Background: The 14N(n,p)14C reaction is of interest in neutron capture therapy, where nitrogen-related dose is the main component due to low-energy neutrons, and in astrophysics, where 14N acts as a neutron poison in the s process. Several discrepancies remain between the existing data obtained in partial energy ranges: thermal energy, keV region, and resonance region. Purpose: We aim to measure the 14N(n,p)14C cross section from thermal to the resonance region in a single measurement for the first time, including characterization of the first resonances, and provide calculations of Maxwellian averaged cross sections (MACS). Method: We apply the time-of-flight technique at Experimental Area 2 (EAR-2) of the neutron time-of-flight (n_TOF) facility at CERN. 10B(n,α)7Li and 235U(n,f) reactions are used as references. Two detection systems are run simultaneously, one on beam and another off beam. Resonances are described with the R-matrix code sammy. Results: The cross section was measured from subthermal energy to 800 keV, resolving the first two resonances (at 492.7 and 644 keV). A thermal cross section was obtained (1.809±0.045 b) that is lower than the two most recent measurements by slightly more than one standard deviation, but in line with the ENDF/B-VIII.0 and JEFF-3.3 evaluations. A 1/v energy dependence of the cross section was confirmed up to tens of keV neutron energy. The low energy tail of the first resonance at 492.7 keV is lower than suggested by evaluated values, while the overall resonance strength agrees with evaluations. Conclusions: Our measurement has allowed determination of the 14N(n,p) cross section over a wide energy range for the first time. We have obtained cross sections with high accuracy (2.5%) from subthermal energy to 800 keV and used these data to calculate the MACS for kT=5 to kT=100 keV.