Calculator Inputs
Formula Used
Moment magnitude from seismic moment (with M0 in N·m):
If you compute M0 from fault properties:
Unit note: 1 dyne·cm = 10⁻⁷ N·m. When using dyne·cm, this page converts to N·m before applying the Mw formula.
How to Use This Calculator
- Select a method: direct moment input or fault parameters.
- Enter values with correct units and realistic ranges.
- Choose Mw decimals and optional energy estimate.
- Press Calculate to display Mw above the form.
- Use CSV or PDF buttons to export your results.
Example Data Table
| Example | Input type | Inputs | Computed Mw |
|---|---|---|---|
| A | Direct M0 | M0 = 1.0e19 N·m | ~ 6.60 |
| B | Direct M0 | M0 = 5.0e21 N·m | ~ 8.40 |
| C | Fault parameters | μ=30 GPa, L=40 km, W=15 km, D=2 m | ~ 6.97 |
Technical Article: Understanding Moment Magnitude Outputs
1) What the moment magnitude scale represents
Moment magnitude (Mw) is a logarithmic measure linked to the earthquake source, not how strongly it felt at one location. It is derived from seismic moment (M0), which captures the product of rock rigidity, rupture area, and average slip. Because the scale is logarithmic, a small Mw change reflects a large physical change.
2) Seismic moment input and unit handling
This calculator accepts M0 in N·m or dyne·cm. The conversion is fixed: 1 dyne·cm = 10−7 N·m. Many catalogs report M0 in scientific notation, such as 3.2×1018 N·m. Internally, all calculations use N·m before applying the Mw relationship, keeping the constant consistent.
3) Fault-parameter method with realistic ranges
When M0 is not known, you can estimate it from fault parameters using M0 = μ·(L·W)·D. Typical crustal rigidity values are 20–40 GPa (2.0×1010–4.0×1010 Pa). Length and width are often in kilometers, while slip is in meters or centimeters. Conversions in this tool standardize everything to pascals and meters.
4) The Mw equation used by this calculator
Mw is computed with Mw = (2/3)·(log10(M0) − 9.1) for M0 measured in N·m. The 9.1 offset is a calibration constant used in the standard Hanks–Kanamori scaling for SI units. If you compare sources, ensure they use the same M0 unit and constant to avoid systematic shifts.
5) What a 1.0 increase in Mw implies
Because Mw is logarithmic and tied to M0, an increase of 1.0 in Mw corresponds to roughly 101.5 ≈ 31.6 times larger seismic moment. That is why Mw 7.0 events are vastly larger than Mw 6.0 events. Use the decimals setting to format results, but remember that input uncertainty often dominates the final precision.
6) Optional energy estimate and TNT equivalent
If enabled, the tool provides an empirical radiated-energy estimate using log10(E[J]) = 1.5·Mw + 4.8. It also converts energy to a TNT equivalent with 1 ton TNT ≈ 4.184×109 J. These values are approximations; real energy release depends on rupture efficiency, depth, and wave attenuation.
7) Interpreting example-sized calculations
As a guide, M0 ≈ 1019 N·m gives Mw ≈ 6.60, while M0 ≈ 5×1021 N·m gives Mw ≈ 8.07. For a fault estimate, μ=30 GPa, L=40 km, W=15 km, and D=2 m yields M0 around 3.6×1019 N·m, placing the event in the mid‑7 range after scaling.
8) Quality checks before downloading reports
Before exporting to CSV or PDF, verify that length and width describe the actual rupture area (not the mapped fault trace) and that slip is an average over that area. Keep units consistent, avoid mixing cm and m unintentionally, and save multiple runs to compare scenarios side‑by‑side using the session history exports.
FAQs
1) Is Mw the same as the Richter magnitude?
No. Richter magnitude is based on waveform amplitude for specific instruments and distances. Mw is derived from seismic moment and better reflects the physical size of large earthquakes without saturating as quickly.
2) Can I enter seismic moment in dyne·cm?
Yes. The calculator converts dyne·cm to N·m using 1 dyne·cm = 10−7 N·m, then applies the standard Mw scaling constant for SI units.
3) Why does my Mw look unexpectedly high?
Check unit conversions first. A common issue is entering kilometers as meters, or centimeters as meters. Also confirm that length and width represent the ruptured area, not an entire fault system.
4) What rigidity value should I use for fault-based estimates?
A common starting range is 20–40 GPa for crustal rock, but it varies by lithology, temperature, and depth. If you have regional studies, use their preferred rigidity for better consistency.
5) What does the energy estimate represent?
It is an empirical approximation of radiated seismic energy, not total strain energy. Different earthquakes with the same Mw can radiate different energy depending on rupture dynamics and stress drop.
6) What is the benefit of saving results in session history?
Saving builds a local table of runs, enabling multi-record exports. This is useful for sensitivity checks, comparing fault scenarios, and producing a single CSV or PDF report of all saved calculations.
7) Can this replace a full seismological inversion?
No. It provides quick, transparent estimates based on standard scaling relations. Professional studies may use waveform inversion, finite-fault models, and regional corrections to refine M0, Mw, and uncertainty.
Professional Notes on Moment Magnitude Calculations
1) What Mw measures
Mw is a logarithmic scale tied to the earthquake source. It is computed from seismic moment M0, which represents the torque-like strength of faulting. Because Mw is based on M0, it avoids the saturation that affects some older magnitude measures for very large events.
2) Seismic moment inputs and units
This calculator accepts M0 in N·m or dyne·cm and converts everything to N·m before evaluating Mw. The conversion is fixed: 1 dyne·cm = 10⁻⁷ N·m. Typical M0 values span roughly 10¹⁵ to 10²³ N·m, depending on rupture size and slip.
3) Fault-parameter method with real ranges
If M0 is unavailable, estimate it with M0 = μ · (L · W) · D. For many crustal rocks, rigidity μ is about 20–40 GPa. Typical ruptures span L from a few to hundreds of kilometers, W about 5–50 km, and slip D from centimeters to several meters.
4) The Mw scaling constant
The page uses Mw = (2/3)(log10(M0) − 9.1) with M0 in N·m, consistent with the common Hanks–Kanamori form. You can invert it to estimate moment from magnitude: M0 ≈ 10^(1.5Mw + 9.1) N·m. If you keep M0 in dyne·cm, the constant changes, so conversion matters.
5) Sensitivity, rounding, and uncertainty
Mw changes slowly compared with M0. Doubling M0 increases Mw by (2/3)·log10(2) ≈ 0.20, while multiplying M0 by 10 increases Mw by about 0.67. The decimal setting only rounds the displayed Mw; the underlying calculation uses full floating-point precision, so exports remain consistent.
6) Energy estimate and TNT comparison
If enabled, radiated energy is estimated by log10(E[J]) = 1.5Mw + 4.8, then converted to tons of TNT using 4.184×10⁹ J per ton. Because the relationship is empirical and energy partitions into heat and damage, treat the value as an order-of-magnitude guide.
7) Interpreting an example with fault geometry
With μ = 30 GPa, L = 40 km, W = 15 km, and D = 2 m, the tool gives M0 ≈ 3.6×10¹⁹ N·m and Mw ≈ 6.97. Changing slip or rupture area by a factor of two shifts Mw by about 0.20, so match geometry to your rupture model.
8) Practical checks before exporting
Before exporting, confirm units and that the chosen method matches how you obtained M0. For fault inputs, ensure L and W describe the ruptured patch, not the whole fault. Saving multiple runs helps compare assumptions side by side.
FAQs
1) Is Mw the same as the Richter magnitude?
No. Mw is derived from seismic moment and is designed to remain reliable for large earthquakes. Richter-type measures are based on wave amplitudes from specific instruments and can saturate for very strong events.
2) Can I enter seismic moment in dyne·cm?
Yes. Select dyne·cm and enter the value. The calculator converts it to N·m using 1 dyne·cm = 10⁻⁷ N·m, then applies the Mw relationship.
3) Why does my Mw look unexpectedly high?
The most common causes are unit mistakes, extra zeros, or mixing km and m in fault dimensions. Recheck rigidity units and ensure L and W describe the ruptured area. Compare your M0 against typical ranges for similar events.
4) What rigidity value should I use?
Many crustal calculations use 20–40 GPa, but rigidity varies with depth, rock type, and temperature. If you have a region-specific model or published value, use that. Otherwise, treat Mw as an estimate with uncertainty.
5) What does the energy estimate represent?
It is an empirical approximation of radiated seismic energy, not the total energy released. Actual energy budgets also include frictional heating and rock damage. Use the estimate mainly for rough comparisons between scenarios.
6) What is the benefit of saving results?
Saved results create a session table and enable exporting multiple rows at once. This is useful for sensitivity studies, unit checks, and comparing different rupture assumptions without losing earlier calculations.
7) Is this calculator suitable for official reporting?
It is best for education and quick analysis. Official magnitudes are typically produced from calibrated seismic networks and inversion workflows. If accuracy is critical, validate constants and inputs against authoritative catalogs or published methods.