Estimating the natural shape of a given hanging deformed rod, made of a known material, is a relevant problem in many industrial, graphic design, or even biological applications. To tackle this problem we examine the static Kirchhoff equations for thin elastic rods in the reverse direction, that is, when the shape at equilibrium is known and the natural shape is unknown. Our study is focussed on the case of an isotropic rod clamped at one end and free at the other, subjected to gravity.