Field data indicate convincingly that the drag coefficient of the ocean surface is sea-state dependent. As a result, under steady forcing by a constant wind velocity the wind stress on the ocean surface varies with time. It also varies with space if the wave development is limited by fetch. A quantitative estimation of the temporal and spatial variation of the wind stress produced by a constant wind velocity is presented. The method of computation combines the duration- or fetch-limited growth functions of wind-generated waves and the similarity relation of the ocean-surface drag coefficient derived from wavelength scaling. The only required input is the wind speed. The results indicate that the average momentum flux from atmosphere to ocean is much larger (about 50 to 100 percent higher, and especially for shorter wind events) in comparison with calculations using the drag coefficient or dynamic roughness formulated either without the wave parameters or based on steady state wave conditions.