Earthquake Magnitude and Energy Calculator

How seismic moment, moment magnitude, and radiated energy are calculated

The U.S. Geological Survey (USGS) page "Earthquake Magnitude, Energy Release, and Shaking Intensity" starts from the fault break itself. Seismic moment is M0 = rigidity × area × slip. Rigidity (μ) is how stiff the rock is against shear. Area is the fault patch that broke, and slip is how far the two sides slid past each other. In metric units, pascals (N/m²) times square metres (m²) times metres (m) gives newton metres (N m).

From seismic moment in N m, the USGS sets moment magnitude as Mw = (2/3)(log₁₀ M0 − 9.1). In older cgs units of dyne cm, where 1 N m = 10⁷ dyne cm per NIST SP 811 Appendix B.8, the USGS "Magnitude Types" table writes 16.1 in place of 9.1. That shift is log₁₀(10⁷) = 7. Working backward from Mw gives M0 = 10^(1.5 Mw + 9.1) N m. If you have S-minus-P wave times from a chart instead, start in the earthquake epicenter distance calculator.

Next, the USGS estimates radiated wave energy in joules by log₁₀ E = 5.24 + 1.44 Mw. Thus E = 10^(5.24 + 1.44 Mw) J. This counts only the energy that leaves the fault as ground waves. Most stored rock strain turns into heat and crushed rock on the fault plane. To switch joules into kilowatt-hours, food calories, BTU, or therms, use the energy converter.

When you compare two quakes with gap ΔM = Mw,1 − Mw,2, three powers of 10 apply. Peak wave height on a seismogram grows by 10^(ΔM), so each whole unit is 10 times taller. Wave energy in the USGS equation grows by 10^(1.44 ΔM). That is 27.54 times per whole unit, or 5.25 times per half-unit (ΔM = 0.5). Seismic moment grows by 10^(1.5 ΔM), or 31.62 times per whole unit.

To compare quakes with blasts, the page also converts joules into tons of TNT. NIST SP 811 Appendix B.8 defines one ton of TNT as 4.184 × 10⁹ J (4.184 GJ), or 10⁹ calories. One kiloton of TNT is 4.184 × 10¹² J. One megaton of TNT is 4.184 × 10¹⁵ J.

USGS moment magnitude and radiated energy equations

M_0 = \mu A D \quad (\text{or } M_0 = 10^{1.5 M_w + 9.1}\text{ N m})
M_w = \frac{2}{3}(\log_{10} M_0 - 9.1) \quad (M_0\text{ in N m})
\log_{10} E = 5.24 + 1.44 M_w \implies E = 10^{5.24 + 1.44 M_w}\text{ J}
\text{TNT tons} = \frac{E}{4.184 \times 10^9\text{ J/ton}}, \quad \frac{E_1}{E_2} = 10^{1.44(M_{w,1} - M_{w,2})}

Worked examples: Mw 7.0 vs. Mw 6.0, fault rupture geometry, and Mw 8.7 vs. Mw 5.8

Default case (Mw 7.0 vs. Mw 6.0): An Mw 7.0 major quake has M0 = 10^19.6 ≈ 3.9811 × 10¹⁹ N m. Its USGS energy log is 15.32, so E ≈ 2.089 × 10¹⁵ J. That equals 499,400 tons of TNT (499.4 kilotons) or 580,400,000 kWh. An Mw 6.0 quake releases 7.586 × 10¹³ J (18,130 tons of TNT), so the Mw 7.0 quake has 10 times the wave height and the 1-unit energy and moment multiples shown above.

Moment and fault modes: If you enter M0 = 10²⁰ N m, the page finds Mw = (2/3)(20 − 9.1) ≈ 7.27 (7.2667). It radiates E ≈ 5.1 × 10¹⁵ J (5.058 × 10¹⁵ J, or 1.209 megatons of TNT). In fault mode, a 1,000 km² fault patch in 30 GPa rock with 1.33 m of slip gives M0 = 3 × 10¹⁰ N/m² × 10⁹ m² × 1.33 m = 3.99 × 10¹⁹ N m. That yields Mw ≈ 7.0006.

USGS Mw 8.7 vs. Mw 5.8 prompt: The USGS page asks how much bigger Mw 8.7 is than Mw 5.8. Here the gap is ΔM = 8.7 − 5.8 = 2.9. The Mw 8.7 quake has 10^2.9 ≈ 794.3 times the wave height. It releases 10^(1.44 × 2.9) ≈ 15,000 times the wave energy (5.861 × 10¹⁷ J, or 140.1 megatons of TNT, vs. 3.908 × 10¹³ J). Its seismic moment is 10^(1.5 × 2.9) ≈ 22,390 times as large.

Assumptions, agency constant differences, and physical limits

• The USGS calls its step from moment magnitude to energy a rough estimate. Its equation log₁₀ E = 5.24 + 1.44 Mw turns a moment magnitude into an estimate of the energy released, not a measured value.
• In fault mode, rock stiffness defaults to 30 GPa because the USGS page prints no single value. Setting it to 20 GPa for softer shallow rock lowers Mw by about 0.12 for the same area and slip. Setting it to 40 GPa for stiffer deep crust rock raises Mw by about 0.08.
• Magnitude gives source size at the fault, not local ground shaking (Mercalli levels I to XII). As the USGS notes, the shallow 1994 Northridge, CA quake (Mw 6.7, 5 to 18 km deep) shook homes harder than the deeper 2001 Nisqually, WA quake (Mw 6.8, 48 to 58 km deep). You can check sway periods and wave modes in the harmonic oscillator calculator and standing-wave calculator.

How to interpret earthquake magnitude, energy, and local shaking

Check expected aftershock counts for your mainshock: Big quakes trigger far more aftershocks than small ones. Send your mainshock size to the aftershock calculator. It finds expected M ≥ 3, M ≥ 4, and M ≥ 5 counts and odds over 1 to 30 days.

Look up building code ground motion for your site: Wall and frame loads depend on local shaking, not magnitude alone. Open the seismic design calculator. It finds ASCE 7 short-period (SDS) and 1-second (SD1) values and design classes A through F.

Use Mw rather than ML or Ms for large old quakes: Old reports often list local Richter ML (which clips near M 6.5) or surface-wave Ms (which clips near M 8.3). For great quakes like 1906 San Francisco (Ms 8.3, modern Mw 7.9) or 1960 Chile (Ms 8.5, modern Mw 9.5), always enter Mw.

Earthquake magnitude and energy questions