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Monte Carlo radiation transport simulations were used to calculate the positron stopping profiles in tungsten positron moderator foils. Stopping profiles were numerically integrated with efficiency kernels derived from Green's function solutions of the 3D diffusion equation to determine the moderation efficiency in both the backscattering and transmission geometries. Stopping profiles and efficiencies were calculated for positron energies from 10 keV to 10 MeV and incident angles from 0° to 75°. The resulting efficiencies agreed with other calculated and measured values in the literature, especially when similar values of the positron diffusion length and surface emission branching ratio were used. Large discrepancies with some of the values reported in the literature are mainly attributed to differences in foil manufacture and surface condition—factors which are known to greatly influence the diffusion length—as well as work function and branching ratios. This work provides tabulated efficiencies for tungsten foil moderators that can be interpolated and integrated with a positron flux having arbitrary energy and angular distributions.