Geology & Earth ScienceSeismologyUniversity
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Moment Magnitude (Mw) Calculator

Modern measure of earthquake size based on seismic moment.

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Magnitude

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Overview

The Moment Magnitude scale (Mw) is a logarithmic measurement used in seismology to quantify the total energy released by an earthquake. It is based on the seismic moment (M₀), which accounts for the physical properties of the fault including the rock's rigidity, the rupture area, and the average displacement.

Symbols

Variables

= Magnitude, = Seismic Moment

Magnitude
Variable
Seismic Moment
dyne-cm

Apply it well

When To Use

When to use: Apply this formula when you need to calculate the magnitude of an earthquake based on its seismic moment, particularly for large events where the local magnitude (Richter) scale becomes inaccurate. It is the standard for quantifying tectonic events globally, assuming the rupture occurs in elastic rock media.

Why it matters: This equation provides a physically meaningful assessment of an earthquake's impact, allowing engineers and emergency planners to understand the scale of crustal deformation. Unlike older scales, it does not saturate at high magnitudes, making it essential for recording 'mega-thrust' earthquakes that release massive amounts of energy.

Avoid these traps

Common Mistakes

  • Using N-m instead of dyne-cm if the constant 10.7 or 6.0 is different.
  • Convert units and scales before substituting, especially when the inputs mix dyne-cm.
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

A seismograph records an earthquake with a seismic moment (M0) of 1.0 × 10²⁴ dyne-cm. Calculate the Moment Magnitude (Mw) for this event.

Seismic Moment1e+24 dyne-cm

Solve for: Mw

Hint: First, find the base-10 logarithm of 10²⁴, multiply by 2/3, and then subtract 10.7.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Moment magnitude scale
  2. Britannica: Moment magnitude scale
  3. Kanamori, H. (1977). The energy release in great earthquakes. Journal of Geophysical Research, 82(29), 2981-2987.
  4. Hanks, T.C.; Kanamori, H. (1979). "A moment magnitude scale". Journal of Geophysical Research. 84 (B5): 2348-2350.
  5. Moment Magnitude Scale, Wikipedia
  6. An Introduction to Seismology, Earthquakes, and Earth Structure, Seth Stein and Michael Wysession
  7. The Seismic Moment Magnitude Scale, Hiroo Kanamori, Journal of Geophysical Research, 1977
  8. USGS Earthquake Glossary