Lithospheric plates bend at subduction zones where the vertical motions of the slabs are converted to surface plate motions. To understand the mechanics of plate bending we derive scaling laws for the deflection at the margin, i.e. radius and dip, from numerical models of a subducting viscoelastic plate. In such dynamic system we find that the buoyancy and the stiffness of the plates control the radius and the dip, as well as the plate motions toward the trench. This mechanical model successfully predicts the curvature of published three-dimensional laboratory and numerical models. For a thorough comparison with the observable, we have also implemented forces additional to the slab pull, such as the suction force and far-field stresses. By increasing or resisting the torque applied at the trench by the slab, these forces can largely rearrange the dip and the radius of slabs and the inherent plate motions, although they do not alter the observed anticorrelation between radius and dip. Similar inverse correlation relationship and dip-radius ranges are shown by most of the subduction zones analysed from a global compilation. Radii in the range of 100-350 km and dips of 30degrees-70degrees for slabs that extends to the bottom of the upper mantle are compatible with the models, and allow estimating an average lithospheric viscosity contrast of 200 in the bending with respect to the ambient mantle. Radii and dips outside of this range are in good agreement with the trends and the magnitudes of models that include suction and far-field forces. In all these subduction zones, the correlation between dip, radius and plate velocity is found to be compatible with that of the models, showing how relevant bending is for the dynamics of Earth.