We present an improved analytic potential energy surface for the F+H 2→FH+H and H+FH′→HF+H′ reactions. The final surface is obtained in two stages. First we create a surface, called No. 4, which is based in the F-H-H barrier region on a previous partly empirical and partly theoretical fit and is based on the F-H⋯H exit channel and H-F-H barrier regions on new large-basis-set configuration interaction calculations. The final surface, called No. 5 incorporates more empirical information for collinear geometries in both the F-H-H and FH⋯H regions but remains a good representation of the ab initio calculations for bending potentials and in the strong-interaction regions. Variational-transition-state theory rate constants and WKB adiabatic barrier heights indicate that the final surface is more accurate than previous surfaces for thermal rate constants and overall reaction thresholds for F+H2→HF+H, F+D2→DF+D, and F+HD→HF+D and for product-state thresholds for HF (n′=3) and DF(n′=4), where n′ is the final vibrational quantum number.