Seismic Moment and Moment Magnitude Calculator (Mw from Fault Size and Slip)
The moment magnitude of an earthquake from the size of the fault that ruptured, the average slip and the rigidity of the rock, with the seismic moment.
Results
Moment magnitude Mw
7.44
Seismic moment M₀
180.000
10¹⁸ N·m
Area of the rupture
2000
km²
The dashed line marks the value you entered.
What this tool does
Moment magnitude Mw measures how much a fault moved, not how the ground shook, and unlike the old Richter scale it does not saturate for the biggest earthquakes. The seismic moment is rigidity × rupture area × average slip, and Mw = ⅔ (log₁₀ M₀ − 9.1) with M₀ in newton-metres. Because of the logarithm, each step of one magnitude means about 32 times more energy released, and a rupture twice as long and wide with twice the slip is worth about 0.6 of a magnitude more.
Formula
M₀ = μ × A × D · M_w = ⅔ (log₁₀ M₀ − 9.1) (M₀ in N·m)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
lk | Length of the rupture along the fault | km |
wk | Width of the rupture (down the dip of the fault) | km |
sl | Average slip on the fault | m |
mu | Rigidity of the rock (shear modulus; about 30 GPa in the crust) | GPa |
MW | Moment magnitude Mw | — |
M0 | Seismic moment M₀ | 10¹⁸ N·m |
AR | Area of the rupture | km² |
Worked example
- Length of the rupture along the fault100 km
- Width of the rupture (down the dip of the fault)20 km
- Average slip on the fault3 m
- Rigidity of the rock (shear modulus; about 30 GPa in the crust)30 GPa
- Moment magnitude Mw7.44
- Seismic moment M₀180.000 10¹⁸ N·m
- Area of the rupture2000 km²
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.