Abstract Gas‐brine relative permeability controls subsurface gas storage, including underground hydrogen and CO2 storage. Here, we measure steady‐state gas‐brine relative permeabilities for H2, N2, and CO2 in a sandstone core at 0.1–6 MPa under identical conditions. A multi‐stage equilibration protocol yields reproducible relative permeability curves and isolates the effects of pressure and gas properties. Gas relative permeability increases with pressure for all three gases, strongest for CO2 and weakest for H2. These variations follow a common interfacial‐tension‐based power‐law scaling that captures the endpoint gas mobility, irreducible water saturation, and crossover saturation within a unified framework, indicating that interfacial effects are the primary control on gas mobility. H2 and N2 behaviors diverge only at the highest pressure examined, suggesting that N2 may serve as a practical proxy for H2 at low to moderate pressures. The results provide quantitative constraints relevant to UHS and CCS.