La energía de los terremotos: TNT, bombas atómicas y más

The Gutenberg-Richter Energy Formula

The Gutenberg-Richter LawA statistical law describing the relationship between earthquake frequency and magnitude: for each unit increase in magnitude, earthquakes become about 10 times less frequent. law is best known for the frequency-magnitude relationship — the observation that small earthquakes are vastly more common than large ones. But Beno Gutenberg and Charles Richter also developed one of the most important formulas in seismology: the relationship between MagnitudeA single number that quantifies the total energy released by an earthquake. Each whole number increase represents roughly 31.6 times more energy released. and Earthquake EnergyThe total seismic energy radiated by an earthquake, measured in joules. A magnitude 9 earthquake releases the energy equivalent of about 25,000 nuclear bombs.. Their empirical formula, derived from measurements on real earthquakes, expresses radiated seismic energy as a function of magnitude.

The formula used in modern form is: log10(E) = 5.24 + 1.44 × Mw, where E is in joules. This gives the seismic energy — the energy radiated as Seismic WaveAn elastic wave generated by an earthquake or explosion that propagates through the Earth. Seismic waves carry the energy released at the earthquake source to distant locations.s, not the total energy released by fault motion (some energy goes into heat, fracturing new rock surfaces, and permanent deformation). For a magnitude 5.0 earthquake, this formula gives approximately 2 × 10^12 joules. For a magnitude 9.0, it gives approximately 2 × 10^18 joules — one million times more.

Earthquake Energy in Human Terms: TNT and Atomic Bombs

To make earthquake energy tangible, seismologists often compare it to familiar explosive devices. One tonne of TNT releases approximately 4.2 × 10^9 joules. One kiloton (1,000 tonnes) of TNT — the unit used for nuclear weapons — releases about 4.2 × 10^12 joules.

A magnitude 5.0 earthquake releases about 480 kilotons of TNT equivalent — similar to a small nuclear weapon. A magnitude 6.0 releases approximately 15 megatons (15,000 kilotons), larger than the most powerful nuclear weapons ever tested. A magnitude 8.0 releases energy equivalent to approximately 15,000 megatons — far exceeding the total yield of all nuclear weapons ever detonated in history. The 1960 Valdivia earthquake at magnitude 9.5 released approximately 180,000 megatons of energy — equivalent to detonating a nuclear bomb of that size, which fortunately does not exist.

Each Magnitude Step = 31.6x More Energy

The most important number to remember about earthquake energy is 31.6 — the factor by which energy increases for each whole magnitude unit. This comes directly from the 1.44 coefficient in the energy formula: 10^1.44 ≈ 27.5, sometimes rounded to 31.6 when accounting for slightly different formulations. Each step up the magnitude scale multiplies the energy by about 31.6.

This means: magnitude 5 to 6 is 31.6 times more energy; magnitude 5 to 7 is 31.6 × 31.6 ≈ 1,000 times more energy; magnitude 5 to 9 is 31.6^4 ≈ one million times more energy. The practical implication is that the largest earthquakes completely dominate global seismic energy release. The global average of about 1,000 magnitude 5.0 earthquakes per year releases less total energy than a single magnitude 8.0 earthquake. A single magnitude 9.5 earthquake releases more energy than all other earthquakes in that year combined, in most years.

Comparing Earthquake Energy to Other Events

The energy scales involved in earthquakes help explain why even apparently small events can be powerful. A magnitude 4.0 earthquake releases energy comparable to 30,000 tonnes of TNT — roughly equivalent to a small tactical nuclear weapon. A magnitude 7.0 releases energy equivalent to 30 megatons, far exceeding the largest nuclear test ever conducted (the USSR's Tsar Bomba at about 50 megatons, which was magnitude 5.0 seismically).

Volcanic eruptions provide another comparison point. The 1980 Mount St Helens eruption released energy roughly equivalent to a magnitude 7.6 earthquake. The 1815 Tambora eruption — the most powerful in recorded history — may have released energy comparable to a magnitude 8+ seismic event. Tropical cyclones release enormous energy, but most of it is thermal rather than mechanical, making direct comparison complex. In terms of purely mechanical energy released suddenly and destructively, large earthquakes are unmatched by any phenomenon short of asteroid impacts.

Where Does All That Energy Go?

Of the enormous energy released during an earthquake, only a fraction travels as Seismic WaveAn elastic wave generated by an earthquake or explosion that propagates through the Earth. Seismic waves carry the energy released at the earthquake source to distant locations.s to cause ground shaking. The Seismic MomentA measure of the total energy released by an earthquake, calculated as the product of the fault area, average displacement, and the shear modulus of the rocks. The basis of moment magnitude. represents the total mechanical work done by fault motion, which is typically 10 to 100 times larger than the radiated seismic energy. Most of the total energy budget goes into heating the fault zone through friction — essentially, the fault surfaces sliding past each other generate heat just as rubbing your hands together does, but at enormous pressures and over great distances.

Some energy goes into creating new fracture surfaces within the fault zone and in the surrounding rock. Some is stored elastically as permanent deformation of the crust — the GPS GeodesyThe use of Global Positioning System receivers to measure tectonic plate motion and crustal deformation with millimeter precision. Reveals how strain accumulates on faults between earthquakes. measurements that detect crustal deformation following large earthquakes are measuring the permanent redistribution of this elastic strain energy. The fraction that radiates as seismic waves — typically 5–25 percent of the total energy budget — is what causes the shaking that destroys buildings. Use the Earthquake Energy Calculator to explore how different magnitudes compare in terms of energy, TNT equivalents, and shaking parameters.

Using the Earthquake Calculator to Explore Energy

Understanding earthquake energy becomes intuitive when you can compare magnitudes interactively. The Earthquake Energy Calculator lets you enter any magnitude and instantly see the energy in joules, TNT equivalents, and Hiroshima bomb equivalents. You can compare two magnitudes side by side to feel the logarithmic difference — the difference between a magnitude 7.0 and 8.0 is always 31.6 times, regardless of which magnitudes you compare.

The calculator also illustrates the frequency-magnitude relationship: for every magnitude 8.0 earthquake, there are roughly 10 magnitude 7.0 earthquakes and 100 magnitude 6.0 earthquakes annually worldwide. Visualising this pyramid helps explain why the rare great earthquakes dominate global energy statistics even though they occur far less frequently than moderate events. The Seismic MomentA measure of the total energy released by an earthquake, calculated as the product of the fault area, average displacement, and the shear modulus of the rocks. The basis of moment magnitude. approach underpinning Moment Magnitude ScaleThe modern standard for measuring earthquake size (Mw), based on the seismic moment — the product of fault area, average slip, and rock rigidity. Accurate for all earthquake sizes. ensures that the calculator's energy values are physically meaningful, grounded in the actual fault mechanics rather than instrument calibration curves.