It has been proposed, or confirmed, that diamond nanoparticles exist in various environments in space: close to active galactic nuclei, in the vicinity of supernovae and pulsars, in the interior of several planets in the Solar system, in carbon planets and other exoplanets, carbonrich stars, meteorites, in X-ray active Herbig Ae/Be stars, and in the interstellar medium. Using density functional theory methods we calculate the carbon K-edge X-ray absorption spectrum of two large tetrahedral nanodiamonds: C 26 H 32 and C 51 H 52 . We also study and test our methods on the astrophysical molecule CH 4 , the smallest C-H tetrahedral structure. A possible detection of nanodiamonds from X-ray spectra by future telescopes, such as the project Arcus, is proposed. Simulated spectra of the diffuse interstellar medium using Cyg X-2 as a source show that nanodiamonds studied in this work can be detected by Arcus, a high resolution X-ray spectrometer mission selected by NASA for a Phase A concept study.