Recent advances in three‐dimensional (3D) imaging of snow and firn combined with numerical modeling of flow through complex geometries have greatly improved the ability to predict permeability values based on microstructure. In this work, we combined 3D reconstructions of polar firn microstructure obtained from microcomputed tomography (mCT) and a 3D lattice‐Boltzmann (LB) model of air flow. We compared the modeled results to measurements of permeability for polar firn with a wide range of grain and pore‐scale characteristics. The results show good agreement between permeability measurements and calculated permeability values from the LB model over a wide range of sample types. The LB model is better at predicting measured permeability values than traditional empirical equations for polar firn.