Moment Magnitude Mw Calculator
Our geology & geophysics calculator computes moment magnitude mw accurately. Enter measurements for results with formulas and error analysis.
Formula
Mw = (2/3)(log10(M0) - 9.1) | M0 = mu x A x D
Moment magnitude Mw is derived from seismic moment M0 using the Hanks-Kanamori formula. M0 can be calculated from fault rigidity (mu), rupture area (A), and average slip displacement (D). Each magnitude unit represents approximately 31.6 times more energy.
Worked Examples
Example 1: 2011 Tohoku Earthquake
Problem: The seismic moment was 3.9 x 10^22 N\u00B7m. Calculate Mw.
Solution: Mw = (2/3)(log10(3.9e22) - 9.1)\nlog10(3.9e22) = 22.591\nMw = (2/3)(22.591 - 9.1) = (2/3)(13.491) = 8.99
Result: Mw = 9.0
Example 2: Fault Parameters Calculation
Problem: A fault has rigidity 30 GPa, area 500 km\u00B2, and 2 m displacement.
Solution: M0 = 30e9 x 500e6 x 2 = 3.0e19 N\u00B7m\nMw = (2/3)(log10(3.0e19) - 9.1) = (2/3)(19.477 - 9.1) = 6.92
Result: Mw = 6.92
Frequently Asked Questions
What is moment magnitude (Mw)?
Moment magnitude (Mw) is the modern standard scale for measuring earthquake size, replacing the older Richter scale for medium to large earthquakes. It is based on the seismic moment, which accounts for the physical properties of the fault rupture including rigidity, fault area, and average displacement. The formula Mw = (2/3)(log10(M0) - 9.1) was developed by Hanks and Kanamori in 1979, where M0 is the seismic moment in Newton-meters.
What is seismic moment and how is it calculated?
Seismic moment (M0) is a physical measure of earthquake energy that combines three fault parameters: the rigidity (shear modulus) of the rock, the area of the fault that ruptured, and the average displacement along the fault. The formula is M0 = mu x A x D, where mu is typically 30 GPa for crustal rocks. Unlike the Richter magnitude, seismic moment has a clear physical interpretation and does not saturate at high magnitudes.
How much more energy does each magnitude unit represent?
Each whole number increase in moment magnitude corresponds to a roughly 31.6 times increase in seismic energy released, and a factor of about 31.6 in amplitude. This means a magnitude 8 earthquake releases approximately 1,000 times more energy than a magnitude 6. A magnitude 9, like the 2011 Tohoku earthquake, releases about 31,623 times the energy of a magnitude 6, which is why large earthquakes are so devastating.
What is the difference between apparent and absolute magnitude?
Apparent magnitude is how bright a star looks from Earth (lower is brighter; the Sun is -26.7). Absolute magnitude is the brightness at a standard distance of 10 parsecs, allowing fair comparison. The relationship involves the distance modulus: m - M = 5 * log10(d/10), where d is distance in parsecs.
Can I use Moment Magnitude Mw Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.