Total radiative thermal neutron-capture γ -ray cross sections for the 182,183,184,186 W isotopes were measured using guided neutron beams from the Budapest Research Reactor to induce prompt and delayed γ rays from natural and isotopically-enriched tungsten targets. These cross sections were determined from the sum of measured γ -ray cross sections feeding the ground state from low-lying levels below a cutoff energy, E crit , where the level scheme is completely known, and continuum γ rays from levels above E crit , calculated using the Monte Carlo statistical-decay code DICEBOX. The new cross sections determined in this work for the tungsten nuclides are σ 0 ( 182 W) = 20.5(14) b and σ 11/2 + ( 183 W m ,5.2 s) = 0.177 (18) b; σ 0 ( 183 W) = 9.37(38) b and σ 5 − ( 184 W m ,8.33 μs) = 0.0247(55) b; σ 0 ( 184 W) = 1.43(10) b and σ 11/2 + ( 185 W m ,1.67 min) = 0.0062(16) b;and, σ 0 ( 186 W) = 33.33(62) b and σ 9/2 + ( 187 W m ,1.38 μs) = 0.400(16) b. These results are consistent with earlier measurements in the literature. The 186 W cross section was also independently confirmed from an activation measurement, following the decay of 187 W, yielding values for σ 0 ( 186 W) that are consistent with our prompt γ -ray measurement. The cross-section measurements were found to be insensitive to choice of level density or photon strength model and only weakly dependent on E crit . Total radiative-capture widths calculated with DICEBOX showed much greater model dependence; however, the recommended values could be reproduced with selected model choices. The decay schemes for all tungsten isotopes were improved in these analyses. We were also able to determine new neutron-separation energies from our primary γ -ray measurements for the respective (n,γ ) compounds: 183 W [S n = 6190.88 (6) keV]; 184 W [S n = 7411.11(13) keV]; 185 W [S n = 5753.74(5) keV]; and, 187 W [S n = 5466.62(7) keV].