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The two sites are based on the same formula, just look in the area "More Information about Earthquake Magnitude and Seismic Moment" you will notice that the formulas MO = ÂμAD, to find out the magnitude of the Earthquake, and logES = 11.8 + 1.5M, for discover the energy to a certain magnitude, are on the two pages.
So there is no real difference between choosing the two pages since they both show the same thing. And I was sure we used the second page in the past, I wonder why it has changed.
I'm glad this was done, because I had a question about an earthquake feat that I had no idea how to solve. Now I can ask the question and get a response.
The new calculator seems to be the same as the old one, so that would be fine (the wayback machine has the old one as well, but it doesn't make a difference, I think)
In regards to the formulas... they are mostly the stuff from page 827 here backwards. IIRC I used some other document for some clarification on something there (the delta, I believe), but it is mostly that one. No time to look into detail into it, right now.