Earthquake Magnitude to Energy

Moment-magnitude energy scaling in plain numbers and ratios.

Worked example — Earthquake Magnitude to Energy

Energy at M1	101.5×6+4.8≈6.31×10¹³ J
Energy at M2	101.5×7+4.8≈2×10¹⁵ J
Energy ratio E2 / E1	101.5×(7−6)≈31.62×

These are the values the calculator shows when the page opens. Change any input above to recompute them.

Loading interactive simulation...

Three magnitudes is thirty thousand times the energy 🖖

Earthquake magnitudes are measured on logarithmic scales because the physical forces involved span an enormous range. The moment magnitude scale, defined as M_w = ²⁄₃(log₁₀ M₀ − 9.1), scales with the seismic moment M₀, which measures the actual energy released by tectonic slip. Because of the 1.5 factor in the energy-magnitude equation, a magnitude 6 earthquake does not release 10% or 20% more energy than a magnitude 5; it releases roughly 31.6 times more energy. A magnitude 8 release is not three times larger than a magnitude 5 — it releases about 31,600 times more energy. This extreme power-law distribution is why small earthquakes, despite being incredibly common, do almost nothing to relieve tectonic stress. Almost all geological strain is released in rare, catastrophic, high-magnitude events.

From a single number to real energy 🖖

This tool takes one abstract number — the magnitude — and turns it into something you can picture: an energy in joules and an equivalent tonnage of TNT. That translation is what makes the scale meaningful. A magnitude 6 earthquake, for instance, radiates roughly 6.3 × 10¹³ J of seismic energy, about the same as the Hiroshima atomic bomb. Sliding the magnitude and watching the TNT figure climb turns an intangible scale into a gut-level comparison.

The quake that shortened the day 🖖

Energy this large doesn't just shake the ground — it rearranges the planet. The 2011 magnitude 9.0 Tōhoku earthquake off Japan shifted enough mass toward Earth's center that the planet spun very slightly faster, shortening the day by about 1.8 microseconds, and it nudged the axis around which Earth's mass balances by roughly 17 cm. The 2004 magnitude 9.1 Sumatra quake trimmed the day even more, close to 6.8 microseconds. The energy scale you're exploring is also, quite literally, a clock.

Common misconception

Damage does not depend on magnitude alone. Depth, distance, local geology, and building quality can dominate local impact.

Problem solved in full

Energy ratio of a magnitude 7 earthquake to a magnitude 6 5 steps
A magnitude 7 earthquake is one point above a magnitude 6. Work out the energy ratio — and then why the popular "ten times bigger" is describing something else entirely.
1. The magnitude scale is defined logarithmically in energy, with both the 1.5 and the 4.8 empirical. The structure that matters is that M sits in an exponent.
  
  $lo g_{10} E = 1.5 M + 4.8 (E in joules)$
2. M = 6 gives 10^13.8 joules — comparable to a small nuclear weapon, released over a few seconds.
  
  $E_{6} = 1 0^{1.5 (6) + 4.8} = 1 0^{13.8} = 6.31 \times 1 0^{13} J$
3. M = 7 gives 10^15.3, from the same expression with the same constants.
  
  $E_{7} = 1 0^{1.5 (7) + 4.8} = 1 0^{15.3} = 2.00 \times 1 0^{15} J$
4. The ratio is where the constants cancel and only the difference in magnitude survives. So the factor per point is 10^1.5 = 31.62 regardless of where you start; two points is 10³, exactly 1000; three points is 31 623.
  
  $\frac{E _{M + Δ}}{E _{M}} = 1 0^{1.5Δ} : Δ = 1 \Rightarrow 31.62, Δ = 2 \Rightarrow 1000, Δ = 3 \Rightarrow 31623$
5. The "ten times" figure is not wrong, it is about amplitude — the size of the trace on the seismogram, which really does grow tenfold per point. Energy goes as the 3/2 power of that, which is where the 1.5 in the formula came from to begin with.
  
  $A_{M + 1} = 10 A_{M} but E_{M + 1} = 31.62 E_{M} ⟹ E \propto A^{3/2}$
Answer

The tool prints 6.31 × 10¹³ J for the M6 and a ratio of 31.62× per magnitude point. Both "ten times" and "thirty-two times" are correct, and they answer different questions: ten times the ground motion, thirty-two times the energy. The consequence is that a magnitude scale flatters large events into looking comparable with small ones. It takes 1000 magnitude-6 earthquakes to match a single magnitude-8, and 31 623 to match a magnitude 9 — which is why counting earthquakes tells you almost nothing about how much energy was released. Set the two magnitudes to 9 and 6 and read that factor off directly.

$\frac{E _{2}}{E _{1}} = 1 0^{1.5 Δ M} = 31.62 per point, 1000 per two$

References (1)

The moment magnitude definition the first block had mis-parenthesised: T. C. Hanks and H. Kanamori, "A moment magnitude scale." Journal of Geophysical Research: Solid Earth 84(B5), 2348–2350, 1979.

By the 42Math team · Updated 2026-07-29

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

M5 vs M6 - A magnitude 6 event releases about 31.6x the energy of magnitude 5.
M7 vs M8 - Each +1 step multiplies energy by roughly 31.6.
M9 vs M8.5 - Magnitude 9 events are extreme outliers in released energy.
M2.5 vs M4 - Small magnitude changes still imply large multiplicative energy jumps.