The exceptional properties of the two-dimensional material graphene make it attractive for multiple functional applications, whose large-area samples are typically polycrystalline. Here, we study the mechanical properties of graphene in computer simulations and connect these to the experimentally relevant mechanical properties. In particular, we study the fluctuations in the lateral dimensions of the periodic simulation cell. We show that over short timescales, both the area A and the aspect ratio B of the rectangular periodic box show diffusive behavior under zero external field during dynamical evolution, with diffusion coefficients D_{A} and D_{B} that are related to each other. At longer times, fluctuations in A are bounded, while those in B are not. This makes the direct determination of D_{B} much more accurate, from which D_{A} can then be derived indirectly. We then show that the dynamic behavior of polycrystalline graphene under external forces can also be derived from D_{A} and D_{B} via the Nernst-Einstein relation. Additionally, we study how the diffusion coefficients depend on structural properties of the polycrystalline graphene, in particular, the density of defects.