Science & Units
Earthquake Magnitude and Energy Table
The single most misunderstood number in seismology is the difference between magnitude 7 and magnitude 9. Most people read the scale as linear and assume a magnitude 9 releases about 30% more energy than a magnitude 7. It releases roughly 31,600 times more. The confusion comes from mixing two different things: magnitude measures amplitude on a seismograph, and energy scales with amplitude raised to the power 1.5.
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The relationship used here is the Gutenberg–Richter energy formula, log₁₀E = 4.8 + 1.5M with energy in joules. Each whole step in magnitude multiplies the recorded amplitude by 10 and the radiated energy by 10^1.5, which is 31.6. Two steps multiply energy by 1,000. Three steps — a 6 to a 9 — multiply it by about 31,600. That is the entire reason a magnitude 9 is a civilisational event and a magnitude 6 is a damaging local one.
One caveat matters more than the arithmetic. Radiated energy is not the same as damage. A shallow magnitude 6 directly under a city can kill more people than a deep magnitude 8 offshore, because damage depends on depth, distance, soil conditions and building codes. The energy figures in these tables describe the source, not the consequences, and they are computed from the reported magnitude rather than measured independently.
Seismic energy released at each magnitude
| Magnitude | Energy (J) | TNT equivalent | Compared with the row above |
|---|---|---|---|
| 1 | 2.00 × 10⁶ | 0.48 kg | — |
| 2 | 6.31 × 10⁷ | 15 kg | 31.6× |
| 3 | 2.00 × 10⁹ | 477 kg | 31.6× |
| 4 | 6.31 × 10¹⁰ | 15 t | 31.6× |
| 5 | 2.00 × 10¹² | 477 t | 31.6× |
| 6 | 6.31 × 10¹³ | 15,080 t | 31.6× |
| 7 | 2.00 × 10¹⁵ | 476,879 t | 31.6× |
| 8 | 6.31 × 10¹⁶ | 15.1 Mt | 31.6× |
| 9 | 2.00 × 10¹⁸ | 476.9 Mt | 31.6× |
Each whole magnitude step releases about 31.6 times more energy — not 10 times. The factor of 10 applies to the amplitude recorded on a seismograph; the energy scales with amplitude to the power 1.5.
What a magnitude difference actually means
| Difference | Amplitude factor | Energy factor | Example pair |
|---|---|---|---|
| 0.2 | 1.58× | 2× | M6.0 versus M6.2 |
| 0.5 | 3.16× | 5.6× | M6.0 versus M6.5 |
| 1 | 10× | 31.6× | M6 versus M7 |
| 2 | 100× | 1,000× | M5 versus M7 |
| 3 | 1,000× | 31,622.8× | M6 versus M9 |
A magnitude 9 earthquake releases about 31,600 times the energy of a magnitude 7. That is why the difference between 7 and 9 is not a bigger version of the same event — it is a different class of event.
Reference events and their energy
| Event | Year | Magnitude | Energy (J) | TNT equivalent |
|---|---|---|---|---|
| Hiroshima bomb (reference, not seismic) | 1945 | ≈6.0 | 6.31 × 10¹³ | 15,080 t |
| Loma Prieta, California | 1989 | 6.9 | 1.41 × 10¹⁵ | 337,605 t |
| Haiti | 2010 | 7.0 | 2.00 × 10¹⁵ | 476,879 t |
| San Francisco (1906) | 1906 | 7.9 | 4.47 × 10¹⁶ | 10.7 Mt |
| Tōhoku, Japan | 2011 | 9.1 | 2.82 × 10¹⁸ | 673.6 Mt |
The energy figures are computed from the reported magnitude, not measured independently — so they inherit the uncertainty of the magnitude itself, which is typically ±0.1 for large modern events.
How to Use These Tables
- To compare two earthquakes, subtract the magnitudes and read the energy factor from the second table: a difference of 1 is 31.6×, 2 is 1,000×, 3 is about 31,600×. Do not compare the magnitudes directly as if they were percentages.
- To convert energy to a familiar scale, use the TNT column: a magnitude 5 is roughly 477 tonnes of TNT, a magnitude 7 is about 477,000 tonnes, and a magnitude 9 is around 477 million tonnes.
- To sanity-check a news report, remember that the energy formula is for radiated seismic energy. Moment magnitude, which is what modern services report, is derived from fault area, slip and rock rigidity, and the 1.5 factor is an empirical fit between the two — good to within a factor of a few, not exact.
- For tsunami and shaking questions, ignore energy entirely and use magnitude, depth and distance. Energy tells you how big the source was; it does not tell you what happened at any particular place.
Common Questions
Is a magnitude 9 earthquake really 1,000 times stronger than a magnitude 7?
It releases about 1,000 times more energy — 10^(1.5×2) — while the amplitude recorded on a seismograph is 100 times larger. "Stronger" is ambiguous; the energy ratio is the number that matters for comparing total size, and the amplitude ratio is what a seismogram shows.
Why does the scale use 1.5 rather than 1?
Because energy in a wave is proportional to amplitude squared, and the Gutenberg–Richter relation was fitted empirically with an extra factor from how rupture area and slip scale with magnitude. The 1.5 exponent is the observed fit, not a derivation from first principles, which is why it holds to within a factor of a few rather than exactly.
Is there an upper limit to magnitude?
There is a physical limit set by the strength of rock and the size of the fault, estimated at around magnitude 9.5 to 10. The largest instrumentally recorded event is the 1960 Valdivia earthquake at magnitude 9.5. Magnitudes above that would require a rupture longer than any known fault system.
How much energy is a magnitude 0 earthquake?
About 63,000 joules by this formula — roughly the energy of a 15-watt bulb left on for an hour. Magnitude 0 is not "no earthquake"; it is the reference point of the original Richter scale, chosen so that a magnitude 0 event would produce a 1-micrometre trace on a particular seismograph at a particular distance.
Do these energy figures match what the USGS publishes?
Within rounding, yes. The USGS uses the same logarithmic relation and publishes roughly 2.0×10^12 J for magnitude 5 and 6.3×10^13 J for magnitude 6, which is what this table produces. Differences come from how many significant figures are shown and from using moment magnitude rather than the original local magnitude.
More Science & Units
Sources
- Earthquake magnitude, energy release and energy increase — US Geological Survey
- How much bigger is a magnitude 8 earthquake than a magnitude 5? — US Geological Survey, Earthquake Hazards Program
- Earthquake energy, intensity and magnitude — Gutenberg & Richter (1956) — Bulletin of the Seismological Society of America
- Magnitude and energy of earthquakes — Annals of Geophysics
Filed with Science calculations.