Geology & Earth ScienceSeismologyA-Level
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Richter Magnitude (Magnitude Scale) Calculator

A logarithmic scale used to express the total amount of energy released by an earthquake.

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Magnitude

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Overview

The Richter Magnitude scale is a logarithmic tool used to quantify the energy released by an earthquake based on the maximum amplitude of seismic waves recorded by a seismograph. It calculates the magnitude by comparing the measured wave amplitude to a specific reference value calibrated for the distance from the epicenter.

Symbols

Variables

M = Magnitude, A = Amplitude, = Reference Amp.

Magnitude
Variable
Amplitude
Variable
Reference Amp.
Variable

Apply it well

When To Use

When to use: This equation is applied when analyzing local or regional earthquakes, typically within 600 kilometers of the recording station. It assumes the use of a Wood-Anderson torsion seismometer and is most accurate for shallow-focus seismic events.

Why it matters: It allows for the standardization of earthquake reporting, enabling clear comparison across different seismic events. The logarithmic nature means that even small increases in magnitude represent significantly larger physical movements in the Earth's crust.

Avoid these traps

Common Mistakes

  • Confusing the scale with a linear one.
  • Using the wrong base for the logarithm.

One free problem

Practice Problem

A seismograph 100 km from an epicenter records a maximum wave amplitude of 10,000 units. If the reference amplitude for a magnitude zero earthquake at that distance is 1 unit, what is the Richter magnitude?

Amplitude10000
Reference Amp.1

Solve for:

Hint: Divide the measured amplitude by the reference amplitude, then take the common logarithm (base 10).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Britannica: Richter scale
  2. Wikipedia: Richter magnitude scale
  3. USGS: Earthquake Glossary
  4. Bolt, B. A. (1993). Earthquakes
  5. Richter, C. F. (1935). An instrumental earthquake magnitude scale. Bulletin of the Seismological Society of America, 25(1), 1-32.
  6. Bolt, B. A. (2005). Earthquakes: 5th Edition. W. H. Freeman and Company.
  7. USGS Earthquake Glossary: Magnitude
  8. Richter magnitude scale (Wikipedia article)