Hypothesis: The mitigation of anthropogenic greenhouse gas emissions and increasing global energy demand are two driving forces toward the hydrogen economy. The large-scale hydrogen storage at the surface is not feasible as hydrogen is very volatile and highly compressible. An effective way for solving this problem is to store it in underground geological formations (i.e. carbonate reservoirs). The wettability of the rock/H2/brine system is a critical parameter in the assessment of residual and structural storage capacities and containment safety. However, the presence of organic matters in geo-storage formations poses a direct threat to the successful hydrogen geo-storage operation and containment safety. Experiments: As there is an intensive lack of literature on hydrogen wettability of calcite-rich formations, advancing (θa) and receding (θr) contact angles of water/H2/calcite systems were measured as a function of different parameters, including pressure (0.1–20 MPa), temperature (298–353 K), salinity (0–4.95 mol.kg−1), stearic acid (as a representative of organic acid) concentration (10-9 − 10-2 mol/L), tilting plate angle (0° − 45°) and surface roughness (RMS = 341 nm, 466 nm, and 588 nm). Findings: The results of the study show that at ambient conditions, the system was strongly water-wet, but became intermediate wet at high pressure. The water contact angle strongly increased with stearic acid concentration making the calcite surface H2-wet. Moreover, the contact angle increased with salinity and tilting plate angle but decreased with temperature and surface roughness. We conclude that the optimum conditions for de-risking H2 storage projects in carbonates are low pressures, high temperatures, low salinity, and low organic surface concentration. Therefore, it is essential to measure these effects to avoid overestimation of hydrogen geo-storage capacities and containment security.