We perform numerical experiments to investigate the accuracy of broad-band moment magnitude, Mwp. We conduct these experiments by measuring Mwp from synthetic seismograms and comparing the resulting values to the moment magnitudes used in the calculation of synthetic seismograms. In the numerical experiments using point sources, we have found that there is a significant dependence of Mwp on focal mechanisms, and that depths phases have a large impact on Mwp estimates, especially for large shallow earthquakes. Numerical experiments using line sources suggest that the effects of source finiteness and rupture propagation on Mwp estimates are on the order of 0.2 magnitude units for vertical fault planes with pure dip-slip mechanisms and 45° dipping fault planes with pure dip-slip (thrust) mechanisms, but that the dependence is small for strike-slip events on a vertical fault plane. Numerical experiments for huge thrust faulting earthquakes on a fault plane with a shallow dip angle suggest that the Mwp estimates do not saturate in the moment magnitude range between 8 and 9, although they are underestimates. Our results are consistent with previous studies that compared Mwp estimates to moment magnitudes calculated from seismic moment tensors obtained by analyses of observed data.