Richter Scale to Moment Conversion Calculator

Earthquake magnitude scales are logarithmic, and each was defined against a specific instrument and wave type, which is why converting between them is not simple arithmetic. Local magnitude ML, the original Richter scale, comes from the peak trace amplitude on a Wood-Anderson torsion seismograph of natural period near 0.8 seconds, corrected for epicentral distance. Surface wave magnitude Ms is measured on Rayleigh waves near a 20 second period. Moment magnitude Mw is not an amplitude reading at all: it derives from the scalar seismic moment M0 = mu x A x D, the product of shear rigidity, rupture area and average slip, through Mw = (2/3) x (log10 M0 - 9.1) with M0 in newton-meters. Conversion matters because the amplitude scales saturate. ML flattens above roughly 6.5 and Ms above about 8.2, because a rupture lasting tens of seconds radiates most of its energy at periods far longer than the fixed measurement period, so the recorded peak stops growing while the fault keeps slipping. The regressions used here are from Scordilis (2006), fitted to global ISC and NEIC catalogs: Mw = 0.67 Ms + 2.07 for Ms of 3.0 to 6.1, and Mw = 0.99 Ms + 0.08 for Ms of 6.2 to 8.2. Residual scatter is about 0.15 to 0.20 magnitude units, so treat any converted value as an estimate good to a few tenths, and never substitute it for a catalog Mw where one exists.

Kiyoo Wadati laid the groundwork in 1931 by showing that Japanese earthquakes could be ranked by plotting recorded amplitude against distance. Charles Richter, working with Beno Gutenberg at Caltech, turned that idea into a numerical scale in 1935, taking the logarithmic form from the stellar magnitude system and calibrating it against a Wood-Anderson instrument at a reference distance of 100 km. The scale was local by construction, tied to one instrument type and one region. Gutenberg extended it in 1945 with body wave and surface wave magnitudes so that distant earthquakes recorded on other instruments could be measured at all. The limits became obvious as large events accumulated: several very different ruptures all scored about 8.3. Keiiti Aki supplied the physical fix in 1966 by measuring the seismic moment of the 1964 Niigata earthquake from long-period waves. Hiroo Kanamori proposed an energy-based magnitude in 1977, and Thomas Hanks and Kanamori formalized moment magnitude in a 1979 paper in the Journal of Geophysical Research. Mw has been the reporting standard at agencies such as the USGS ever since, and the conversion regressions published by Emmanuel Scordilis in 2006 exist mainly so that decades of older ML and Ms catalog entries can be placed on that common footing.