The 1700 Cascadia earthquake attained moment magnitude 9 according to new estimates based on effects of its tsunami in Japan, computed coseismic seafloor deformation for hypothetical ruptures in Cascadia, and tsunami modeling in the Pacific Ocean. Reports of damage and flooding show that the 1700 Cascadia tsunami reached 1--5 m heights at seven shoreline sites in Japan. Three sets of estimated heights express uncertainty about location and depth of reported flooding, landward decline in tsunami heights from shorelines, and post-1700 land-level changes. We compare each set with tsunami heights computed from six Cascadia sources. Each source is vertical seafloor displacement calculated with a three-dimensional elastic dislocation model. For three sources the rupture extends the 1100 km length of the subduction zone and differs in width and shallow dip; for the other sources, ruptures of ordinary width extend 360--670 km. To compute tsunami waveforms, we use a linear long-wave approximation with a finite difference method, and we employ modern bathymetry with nearshore grid spacing as small as 0.4 km. The various combinations of Japanese tsunami heights and Cascadia sources give seismic moment of 1--9 ¿ 1022 N m, equivalent to moment magnitude 8.7--9.2. This range excludes several unquantified uncertainties. The most likely earthquake, of moment magnitude 9.0, has 19 m of coseismic slip on an offshore, full-slip zone 1100 km long with linearly decreasing slip on a downdip partial-slip zone. The shorter rupture models require up to 40 m offshore slip and predict land-level changes inconsistent with coastal paleoseismological evidence.