We used polarized neutron reflectometry (PNR) to determine the absolute magnetic moment of uncovered and V-covered Fe films in the thickness range from $0.3\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}5.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The films were prepared by molecular beam epitaxy on a V(100) buffer layer grown on a MgO(100) crystal. The magnetic moment shows a linear dependence on the Fe film thickness with a reduction (compared to the Fe bulk value) of the magnetic moment equivalent to $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ bulk Fe for the V-covered films and a reduction equivalent to $0.03\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ bulk Fe for the uncovered Fe films. For the case of the $\mathrm{V}∕\mathrm{Fe}∕\mathrm{V}$ samples we observe a much smaller reduction of the magnetic moment than reported for experiments on $\mathrm{Fe}∕\mathrm{V}$ multilayers. As theoretical calculations show a strong decrease of the magnetic moment for an interface alloy we conclude that the larger reduction of the magnetization in $\mathrm{Fe}∕\mathrm{V}$ multilayers is due to an increase in interface roughness with increasing film thickness. For the uncovered Fe(100) films we find a much smaller reduction of the magnetic moment than in earlier in situ PNR experiments on $\mathrm{V}(110)∕\mathrm{Fe}(110)$ where we observed a reduction equivalent to $0.4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ bulk Fe.