简要叙述地震震级概念的提出及其历史发展。文中指出，矩震级M_W是目前量度地震大小最理想的物理量。与传统上使用的其他震级标度相比，矩震级不会饱和，对于所有地震，无论大小、深浅，无论使用远场、近场地震波资料，大地测量和地质资料中的何种资料，均可测量矩震级，并能与熟知的震级标度如面波震级M_S相衔接。矩震级是一个均匀的震级标度，适于震级范围很宽的统计。矩震级是国际地震学界选定的首选震级，负责向公众发布地震信息的部门优先采用的发布的震级。文中介绍了计算矩震级所用的公式，详细解说了具体的计算步骤，分析了由于采用的计算矩震级公式的不同，采取的具体的数值计算步骤的不同引起的问题以及解决这些问题的相关的规定。

In this paper, we given a brief introduction on the putting forward and development history of earthquake magnitude concept. Moment magnitude M_W is the best physical quantity for measure earthquake. Comparing with other magnitude scales, it is can not saturation and can be measured for all earthquakes, not only big and small earthquake, deep and shallow earthquake, but also using far field and near field seismic wave data, geodesy data and geology data， and can connect with known magnitude scales for example surface wave magnitude. Moment magnitude is a uniform magnitude, applies to broad magnitude statistics. It is a preferred magnitude for international seismology, and a prior release magnitude for the responsible agency for providing information about earthquakes to the public. We introduced all formulas used in calculation moment magnitude, and calculation steps in detail. We also analysed some problems and rules to solve these problems for using different formulas and numerical value calculation steps.