This paper presents a systematic characterization of pure hydrogen capacitively coupled discharges, produced in a parallel plate cylindrical setup. A two-dimensional, time-dependent fluid model is used to describe the production, transport, and destruction of electrons and positive ions H+, H2+, and H3+, at different frequencies (13.56–60 MHz), pressures (0.2–8 Torr), rf applied voltages (50–450 V) and geometric dimensions (1.6–12.8 cm radii and 1.6–6.4 cm interelectrode distances). A good agreement is found between calculation results and experimental measurements for the coupled electrical power, the plasma potential, and the self-bias potential, at various frequencies and rf applied voltages. However, the model generally underestimates the electron density with respect to its measured values. The paper discusses different space-time events, such as the development of double-ionization structures or the occurrence of field inversion and field reversal phenomena. The dependencies on pressure and frequency of the time-average electric field distribution are analyzed and related to the electron displacement within space-charge sheaths. This study is later used to understand the variations of the hydrogen dissociation rate, with changes in discharge operating conditions. The influence of reactor dimensions on the spatial profiles of the plasma potential, the rf electric field, the electron density, and the electron mean energy are analyzed in terms of discharge symmetry. An investigation of the space-time averaged rf electric field variations, with changes in the applied voltage, pressure, and geometric dimensions is carried out. These variations are shown to follow a universal similarity curve, if an adequate normalization is used when plotting the rf electric field as a function of pressure. This innovative representation of rf discharges allows a univocal definition of a reactor working point, for given operating conditions.