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Science

Earthquake Magnitude ↔ Energy Calculator

Enter an earthquake magnitude (moment magnitude Mw) to instantly see the released seismic energy in joules, TNT equivalent and Hiroshima-bomb units. Pick a historical preset to feel how big each step in magnitude really is.

Released energy

TNT equivalent

Equivalent to a 15 kt Hiroshima bomb

Energy ratio

Each step in magnitude multiplies energy by ≈ 31.6 (10^1.5); a +2 step is 1 000×.

Formula

log₁₀ E = 1.5·M + 4.8 (E in joules) → E = 10^(1.5·M + 4.8)

Uses the Gutenberg–Richter (1956) energy–magnitude relation, which estimates the seismic energy Es radiated by an earthquake. Real radiated energy is affected by focal mechanism, rupture depth and crustal structure, with uncertainty up to ±1 order of magnitude.

Formula

log₁₀ E = 1.5·M + 4.8 ⇒ E = 10^(1.5·M + 4.8) (E in joules)

Frequently asked

Why does +1 magnitude multiply energy by ~31.6 rather than 10?

Two different formulas. Magnitude itself is defined on amplitude (or seismic moment), so +1 magnitude = ×10 in ground-motion amplitude. But energy is not linear in amplitude — Gutenberg & Richter (1956) showed that log E = 1.5·M + 4.8, which means ΔM = 1 corresponds to Δlog E = 1.5, i.e. ×10^1.5 ≈ 31.6× energy. ΔM = 2 is ×1 000 and ΔM = 3 is ≈ ×31 623. That's why a single M 9.0 quake releases roughly 31 623× the energy of an M 6.0 — and why one great earthquake dwarfs decades of smaller seismicity combined.

How is moment magnitude (Mw) different from the original Richter scale (ML)?

The original Richter scale (ML, 1935) was calibrated for short-period Wood–Anderson seismographs at ≤ 100 km in Southern California and measures peak amplitude. It saturates around magnitude 7 — bigger ruptures don't keep increasing the peak amplitude proportionally. Moment magnitude (Mw, Hanks & Kanamori 1979) is computed from seismic moment M₀ — Mw = (2/3)·log₁₀ M₀ − 6.07 — which captures rupture area, slip and rock rigidity. It doesn't saturate, so it's the modern global standard. ML and Mw agree within ±0.2 at moderate magnitudes; for great quakes only Mw is reliable. The 1960 Chile quake measures ML ≈ 8.6 but Mw 9.5.

Can earthquake energy really be compared with nuclear bombs?

Yes — at the energy-budget level, but the physics is very different. A nuclear weapon dumps its energy at a single point within microseconds at million-degree temperatures. An earthquake releases energy over seconds to minutes along a fault that can be kilometres to thousands of kilometres long, spreading energy through a huge crustal volume. Per ton of TNT the destructive footprint of an earthquake is far smaller than a bomb of the same yield because most seismic energy goes into fault friction (heat) and non-damaging body- and surface-waves. Even so, TNT and "Hiroshima-equivalents" are useful intuition: an M 9.0 quake releases about 199 Mt TNT — roughly 13 000 Hiroshima bombs — yet the same total energy spread along hundreds of kilometres of fault.

Why does the energy I get differ from numbers I see quoted in the news?

A few reasons: (1) this tool uses the classical Gutenberg–Richter estimate of radiated seismic energy Es, while news outlets sometimes quote the total seismic-moment energy M₀·g or total strain-energy release, which can be 10–50× higher. (2) Modern source-spectral methods (e.g. Choy & Boatwright 1995) integrate P- and S-wave spectra and typically give Es about 10× lower than G-R for the same Mw. (3) USGS, JMA, and other agencies often report Mw values that differ by ±0.1–0.3 for the same quake, which the exponential formula magnifies into several-fold energy differences. (4) Magnitude is logarithmic — 0.2 in Mw already doubles the energy. Treat the tool's output as an order-of-magnitude figure, not a precise radiated-energy measurement.

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