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Richter Magnitude to Energy Calculator (Joules & TNT)

Q: What is the largest earthquake ever recorded, and how much energy did it release?

The **1960 Valdivia, Chile earthquake** holds the record at Mw 9.5 (USGS). Using the formula: E = 10^(4.8 + 1.5×9.5) = 10^19.05 ≈ 1.12×10¹⁹ J, equivalent to roughly **2,680 Mt of TNT** — about 178,000 Hiroshima bombs. It ruptured ~1,000 km of the Nazca-South American plate boundary and generated a transoceanic tsunami that killed people as far away as Hawaii and Japan.

Q: How does earthquake energy compare to nuclear weapons?

The **Hiroshima 'Little Boy' bomb** yielded approximately 15 kilotons of TNT (6.3×10¹³ J), comparable to a M ~6.0 earthquake. The largest nuclear device ever detonated, the **Tsar Bomba (1961)**, yielded 50 Mt TNT — comparable to about M 8.35. The 2011 Tōhoku earthquake (M 9.0, ~477 Mt TNT equivalent) released roughly **9.5× more energy than the Tsar Bomba**. Nuclear monitoring agencies like the CTBTO use seismic stations to detect and characterize underground nuclear tests using these same energy-magnitude relationships.

Q: How accurate is the Gutenberg-Richter energy formula?

The formula log₁₀(E) = 4.8 + 1.5·M is an **empirical approximation** with inherent uncertainty of roughly ±0.5 in the exponent, meaning energy estimates carry a factor of ~3× uncertainty. It was calibrated on a limited dataset of 20th-century California earthquakes and is most reliable for tectonic earthquakes in the M 3–8 range. For very deep earthquakes, volcanic tremors, or induced seismicity, the constants may shift slightly. The USGS and IRIS use more precise moment tensor solutions for authoritative energy estimates of major events.

How much energy does an earthquake release? An M 6.0 equals ~15 kt of TNT and each +1.0 multiplies energy by 31.6. Convert magnitude to joules instantly.

Data verified · July 2026
Edited by Martín Rodríguez
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How to use this calculator

Follow this tool’s steps, then review its formula, assumptions, and limits below.

Step by step

Enter the Richter magnitudeType the magnitude value reported by USGS, ANSS or another seismic bulletin (e.g., 7.0 for a major earthquake).

Click CalculatePress the Calculate button to apply the Gutenberg-Richter formula log10(E) = 4.8 + 1.5 x M.

Read the energy resultReview the released energy in joules and its TNT equivalent in kilotons or megatons.

The Richter Scale (local magnitude, M_L) and the modern Moment Magnitude (Mw) used by the US Geological Survey (USGS) quantify earthquake energy on a base-10 logarithmic curve. Each whole-number step up the scale equals roughly 31.6× more energy released. The Gutenberg-Richter relation — log₁₀(E) = 4.8 + 1.5·M, E in joules — was originally calibrated on Southern California earthquakes by Charles Richter and Beno Gutenberg at Caltech. A magnitude 7.0 quake releases about 2×10¹⁵ J ≈ 480 kilotons of TNT (≈ 32 Hiroshima bombs). Use this calculator for any USGS-reported magnitude — from the 1906 San Francisco (M 7.9) quake to the 2011 Tōhoku (Mw 9.0) event monitored by ANSS — to convert magnitude into joules and TNT equivalents.

When to use this calculator

Comparing the destructive potential of historical earthquakes — e.g., understanding why the 1960 Valdivia M 9.5 released ~1,000× more energy than the 1994 Northridge M 6.7 quake.
Converting seismic bulletin magnitudes into TNT equivalents for civil engineering and emergency management risk assessments.
Estimating the energy yield of underground nuclear tests detected seismically — a practice used in nuclear non-proliferation monitoring (CTBTO).
Teaching geophysics or earth science students the exponential nature of the Richter scale with concrete joule and TNT values.
Evaluating aftershock sequences: determining how much cumulative energy has been released after a mainshock by summing individual event energies.

Richter / Moment Magnitude: Energy and TNT Equivalent by Scale Level

Magnitude (M)	Energy (Joules)	TNT Equivalent	Real-World Comparison
2.0	6.3 × 10⁷ J	~15 kg TNT	Small construction blast
3.0	2.0 × 10⁹ J	~480 kg TNT	Mining explosion
4.0	6.3 × 10¹⁰ J	~15 t TNT	Small quarry blast
5.0	2.0 × 10¹² J	~480 t TNT	Atomic demolition munition
6.0	6.3 × 10¹³ J	~15 kt TNT	Hiroshima bomb (Little Boy)
7.0	2.0 × 10¹⁵ J	~478 kt TNT	~32× Hiroshima
8.0	6.3 × 10¹⁶ J	~15 Mt TNT	~1,000× Hiroshima; Tsar Bomba class
9.0	2.0 × 10¹⁸ J	~478 Mt TNT	2011 Tōhoku earthquake
9.5	1.1 × 10¹⁹ J	~2,600 Mt TNT	1960 Valdivia — largest ever recorded

Fuente: USGS — Earthquake Magnitude, Energy, and Shaking Intensity. Formula: log₁₀(E) = 4.8 + 1.5 × M (Gutenberg & Richter, 1956). TNT conversion: 1 t TNT = 4.184×10⁹ J (NIST).

How it works

How It's Calculated

The relationship between earthquake magnitude and energy was established by Beno Gutenberg and Charles Richter. The standard empirical formula used by seismologists is:

log₁₀(E) = 4.8 + 1.5 × M

Where:
  E = energy released at the focus, in joules (J)
  M = Richter (local) magnitude or moment magnitude (Mw)
  4.8 and 1.5 = empirically derived constants (Gutenberg & Richter, 1956)

To solve for E directly:
  E = 10^(4.8 + 1.5 × M)

TNT equivalent (in tonnes):
  E_TNT = E / 4.184×10⁹
  (1 tonne of TNT = 4.184×10⁹ J by definition)

Step-by-step for M = 7.0:
1. Exponent = 4.8 + 1.5 × 7.0 = 4.8 + 10.5 = 15.3
2. E = 10^15.3 = 1.995 × 10¹⁵ J ≈ 2×10¹⁵ J
3. TNT = 2×10¹⁵ / 4.184×10⁹ = 477,730 tonnes ≈ 478 kt TNT
4. Hiroshima comparison: 478,000 / 15,000 ≈ ~32× the Hiroshima bomb (Little Boy ≈ 15 kt TNT)

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Reference Table

Data derived from the Gutenberg-Richter formula; TNT equivalents use 4.184×10⁹ J/tonne.

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Typical Use Cases with Real Numbers

Example 1 — 1994 Northridge, CA (M 6.7):

Exponent = 4.8 + 1.5 × 6.7 = 4.8 + 10.05 = 14.85

E = 10^14.85 ≈ 7.08 × 10¹⁴ J

TNT ≈ 169,300 tonnes ≈ 169 kt TNT

This quake caused $20 billion in damage and killed 57 people — yet released only ~35% of a magnitude 7.0 event's energy.

Example 2 — 2011 Tōhoku, Japan (M 9.0):

Exponent = 4.8 + 1.5 × 9.0 = 18.3

E = 10^18.3 ≈ 1.995 × 10¹⁸ J

TNT ≈ 477 Mt TNT (~31,800× Hiroshima)

Released more energy than all earthquakes worldwide in the entire 20th century combined — triggering a tsunami with 40-meter wave heights.

Example 3 — Typical Felt Earthquake (M 4.5):

Exponent = 4.8 + 1.5 × 4.5 = 11.55

E = 10^11.55 ≈ 3.55 × 10¹¹ J

TNT ≈ 84.8 tonnes TNT

Widely felt but rarely causes structural damage; corresponds to the energy of about 85 tonnes of conventional explosive.

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Common Errors

1. Confusing amplitude with energy: The Richter scale was originally defined by ground amplitude (10× per magnitude unit), not energy. Energy scales as 10^1.5 per unit ≈ 31.6×, not 10×. Saying "M 7 is 10× stronger than M 6" is wrong for energy — it's ~31.6× stronger.

2. Mixing Richter (M_L) with Moment Magnitude (Mw): For earthquakes above M 6.0, seismologists use Mw (moment magnitude), not M_L. The formula log₁₀(E) = 4.8 + 1.5·M applies to both approximately, but M_L saturates (gives unreliable readings) above ~6.5. Always check which scale the bulletin reports.

3. Forgetting the logarithmic base: Plugging M into the formula linearly (e.g., computing 4.8 + 1.5 × 7 = 15.3 and reading 15.3 J instead of 10^15.3 J) understates energy by 14 orders of magnitude. The result is always an exponent, not a direct joule value.

4. Using wrong TNT conversion factor: Some sources cite 1 tonne TNT = 4.2×10⁹ J (rounded), others use 4.184×10⁹ J (NIST/thermochemical standard). Using the wrong value introduces up to 0.4% error — negligible for most purposes but important in nuclear yield estimation.

5. Assuming surface magnitude (Ms) equals Mw: The surface-wave magnitude Ms is derived from 20-second surface waves and diverges significantly from Mw for deep-focus earthquakes. A deep M 7.0 quake may have Ms 6.5 due to reduced surface-wave excitation, leading to underestimation of energy if Ms is used directly.

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Related Calculators

Since no internal related slugs were specified, explore other science calculators on Hacé Cuentas for unit conversions, physics formulas, and more.

Example: USGS-reported M 7.0 earthquake

Magnitude (M): 7.0 (USGS Mw).

Exponent: 4.8 + 1.5 × 7.0 = 15.3.

Energy: E = 10^15.3 ≈ 2 × 10¹⁵ J.

TNT equivalent: 2×10¹⁵ J ÷ 4.184×10⁹ J/t (NIST standard) ≈ 478 kt TNT.

Hiroshima comparison: 478 kt / 15 kt ≈ 32× the Little Boy bomb.

~480 kt TNT (about 32× the Hiroshima bomb) — comparable to the 1989 Loma Prieta event in the Bay Area.

Frequently asked questions

What does the Richter scale actually measure?

The original Richter scale (local magnitude, M_L) measures the peak amplitude of seismic waves recorded on a Wood-Anderson seismograph at a standard distance of 100 km, then adjusts for distance. It is a base-10 logarithmic scale: each unit increase = 10× greater ground motion amplitude. However, because wave amplitude relates to energy by a power of 1.5, each unit increase corresponds to approximately 31.6× more energy released, not 10×.

Why does a magnitude 9 feel so much more destructive than a magnitude 7 if it's only 2 numbers higher?

Because the scale is logarithmic, M 9.0 releases 10^(1.5×2) = 10³ = 1,000× more energy than M 7.0. The 2011 Tōhoku M 9.0 earthquake released roughly 1.995×10¹⁸ J — equivalent to ~477 Mt of TNT — compared to ~478 kt for a M 7.0. That 1,000× energy difference translates into dramatically larger fault rupture areas, longer shaking durations, and larger tsunamis.

Is the Richter scale still used today?

Not as the primary scale for large earthquakes. Modern seismology relies on the Moment Magnitude Scale (Mw), introduced by Hanks and Kanamori (1979), because it does not saturate at high magnitudes and is directly tied to physical fault properties (seismic moment = shear modulus × rupture area × average slip). The USGS and most global networks report Mw for events above ~M 3.5. However, the Gutenberg-Richter energy formula log₁₀(E) = 4.8 + 1.5·M works reliably with Mw as well.

What is the largest earthquake ever recorded, and how much energy did it release?

The 1960 Valdivia, Chile earthquake holds the record at Mw 9.5 (USGS). Using the formula: E = 10^(4.8 + 1.5×9.5) = 10^19.05 ≈ 1.12×10¹⁹ J, equivalent to roughly 2,680 Mt of TNT — about 178,000 Hiroshima bombs. It ruptured ~1,000 km of the Nazca-South American plate boundary and generated a transoceanic tsunami that killed people as far away as Hawaii and Japan.

How does earthquake energy compare to nuclear weapons?

The Hiroshima 'Little Boy' bomb yielded approximately 15 kilotons of TNT (6.3×10¹³ J), comparable to a M ~6.0 earthquake. The largest nuclear device ever detonated, the Tsar Bomba (1961), yielded 50 Mt TNT — comparable to about M 8.35. The 2011 Tōhoku earthquake (M 9.0, ~477 Mt TNT equivalent) released roughly 9.5× more energy than the Tsar Bomba. Nuclear monitoring agencies like the CTBTO use seismic stations to detect and characterize underground nuclear tests using these same energy-magnitude relationships.

What is the difference between 'energy released' and 'energy felt at the surface'?

The formula log₁₀(E) = 4.8 + 1.5·M estimates total energy released at the earthquake's hypocenter (focus). Only a fraction of this reaches the surface as shaking — much is absorbed by rock, converted to heat along the fault, or radiated as seismic waves that travel deep into the Earth. The seismic efficiency (fraction of energy radiated as seismic waves) typically ranges from 1% to 6% of total strain energy. This means the energy humans feel is far less than the total calculated energy.

Can the Richter scale have negative values?

Yes. The Richter scale has no upper or lower bound. Sensitive modern seismographs detect earthquakes as small as M −2 or even M −3 in mining and geothermal contexts. A M −1.0 event would release: E = 10^(4.8 + 1.5×(−1)) = 10^3.3 ≈ 2,000 J — roughly the energy of dropping a 20 kg weight from 10 meters. Conversely, while no physical upper limit exists mathematically, fault mechanics and planetary crustal thickness constrain realistic maxima to approximately M 9.5–10.0.

How accurate is the Gutenberg-Richter energy formula?

The formula log₁₀(E) = 4.8 + 1.5·M is an empirical approximation with inherent uncertainty of roughly ±0.5 in the exponent, meaning energy estimates carry a factor of ~3× uncertainty. It was calibrated on a limited dataset of 20th-century California earthquakes and is most reliable for tectonic earthquakes in the M 3–8 range. For very deep earthquakes, volcanic tremors, or induced seismicity, the constants may shift slightly. The USGS and IRIS use more precise moment tensor solutions for authoritative energy estimates of major events.

Sources & references

Methodology & trust

Editorial

ciencia calculator with its formula verified automatically against USGS — Earthquake Magnitude, Energy, and Shaking Intensity, per our editorial policy and methodology.

Updates

Updated: July 2026. Parameters are verified periodically against the cited sources.

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Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

APA format

Rodríguez, M. (2026). Richter Magnitude to Energy Calculator (Joules & TNT). Hacé Cuentas. https://hacecuentas.com/en/richter-scale-magnitude-energy

BibTeX

@misc{hacecuentas_richter_scale_magnitude_energy_2026,
  author       = {Rodríguez, Martín},
  title        = {{Richter Magnitude to Energy Calculator (Joules & TNT)}},
  year         = {2026},
  howpublished = {\url{https://hacecuentas.com/en/richter-scale-magnitude-energy}},
  note         = {Hacé Cuentas}
}

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