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Moment Magnitude Scale

Converts an earthquake's seismic moment into the moment magnitude scale, the modern standard for reporting large earthquake sizes.

Written by the Vorzep Team

GeologySeismologyEarthquakes

Moment Magnitude CalculatorMw from Seismic Moment

Mw = (2/3) · log10(M0) − 10.7
Mw = moment magnitude  ·  M0 = seismic moment (dyne·cm)
⟹ Solve⟷Mw, M0
dyne·cm
Mw
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Moment Magnitude—
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M0: —Mw: —
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Mw = (2/3) · log10(M0) − 10.7  ·  M0 in dyne·cm

Variables

SymbolQuantityUnit
MwMoment magnitude
M0Seismic momentdyne*cm

What it means

The Moment Magnitude (Mw) scale is the modern standard for measuring earthquake size, replacing the Richter scale for large earthquakes. It is based on the seismic moment M0 and is calculated using the formula given. The constant 10.7 is for M0 in dyne‑cm. Mw is proportional to the logarithm of the seismic moment and does not saturate for large events. It is used by the USGS and other agencies for reporting earthquake sizes. Understanding Mw is essential for seismologists, engineers, and the public to assess earthquake energy and potential damage.

Worked example

Moment Magnitude Scale – Two Detailed Examples

Real‑World
Scenario: A seismologist calculates the seismic moment of an earthquake as M₀ = 1.0×10²⁶ dyne·cm (where 1 N·m = 10⁷ dyne·cm). Using the moment magnitude formula Mw = (2/3)×log₁₀(M₀) − 10.7, they compute Mw = (2/3)×26 − 10.7 = 17.33 − 10.7 = 6.63 ≈ 6.6. This moment magnitude is consistent with a strong earthquake that can cause significant damage. The scientist reports this value to the global seismic network.
ParameterValue
M₀ (dyne·cm)1.0e26
1Mw = (2/3)×log₁₀(1.0e26) − 10.7 = (2/3)×26 − 10.7 = 17.33 − 10.7 = 6.633
Result Mw ≈ 6.6 ✓ Moment magnitude
Scenario: A great earthquake has M₀ = 1.0×10²⁹ dyne·cm. The moment magnitude is Mw = (2/3)×29 − 10.7 = 19.33 − 10.7 = 8.633 ≈ 8.6. This is a massive earthquake, capable of causing widespread destruction and generating tsunamis. The magnitude is used by disaster response agencies to mobilise international aid and coordinate rescue efforts.
ParameterValue
M₀1.0e29
1Mw = (2/3)×29 − 10.7 = 19.33 − 10.7 = 8.633
Result Mw ≈ 8.6 ✓ Great earthquake
Insight: The moment magnitude scale (Mw) is the most reliable scale for measuring large earthquakes. It is based on the seismic moment and does not saturate, unlike the Richter scale.

Common mistakes

  • Moment magnitude Mw: Mw = (2/3)·log₁₀(M₀) − 10.7 – M₀ in dyne·cm (or N·m with different constant).
  • Log base: Use log₁₀ – not natural log.
  • Constant 10.7: Valid when M₀ is in dyne·cm – for SI (N·m), use 6.0? Actually, check: with M₀ in N·m, the formula is Mw = (2/3)·log₁₀(M₀) − 6.0. But the given constant is 10.7 for dyne·cm (1 N·m = 10⁷ dyne·cm).
  • No saturation: Moment magnitude does not saturate for large earthquakes.
  • Comparable: Mw is the preferred scale for large earthquakes.

Applications

The moment magnitude scale, Mw = (2/3)·log₁₀(M₀) − 10.7, is the most reliable measure for large earthquakes, relating magnitude to seismic moment (M₀ in dyne‑cm). It does not saturate like the Richter scale and provides a consistent measure across all magnitudes. Seismologists use Mw to quantify the size of major earthquakes globally, as it directly reflects the rupture area and slip. It is used in seismic hazard analysis, building codes, and public information. By using Mw, scientists can compare historical and recent earthquakes consistently. This scale is now the standard for earthquake magnitude reporting in many regions.

  • Reporting of earthquake magnitudes by seismological agencies
  • Seismic hazard assessment and building code definition
  • Comparison of earthquake sizes for research and public awareness
  • Source physics studies and scaling laws
  • Educational understanding of modern magnitude scales