The opacity of alkali atoms, most importantly of Na and K, plays a crucial role in the atmospheres of brown dwarfs and exoplanets. We present a comprehensive study of Na–H2 collisional profiles at temperatures from 500 to 3000 K, the temperatures prevailing in the atmosphere of brown dwarfs and Jupiter-mass planets. The relevant H2 perturber densities reach several 1019 cm−3 in hot (Teff ≳ 1500 K) Jupiter-mass planets and can exceed 1020 cm−3 for more massive or cooler objects. Accurate pressure-broadened profiles that are valid at high densities of H2 should be incorporated into spectral models. Unified profiles of sodium perturbed by molecular hydrogen were calculated in the semi-classical approach using up-to-date molecular data. New Na–...