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How It Works
A seismometer records ground motion as a trace on a seismograph. The amplitude of that trace, combined with a distance correction, gives the Richter magnitude. For larger earthquakes the moment magnitude scale (Mw) is preferred because it is tied to the physical energy released along the fault rather than to instrument readings that can saturate above magnitude 7.
This calculator covers five related equations: Richter magnitude, seismic moment (M₀ = μ × A × d), moment magnitude, seismic energy, and the energy-moment conversion. Select an equation type above, then choose which variable to solve for.
Example Problem
A seismometer 100 km from an earthquake records a maximum trace amplitude of 10 mm. The distance correction factor (-log A₀) for 100 km is 3.0. What is the Richter magnitude?
- M = log₁₀(10) + 3.0 = 1.0 + 3.0 = 4.0
A magnitude 4.0 earthquake is typically felt indoors but rarely causes damage. Each whole number increase represents roughly 31.6 times more energy released.
Frequently Asked Questions
How is earthquake magnitude calculated?
For the Richter scale, magnitude equals log₁₀ of the maximum seismograph amplitude plus a distance correction factor. The moment magnitude scale uses Mw = (2/3)(log₁₀ M₀ − 16.1), where M₀ is the seismic moment measured in dyn·cm.
What is the difference between Richter scale and moment magnitude?
The Richter scale is based on seismograph readings and works well for local earthquakes below magnitude 7. The moment magnitude scale measures the actual energy released at the fault, making it accurate for all sizes including great earthquakes above magnitude 8.
How much energy does a magnitude 7 earthquake release?
Using E = 10^(11.8 + 1.5 × 7), a magnitude 7 earthquake releases about 2 × 10²² ergs (roughly equivalent to 475,000 tons of TNT). Each whole magnitude step multiplies the energy by about 31.6.
What is seismic moment and why does it matter?
Seismic moment (M₀) equals rock rigidity times fault area times average slip. It captures the physical size of the earthquake source, which makes it the foundation for the moment magnitude scale used by seismological agencies worldwide.
Can a seismometer detect earthquakes on the other side of the world?
Yes. Modern broadband seismometers can record earthquakes anywhere on Earth if the magnitude is roughly 5 or higher. Seismic waves travel through the planet's interior, and global networks use these recordings to locate and characterize events within minutes.
Related Calculators
- Seismic Geophone Calculator -- determine subsurface layer depth from seismic refraction travel times.
- Soil Resistivity Calculator -- measure soil resistivity for grounding and geophysical surveys.
- Geotextile Calculator -- calculate permittivity and transmissivity for geotechnical drainage.
- Logarithm Calculator -- compute the log-scale values used in Richter magnitude formulas.
- Energy Unit Converter -- convert seismic energy between joules, ergs, and other units.