Earthquake Magnitude and Energy Calculator

Magnitude and Intensity Are Different Numbers

Every earthquake gets one magnitude, a measure of its size at the source. Intensity is how hard the ground shook at a particular place, so one earthquake has many intensities. USGS says intensity varies “depending mostly on the distance from the fault rupture area.” In the United States intensity is reported on the Modified Mercalli Intensity (MMI) scale, written in Roman numerals. This calculator works with magnitude only. It cannot tell you what a given town felt.

Depth matters as much as size. USGS points out that the M6.7 Northridge, California earthquake of 1994 shook harder, and over a wider area, than the slightly larger M6.8 Nisqually, Washington earthquake. Northridge started 3 to 11 miles down and Nisqually 30 to 36 miles down.

The Formulas Behind the Energy Numbers

Modern magnitudes are moment magnitudes (Mw). They start from the seismic moment, Mo = rigidity × fault area × slip, which is a measure of how much rock moved and how far. Hanks and Kanamori defined the scale in 1979. In the form USGS gives, with Mo in newton-meters:

• Moment from magnitude: Mw = ⅔ (log₁₀ Mo − 9.1), so Mo = 10^(1.5 Mw + 9.1) N·m.
• Radiated energy: USGS lists log₁₀ E = 11.8 + 1.5 M with E in ergs. One erg is 10⁻⁷ joule, so in joules log₁₀ E = 1.5 M + 4.8.
• Comparing two quakes: energy ratio = 10^(1.5 × magnitude difference) and wave amplitude ratio = 10^(magnitude difference).

The two relations agree. Kanamori (1977) estimated the energy of a great earthquake as about Mo ÷ 20,000. Applying that to 10^(1.5M + 9.1) gives 10^(1.5M + 4.8) again.

Worked example, M7.0 against M6.0. The gap is 1.0. Energy ratio = 10^1.5 = 31.6, which is the “32 times” USGS quotes. Amplitude ratio = 10^1 = 10. The M7.0 has a moment of 3.98 × 10¹⁹ N·m and radiates about 2.00 × 10¹⁵ J. Dividing by 4.184 × 10⁹ J per ton of TNT (NIST) gives 476.9 kilotons. The M6.0 has 1.26 × 10¹⁸ N·m and 6.31 × 10¹³ J, about 15.1 kilotons of TNT. It takes about 32 M6.0 earthquakes to release the energy of one M7.0.

Ten Times the Shaking Record, About 32 Times the Energy

Both numbers are true, and they measure different things. A one-unit step means the waves on a seismogram are 10 times taller. The energy behind those waves grows faster, by 10^1.5, about 31.6. Two steps multiply: M7.0 against M5.0 is 1,000 times the energy (about 32 × 32) and 100 times the amplitude. Three steps, M7.0 against M4.0, is 31,623 times the energy. Older USGS material rounds the per-step factor to 31; the newer page says 32. Both are 10^1.5 rounded.

The same USGS page also gives a rougher conversion, log E = 5.24 + 1.44 Mw, without stating units. A slope of 1.44 would mean about 27.5 times per step. This calculator uses the 1.5 slope, which matches the USGS “How Much Bigger” calculator and the 32-times rule.

Energy, Moment and TNT by Magnitude

A small M3.0 releases about 476.9 kg of TNT equivalent. Each full step multiplies that by about 32. Historical magnitudes come from the USGS list of preferred magnitudes (revised June 2013); the 1700 Cascadia event is an estimate from tsunami records in Japan.

Famous Earthquakes Compared

The first row reproduces the USGS “How Much Bigger” calculator, which reports 794.328 times bigger and 22387.211 times stronger for M8.7 against M5.8. A Cascadia-size M9 would release about 2,818 times the energy of Northridge. Yet the last row is the reminder about intensity: Nisqually released about 1.4 times Northridge’s energy, but Northridge did more shaking where people lived.

Moment Magnitude vs the Richter Scale

The local magnitude (ML) that Richter and Gutenberg defined in 1935 was built for local earthquakes. USGS lists its useful range as about 2.0 to 6.5 and says it is “not commonly used anymore, except for small earthquakes recorded locally.” For large quakes, older scales stop growing when the rupture is longer than the seismic waves used to measure it. Kanamori’s 1977 paper describes this “saturation”, and moment magnitude was designed to avoid it. News reports that say “on the Richter scale” almost always mean a USGS moment magnitude.

Common Mistakes

• Treating a magnitude 8 as twice a magnitude 4. The scale is logarithmic. Four steps is 10,000 times the amplitude and about a million times the energy.
• Using 10 times for energy. Ten times is amplitude. Energy is about 32 times per step.
• Expecting magnitude to predict damage. Depth, distance, soil and building quality decide the shaking and the damage.
• Reading TNT figures as explosive force at your house. The energy is released along the whole rupture and spread over a wide area, not concentrated at one point.
• Mixing magnitude types. Some reports give a different type, such as ML or mb, and early magnitudes can be revised. Compare final Mw values when you can.

What These Numbers Do Not Tell You

The energy here is an estimate from magnitude, not a measurement. USGS also estimates radiated energy directly from seismograms (the energy magnitude, Me), so treat the figure here as an approximation. The calculator does not estimate intensity at a location, aftershock chances, tsunami risk or building damage. For a real event, the USGS event page gives the final magnitude and maps of the shaking. For preparedness, follow your state or local emergency management agency.

Frequently Asked Questions

How to Use This Calculator

1. Enter the larger magnitude — use the moment magnitude (Mw) from the USGS event page; the default is 7.0.
2. Enter the smaller magnitude — the default is 6.0; the order does not matter, the calculator puts the larger first.
3. Read the ratios — energy ratio (about 32 per step) and wave amplitude ratio (10 per step).
4. Check the absolute numbers — seismic moment in newton-meters and radiated energy in joules and tons of TNT for each quake.