Gibson's formula is widely used due to its simplicity. Yet, it will lose its effectiveness gradually with the increase of relative density (or the ratio of cell-wall thickness t to length L, t/L) and deformation of hexagonal honeycombs. In this paper, the right hexagonal honeycombs with uniform cells but in different densities were analyzed via finite element analysis. A nonlinear modified factor was introduced here to describe the geometric nonlinear behavior of honeycombs. It can be concluded from the numerical results that, for low density honeycombs, the nonlinear modified factor only relates to the deformation and doesn't relate to density. Then, a constitutive relation for low density honeycombs was obtained by giving a fitting formula to the modified factor. For extending this result to high density honeycombs, another nonlinear modified factor was introduced. This modified factor is dependent on both density and deformation. Similarly, a cubic polynomial was used to fit it. Consequently, the geometrical nonlinear constitutive relation which suitable to various density right hexagonal honeycombs with uniform cells was obtained. The constitutive relation with less parameters and accurate prediction may be promising in applications. And the method used in this paper can be easily extended to general hexagonal honeycomb materials.