A single calibration curve which relates seismic moment (Mo to the AR parameter, a time domain sum of the area under the surface-wave envelope, has been found applicable to 20 WWSSN long-period instruments recording surface waves over predominantly oceanic paths of up to 17,000 km epicentral distance, and Ms up to 8.0. The method is easy and Mo estimates are obtained in a routine procedure with errors of a factor of 2 for continental events and a factor of 3 for oceanic events. Analog or digital data can be used from a few stations with only an approximate knowledge of the recording instrument, type of path, and mechanism of the event. Theoretical Mo versus AR curves are derived from the average spectral theory of Geller (1976) and the empirically determined curve is consistent with the predicted. The AR method is shown to be more sensitive to longer period contributions to the wave train as the event size increases, establishing its usefulness for studying earthquakes with a wide range of Ms values. The method is applied to 12 events occurring in 1974 to 1975 with unknown Mo.