In nanoimprint lithography (NIL) viscous flow in polymeric thin films is the primary mechanism for the generation and the relaxation of the structures. Here we quantify the impact of confinement on the flow rate. Pattern relaxation experiments were carried out above the glass transition temperature as a function of film thickness. The results are adequately fitted by a simple expression for the flow rate valid at all confinements. This expression, based on Newtonian viscosity, should be of use in NIL process design and for the measurement of the rheological properties of confined polymers.