Moment Magnitude Calculator

Find earthquake moment magnitude (Mw) and seismic moment from fault rupture length, width, average slip, and crustal shear modulus.

🌍 Moment Magnitude Calculator
Shear modulus (μ)
GPa
Fault length (L)
km
Fault width (W)
km
Average slip (D)2 m
m
0.0115
Moment magnitude (Mw)
—
Seismic moment (M0)
—
Rupture area
—
Step-by-step working

🌍 What is Moment Magnitude?

Moment magnitude (Mw) is the modern standard scale for reporting earthquake size, based directly on the physical seismic moment released by fault rupture rather than a single seismogram's amplitude. It is computed as Mw = (2/3) x (log10(M0) - 9.1), where the seismic moment M0 = mu x A x D combines crustal shear modulus, rupture area, and average fault slip.

Seismologists rely on moment magnitude to report the size of significant earthquakes, especially large ones, compare earthquake energy release across a global catalog on a consistent basis, and relate observed fault geometry (from aftershocks, satellite deformation, or field mapping) directly to earthquake size using real physical rupture parameters.

A common point of confusion is treating moment magnitude and local (Richter) magnitude as interchangeable at all sizes. They agree closely for moderate earthquakes, but local magnitude saturates (stops growing accurately) above roughly magnitude 6.5 to 7, while moment magnitude, being based on physical rupture, remains accurate even for the largest recorded earthquakes (magnitude 9 and above).

This calculator computes seismic moment and moment magnitude from your fault's shear modulus, rupture length, rupture width, and average slip, and plots how moment magnitude grows with average slip at fixed fault dimensions.

📐 Formula

M0 = μAD      Mw = (2/3)(log10(M0) − 9.1)
μ = shear modulus (Pa), A = rupture area = L×W (m²)
D = average slip (m), M0 = seismic moment (N·m)
Example: μ = 30 GPa, L = 50 km, W = 15 km, D = 2 m → M0 ≈ 4.5×1019 N·m, Mw ≈ 7.04.

📖 How to Use This Calculator

Steps

1
Enter the crustal shear modulus. Type the shear modulus of the crust, typically around 30 to 32 GPa, in gigapascals.
2
Enter the fault length and width. Type the rupture's length and width, both in kilometers.
3
Enter the average slip. Type the average displacement (slip) across the ruptured fault, in meters.

💡 Example Calculations

Example 1 — Moderate Large Earthquake

μ = 30 GPa, L = 50 km, W = 15 km, D = 2 m

1
A = 50×15 = 750 km²
2
M0 = 3×1010 × 7.5×108 × 2 = 4.5×1019 N·m
Mw = (2/3)(19.653−9.1) = 7.04
Try this example →

Example 2 — Moderate Regional Earthquake

μ = 30 GPa, L = 10 km, W = 8 km, D = 0.5 m

1
A = 10×8 = 80 km²
2
M0 = 1.2×1018 N·m
Mw = 5.99
Try this example →

Example 3 — Great Subduction Earthquake

μ = 32 GPa, L = 200 km, W = 40 km, D = 8 m

1
A = 200×40 = 8,000 km²
2
M0 = 2.048×1021 N·m
Mw = 8.14 (a great earthquake, comparable to major subduction zone events)
Try this example →

❓ Frequently Asked Questions

What is moment magnitude (Mw)?+
Moment magnitude is a logarithmic earthquake size scale based directly on the physical seismic moment released by fault rupture, rather than on a single seismogram's amplitude. It is the modern standard scale for reporting earthquake size, especially for large earthquakes where older scales like local (Richter) magnitude become inaccurate.
What is the formula for moment magnitude?+
Mw = (2/3) x (log10(M0) - 9.1), where M0 is the seismic moment in newton-meters. Seismic moment itself is M0 = mu x A x D, the product of crustal shear modulus, fault rupture area, and average slip distance across the fault.
What is seismic moment?+
Seismic moment (M0) is a direct physical measure of the total energy released by fault rupture, computed as the product of the rock's shear modulus (rigidity), the rupture area (fault length times width), and the average slip (displacement) across that ruptured area.
Why is moment magnitude preferred over the Richter scale for large earthquakes?+
Local (Richter) magnitude is based on a single seismogram's peak amplitude, which stops growing meaningfully once the fault rupture becomes very large relative to the seismic wavelengths being measured, a phenomenon called saturation. Moment magnitude, based on the physical rupture itself, does not saturate and remains accurate for the largest recorded earthquakes.
How much does seismic moment increase per unit of magnitude?+
Since Mw = (2/3)*log10(M0) plus a constant, each one-unit increase in Mw corresponds to a 10^1.5, or about 31.6-fold, increase in seismic moment. This compounds quickly: a magnitude 9 earthquake releases roughly 31.6 squared, or about 1000 times more seismic moment than a magnitude 7.
What is a typical shear modulus value for Earth's crust?+
Continental crust typically has a shear modulus around 30 to 32 GPa (gigapascals). This value can vary somewhat with rock type, temperature, and depth, deeper or denser rock generally has a somewhat higher shear modulus.
How is rupture area estimated for a real earthquake?+
Seismologists estimate rupture length and width from aftershock distributions, surface fault rupture mapping, InSAR satellite deformation data, or finite-fault seismic inversion. This calculator takes length and width as direct inputs, matching how these physical measurements are typically reported.
Can this calculator be used in reverse, going from magnitude to fault size?+
Not directly, this calculator computes moment magnitude forward from physical fault parameters. Estimating fault dimensions from a known magnitude requires separate empirical scaling relationships (such as Wells and Coppersmith 1994), which relate magnitude statistically to typical rupture length, width, and displacement for different fault types.
What is the largest moment magnitude ever recorded?+
The 1960 Valdivia earthquake in Chile holds the record at approximately Mw 9.4 to 9.6, the largest instrumentally recorded earthquake. Its rupture zone extended roughly 1,000 kilometers along the Chilean coast, illustrating just how large fault rupture area becomes for the very largest earthquakes.
What units does this calculator use?+
Shear modulus is entered in gigapascals (GPa), fault length and width in kilometers, and average slip in meters. Seismic moment is reported in newton-meters (N*m), and moment magnitude is a dimensionless number on the standard Mw scale.
Tags: Moment Magnitude Calculator Seismic Moment Calculator Earthquake Magnitude Calculator Mw Calculator Fault Rupture Calculator Calculator Formula Free Online

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What is moment magnitude (Mw)?

Moment magnitude is a logarithmic earthquake size scale based directly on the physical seismic moment released by fault rupture, rather than on a single seismogram's amplitude. It is the modern standard scale for reporting earthquake size, especially for large earthquakes where older scales like local (Richter) magnitude become inaccurate.

What is the formula for moment magnitude?

Mw = (2/3) x (log10(M0) - 9.1), where M0 is the seismic moment in newton-meters. Seismic moment itself is M0 = mu x A x D, the product of crustal shear modulus, fault rupture area, and average slip distance across the fault.

What is seismic moment?

Seismic moment (M0) is a direct physical measure of the total energy released by fault rupture, computed as the product of the rock's shear modulus (rigidity), the rupture area (fault length times width), and the average slip (displacement) across that ruptured area.

Why is moment magnitude preferred over the Richter scale for large earthquakes?

Local (Richter) magnitude is based on a single seismogram's peak amplitude, which stops growing meaningfully once the fault rupture becomes very large relative to the seismic wavelengths being measured, a phenomenon called saturation. Moment magnitude, based on the physical rupture itself, does not saturate and remains accurate for the largest recorded earthquakes.

How much does seismic moment increase per unit of magnitude?

Since Mw = (2/3)*log10(M0) plus a constant, each one-unit increase in Mw corresponds to a 10^1.5, or about 31.6-fold, increase in seismic moment. This compounds quickly: a magnitude 9 earthquake releases roughly 31.6 squared, or about 1000 times more seismic moment than a magnitude 7.

What is a typical shear modulus value for Earth's crust?

Continental crust typically has a shear modulus around 30 to 32 GPa (gigapascals). This value can vary somewhat with rock type, temperature, and depth, deeper or denser rock generally has a somewhat higher shear modulus.

How is rupture area estimated for a real earthquake?

Seismologists estimate rupture length and width from aftershock distributions, surface fault rupture mapping, InSAR satellite deformation data, or finite-fault seismic inversion. This calculator takes length and width as direct inputs, matching how these physical measurements are typically reported.

Can this calculator be used in reverse, going from magnitude to fault size?

Not directly, this calculator computes moment magnitude forward from physical fault parameters. Estimating fault dimensions from a known magnitude requires separate empirical scaling relationships (such as Wells and Coppersmith 1994), which relate magnitude statistically to typical rupture length, width, and displacement for different fault types.

What is the largest moment magnitude ever recorded?

The 1960 Valdivia earthquake in Chile holds the record at approximately Mw 9.4 to 9.6, the largest instrumentally recorded earthquake. Its rupture zone extended roughly 1,000 kilometers along the Chilean coast, illustrating just how large fault rupture area becomes for the very largest earthquakes.

What units does this calculator use?

Shear modulus is entered in gigapascals (GPa), fault length and width in kilometers, and average slip in meters. Seismic moment is reported in newton-meters (N*m), and moment magnitude is a dimensionless number on the standard Mw scale.

📌 Quick Tips

💡Moment magnitude is the modern standard scale for reporting earthquake size, especially for large events, unlike local (Richter) magnitude, it does not saturate at high values, since it's based directly on the physical rupture rather than a single seismogram's amplitude.
💡Seismic moment M0 = mu x A x D grows with rupture area and slip, both of which scale up dramatically for larger earthquakes, this is why the largest earthquakes (M8-M9+) rupture faults hundreds of kilometers long.
💡Typical crustal shear modulus is around 30 to 32 GPa for continental crust; the value can differ somewhat by rock type and depth, always check the specific study or dataset if precision matters.
💡Every one-unit increase in moment magnitude corresponds to roughly a 32-fold increase in seismic moment (and radiated energy), which is why the difference between a magnitude 7 and magnitude 9 earthquake, only 2 units apart, represents roughly a thousand-fold difference in size.
💡This calculator computes seismic moment from fault geometry (a forward calculation), the reverse (estimating fault dimensions from an observed magnitude) requires additional scaling relationships (like Wells and Coppersmith 1994) beyond this calculator's scope.