The magnitude scale MJ, defined by TSUBOI (1954), is widely used for local earthquakes in Japan. JMA (Japan Meteorological Agency) has officially applied it to amplitude data obtained by the JMA network of seismographic stations. The average period of the waves used is usually about 3sec. The MJ scale agrees approximately with the 20sec surface-wave magnitude MS around MS=7. However, MJ deviates very systematically from MS as MS decreases, and MJ is overestimated by as much as 0.6 at MS=4. For determining the equivalent of MS from JMA data, the new formula is defined to be MS(JMA)=1.32logA+2.61log Δ-4.18, where A(μm) is the combined maximum horizontal amplitudes available from JMA and Δ(km) is the epicentral distance. The new formula is regressed against reliable MS values. The MS(JMAA) and MS values from the observed data are essentially equivalent between MS=4 and 8.5. The coefficient of log A in the new formula is explained from the scaling law of seismic spectra, if the difference of the wave period used between the present study and the original definition of MS is considered.