We report on the structural, energetic, and electronic properties which explain the behavior of atomic hydrogen in a W monovacancy. Based on the density functional theory, we calculate the most stable configurations of up to eleven hydrogen atoms in a monovacancy using the SIESTA and the VASP codes. We discuss about the deformation produced in a unit cell when a vacancy is formed and subsequently filled with different number of H atoms. We estimate the formation and the binding energies as a function of hydrogen accumulation in the monovacancy, comparing to data previously reported and highlighting the origin of the disparity of the results. Our calculations show that the maximum number of hydrogen atoms that the monovacancy can trap depends on the procedure followed for its filling, being 10 when it is filled in sequentially and larger than 11 when it is filled in via simultaneous insertion of the hydrogen atoms. Finally, we study the influence of the valence charge density and charge redistribution in the formation of the most stable structures.