Moment magnitude Mw calc (fault→M0→Mw)

Example preset

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Inputs

Fault length L (km)

Fault width W (km)

Average slip D (m)

Rigidity modulus μ (GPa)

Results

Moment magnitude Mw

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Seismic moment M0

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Calculation procedure

Assumptions & limits

This is an educational approximation based on a rectangular fault model (A=L×W) and simplified with uniform slip and constant rigidity.
Use this tool as a learning estimate and verify hazard-related decisions with official and professional sources.
M0 has the same dimension as N m (J), but it is not the radiant energy itself.
The offset of the Mw formula uses k=6.06 (there are slight differences depending on literature and customs).

FAQ

What is M0 (earthquake moment)?

It is an index of earthquake scale estimated from fault area, average slip, and rigidity.

What is Mw (moment magnitude)?

This is a logarithmically scaled magnitude of M0, and is an index that is difficult to saturate even in large earthquakes.

Is M0 earthquake energy?

Although the dimensions are the same, it is not the radiant energy itself.

What is dyne·cm?

This is the unit used to express seismic moment in the CGS unit system. 1 N·m = 10^7 dyne·cm.

How should I choose the rigidity value?

Use the rigidity given in your lesson or reference sheet when possible. If you are comparing scenarios, keep the rigidity fixed and change only one fault parameter at a time.

How to interpret Mw and M0

What this page calculates

This page converts fault length, width, average slip, and rigidity into seismic moment M0 and moment magnitude Mw. It can also convert between M0 and Mw directly or solve for one missing fault parameter in a classroom setting.

Suggested workflow

Start with one reference scenario from your lesson or handout. Change only one fault parameter at a time so the effect on M0 and Mw stays easy to explain.

What to verify before using the result

Keep the length and width units in kilometres, slip in metres, and rigidity in gigapascals. If you compare two cases, make sure the same formula convention and Mw offset are used in both runs.

Important limits

This is a simplified rectangular-fault model for learning. Real earthquakes involve geometry, rupture complexity, and source effects that this page does not model.

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