AkCalculators

Seismic energy — how magnitude relates to energy, TNT equivalents and notable earthquakes

Earthquakes are described commonly by a magnitude scale and sometimes by the energy they release. Magnitude is a logarithmic measure that compresses a huge dynamic range of released energy into manageable numbers; a one-unit increase in magnitude corresponds roughly to about 32 times more energy release. Converting between magnitude and energy provides an intuitive sense of the true physical scale of shaking and allows comparisons to familiar energy releases like TNT explosions.

Magnitude and energy — the empirical relation

A widely used empirical relation to estimate seismic energy E (in joules) from magnitude M (Richter-like) is:

log₁₀(E) = 1.5 × M + 4.8

Solving for E yields

E = 10^(1.5 M + 4.8) (joules)

This relation is approximate and intended to give order-of-magnitude energy estimates. It has been used historically to illustrate the energy released by earthquakes; however there are multiple magnitude scales (local Richter, surface-wave, body-wave and moment magnitude Mw), and careful energy budgeting of an earthquake relies on seismic moment and moment magnitude rather than simple empirical formulas.

Why logarithms? — a short intuition

Energy release from earthquakes spans enormous ranges: small microseismic events release joules or less, while the largest megathrust quakes release >10^18 joules. A logarithmic scale compresses this range into manageable magnitudes roughly between 0 and 10. The factor 1.5 in the formula encodes that an increase of 1 magnitude corresponds roughly to a 10^(1.5) ≈ 31.6-fold increase in energy.

Converting energy to TNT equivalents

People often like to express seismic energy in “TNT equivalents” to build intuition. Standard conversion factors are:

• 1 kiloton of TNT ≈ 4.184 × 10^12 J
• 1 megaton of TNT ≈ 4.184 × 10^15 J

So if an earthquake releases 4.184 × 10^15 J, that is about 1 megaton of TNT in energy terms. Note: the mechanisms and timescales differ — seismic energy is spread over seconds to minutes across Earth’s crust, while a nuclear detonation releases energy extremely rapidly at a point; the analogy is purely for energy magnitude comparison.

Examples of famous earthquakes (magnitude and approximate energy)

Below are representative approximations using the relation above. Values are approximate — used here for intuitive comparison.

• 1960 Great Chile Earthquake — M 9.5
  log10 E = 1.5×9.5 + 4.8 = 19.05 → E ≈ 1.12 × 10^19 J (≈ 2.7 megatons TNT). This remains the largest recorded instrumentally.
• 2004 Sumatra–Andaman Earthquake — M 9.1–9.3
  For M=9.1: log10 E ≈ 18.45 → E ≈ 2.82 × 10^18 J (≈ 0.67 megaton TNT). For M=9.3 energy is larger.
• 2011 Tōhoku (Japan) Earthquake — M 9.1
  M=9.1 → E ≈ 2.82 × 10^18 J (≈ 0.67 megaton TNT). The devastating tsunami was responsible for massive destruction; the energy number helps show physical scale but does not capture all destructive mechanisms.
• 2010 Haiti Earthquake — M 7.0
  log10 E = 1.5×7.0 + 4.8 = 15.3 → E ≈ 1.99 × 10^15 J (≈ 0.000476 megaton ≈ 0.476 kiloton TNT). This energy, concentrated near populated areas and with shallow depth, caused catastrophic damage.
• 1994 Northridge (California) — M 6.7
  M=6.7 → log10 E ≈ 14.85 → E ≈ 7.08 × 10^14 J (≈ 0.169 kiloton TNT).

These examples show how energy grows rapidly with magnitude: the Chile M9.5 event released on the order of 10^19 joules, while a damaging M7.0 event releases ~10^15 joules — a factor of about 10,000 difference in energy.

Richter vs moment magnitude (Mw) and energy

Modern seismology prefers moment magnitude (Mw) for large events because it is based on seismic moment (a physics-based measure of fault slip and area) and scales uniformly for the largest earthquakes. Magnitude-energy empirical relations are useful for quick estimates; moment magnitude can be related to seismic moment M0 (in N·m) via:

Mw = (2/3) log10(M0) − 6.07

Seismic moment M0 can be converted to the radiated seismic energy with more detailed models; this calculator focuses on the simpler log10 E = 1.5 M + 4.8 relation for intuitive estimates.

Limitations and cautions

Use the magnitude-energy conversions for order-of-magnitude intuition only. The empirical relation's constants can vary with dataset and scale. Also, the fraction of total tectonic energy that is radiated seismically (radiated seismic energy) is typically a small portion of the total strain energy involved in faulting; estimates differ by event. Always rely on seismological analyses for precise energy budgets.

Practical uses

Quick energy estimates are useful for public communication ("this quake released energy comparable to X kilotons of TNT") and for classroom demonstrations illustrating the enormous energies involved. Engineers and seismologists, however, will use seismic moment, spectral analysis and rupture models for detailed hazard assessment.

How to use this calculator

1. To compute energy from magnitude: enter a magnitude (M) and choose an energy unit (J, MJ, kilotons TNT, etc.). Click Compute.
2. To estimate magnitude from energy: enter an energy value and its unit, and click Compute Magnitude. The result is an approximate magnitude equivalent using the inverse empirical formula.
3. Enable “Show step-by-step” to see the intermediate logarithms and conversions and export results to CSV for reports.

This calculator is educational — it helps convert between commonly used measures of earthquake size and provides context with TNT-equivalent and famous quake examples. For accurate seismological analysis use peer-reviewed data and seismological agency reports.