Lattice simulations of QED in 2+1 dimensions are done both in the Lagrangian and Hamiltonian formalism. Though equivalent in the continuum limit, at finite lattice spacing there is no trivial correspondence among the physical parameters, and a matching is required. This can be done non-perturbatively, finding the Hamiltonian parameters that reproduce the $a_t \to 0$ limit of asymmetric lattice actions. In this work we consider the pure gauge theory on a torus $L^2 \times T$ for several values of $\beta$ and of the anisotropy $\xi$. We show how to extract the mass gap of the theory and how to compute the renormalized anisotropy using both the static potential and the Wilson flow evolution of gauge fields.