Moment Magnitude Calculator
Convert between seismic moment and moment magnitude: Mw = ⅔ · log₁₀(M₀) − 10.7. Solve for Mw, M₀, or the moment from fault geometry.
Inputs
Choose what to solve for, then fill in the fields. Scientific notation such as 4e19 or 1.5e22 is accepted. Units convert automatically.
Results
Enter values and press Calculate. Your answer will appear here.
Fault geometry
The seismic moment is the product of the shear modulus, the ruptured fault area and the average slip: M₀ = μ · A · D. The area is the along-strike length times the down-dip width.
Magnitude vs. seismic moment
On a log axis for M₀ the relation is a straight line of slope 1.5 in (Mw, log M₀) space. Each whole magnitude step multiplies the seismic moment by 101.5 ≈ 31.6, and the radiated energy by the same factor.
What is being calculated
Notable earthquakes
| Event | Year | Mw | M₀ (N·m) | Energy |
|---|
M₀ and energy computed from the listed Mw with the same engine. Published values vary by a few tenths of a magnitude unit depending on the inversion.
Magnitude ladder
| Mw | Seismic moment M₀ | Radiated energy Es | TNT equivalent |
|---|
Every step of 1.0 in Mw multiplies M₀ by 31.6 and Es by 31.6. Every step of 0.2 — the usual rounding on bulletin reports — is a factor of about 2.
Key relations and unit conversions
| Quantity | Relation |
|---|---|
| Moment magnitude | Mw = ⅔ log₁₀(M₀) − 10.7 [M₀ in dyn·cm] |
| Moment magnitude, SI | Mw = ⅔ log₁₀(M₀) − 6.03 [M₀ in N·m] |
| IASPEI standard | Mw = ⅔ (log₁₀ M₀ − 9.1) [M₀ in N·m] |
| Seismic moment | M₀ = μ · A · D |
| Radiated energy | log₁₀ Es = 1.5 Mw + 4.8 [Es in J] |
| Energy from moment | Mw = ⅔ log₁₀ Es − 3.2 |
| Moment ratio per Mw unit | ΔM₀ = 101.5 ≈ 31.62 |
| Energy ratio per Mw unit | ΔEs = 101.5 ≈ 31.62 |
| Seismic moment units | 1 N·m = 10⁷ dyn·cm · 1 dyn·cm = 10⁻⁷ N·m |
| Energy units | 1 J = 10⁷ erg · 1 t TNT = 4.184 × 10⁹ J · 1 kt = 4.184 × 10¹² J |
| Magnitude saturation | ML ≈ 7 · mb ≈ 6.5–7 · Ms ≈ 8.3–8.5 · Mw never saturates |
| Typical shear modulus | crust 30 GPa · mantle 60–70 GPa · sediments 5–15 GPa |
Formula
- Mw: moment magnitude, dimensionless
- M₀: seismic moment, in dyn·cm (or N·m with the constant −6.03)
- μ: shear modulus of the rock, ≈ 30 GPa for the crust
- A: ruptured fault area, A = L × W
- D: average slip across the fault plane
Example — Tōhoku 2011. Published M₀ ≈ 5.0 × 10²² N·m. In dyn·cm that is 5.0 × 10²⁹ dyn·cm. Then Mw = ⅔ log₁₀(5.0 × 10²⁹) − 10.7 = ⅔ (29.70) − 10.7 = 19.80 − 10.7 = 9.10.
The moment magnitude was introduced by Kanamori in 1977 precisely because the older scales saturate. Surface-wave magnitude Ms stops growing above about 8.3, and body-wave magnitude mb above about 6.5, because the waves they measure have periods short enough to be radiated by only part of a very large rupture. The seismic moment, by contrast, is a static property of the whole rupture and keeps growing without bound, so Mw remains meaningful for the largest events ever recorded.
The seismic moment itself has a direct physical meaning: it is the product of the shear modulus of the rock, the area that ruptured, and the average slip on that area. Doubling any of the three doubles M₀, which adds ⅔ log₁₀(2) ≈ 0.20 to Mw. That is why a fault with twice the length produces only about 0.2 more magnitude — the scale is logarithmic and compresses enormous physical differences into small numerical ones.
The radiated energy is a different quantity. Only a small fraction of the elastic energy released by an earthquake leaves as seismic waves; the rest goes into friction and fracture. The empirical Gutenberg–Richter relation log₁₀ Es = 1.5 Mw + 4.8 gives the seismic part in joules, and because the coefficient 1.5 matches the moment relation, energy and moment grow at the same rate with magnitude.
Advanced mode also reports the radiated energy Es, the TNT equivalent, the fault area and the average stress drop when the fault parameters are supplied, plus the full set of moment and energy unit conversions.
References
- Wikipedia, Moment magnitude scale: definition, the −10.7 constant and the SI form
- Wikipedia, Seismic moment: M₀ = μ A D and its units
- Wikipedia, Kanamori energy equation: log Es = 1.5 Mw + 4.8
- Wikipedia, Seismic magnitude scales: saturation of ML, mb and Ms
- NIST SP 811, Guide for the Use of the SI: unit conversion factors
How to Use This Tool
- Choose what to solve for: Mw from M₀, M₀ from Mw, or Mw from fault geometry.
- Pick a preset, or type the known value and choose its unit.
- In Advanced, check the radiated energy, TNT equivalent and full unit conversions.
- Click Calculate.
- Read the highlighted answer, then check the fault diagram and the magnitude–moment chart.
What This Tool Offers
- Solves Mw = ⅔ log₁₀ M₀ − 10.7 for Mw, M₀ or the fault parameters
- Automatic unit conversion for seismic moment and radiated energy
- Moment computed from fault length, width, slip and shear modulus
- Radiated energy and TNT equivalent
- Scaled fault diagram and a magnitude–moment chart with slope 1.5
- Notable earthquake table and a full magnitude ladder
- Ready-made presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Mw | Moment magnitude | |
| M0 | Seismic moment | dyne*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| Parameter | Value |
|---|---|
| M₀ (dyne·cm) | 1.0e26 |
| Parameter | Value |
|---|---|
| M₀ | 1.0e29 |
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
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