The magnetization of Fe4N and Fe16N2 has been calculated from first principles, employing the full-potential linearized-augmented-plane-wave method. The calculated magnetization of Fe4N is in fair agreement with experimental results. The differences between calculated and experimental values are at most 10%. The calculated magnetization of Fe16N2, however, is 30% smaller than the huge value of 0Msat3.2 T reported recently for iron-nitride thin films, which were characterized as single-phase Fe16N2. Based on this result and on a comparison between calculated and experimental hyperfine fields we conclude that the -Fe16N2 phase cannot be responsible for the ultrahigh magnetization reported for single-phase iron-nitride thin films.