The neutron capture cross section of the unstable nucleus 185W has been derived from experimental photoactivation data of the inverse reaction 186W(gamma,n)185W. The new result of sigma = (687 +- 110) mbarn confirms the theoretically predicted neutron capture cross section of 185W of sigma = 700 mbarn at kT = 30 keV. A neutron density in the classical s-process of n_n = (3.8 +0.9 -0.8} * 1e8 cm-3 is derived from the new data for the 185W branching. In a stellar s-process model one finds a significant overproduction of the residual s-only nucleus 186Os.