle proposed refinements in the mid-1990s separating eruption magnitude, based on erupted mass, from intensity, based on mass eruption rate, addressing the criticism that a single index conflates size with vigour.