Richter Scale

The Richter Scale calculator computes the magnitude of an earthquake based on the amplitude of the quake and the amplitude of a standard quake (0.001 mm).

INSTRUCTIONS: Choose units and enter the following:

• (I) Amplitude of the Earthquake

Richter Scale Magnitude (M): The calculator returns the magnitude as a real number.

The Math / Science

This Richter Scale calculator computes the magnitude of a seismic event such as an earthquake using the Richter Scale method, which expresses magnitude relative to a standard amplitude (S).

The input is the intensity of the earthquake typically measured 100 kilometers from the epicenter of the event.  The standard amplitude (S) is defined to be 1 micron (0.001mm).

Methodology

How do we measure an earthquake's intensity?  And how do we compare the magnitudes of earthquakes.  This formula defines a scale devised in 1935 by Charles Richter and commonly used today, which derives a comparative magnitude for a seismic event.

The intensity of an earthquake, I, is typically measured as the seismic amplitude recorded approximately 100 km from the epicenter of the event.  The Richter Scale then defines the relative magnitude by the following formula:

`M = log (I/S)`

where:

• M = Richter Scale Magnitude
• I = amplitude of the quake
• S = Standard amplitude of a quake, an amplitude of 1 micron.  One micron amplitude is then zero on the Richter Scale.

The difference in intensities of earthquakes can be enormous, so the scale provides a more manageable way to compare earthquake magnitudes.  Because it is a logarithmic scale, each integer increase on  the Richter scale (from 1.0 to 2.0 to 3.0 to 4.0 etc) represents an intensity increase by a factor of ten.

Early in the century the earthquake in San Francisco registered 8.3 on the Richter scale. In the same year, another earthquake was recorded in South America that was four time stronger. What was the magnitude of the earthquake in South American?