Hydrogen (H2) is considered a promising fuel to contribute to net-zero carbon emission goals. While hydrogen itself is not a greenhouse gas, leakage of hydrogen fuels causes indirect warming due to hydrogen’s influence on methane, tropospheric ozone, and stratospheric water vapor, with the methane term dominating the impact. Some studies consider a simple four-equation box model to explore the climate consequences of leakage from hydrogen fuel use relative to methane, while others have employed much more detailed global photochemical models. Here we use a comprehensive photochemical box model including 66 reactions to show and quantify how the analogous four-equation system is missing a critical OH feedback, leading it to overestimate the time-integrated methane response to a pulse of hydrogen by over 100%. We estimate a hydrogen global warming potential (GWP) relative to carbon dioxide of 28−11+18 on the 20-year time horizon and 10−4+7 on the 100-year time horizon based on the 66-reaction model and information from the literature. GWPs provide a measure of the relative global warming impact of emission of one gas compared to a selected reference gas per unit mass emitted. While CO2 is generally chosen for the reference, any gas can be used. We present the GWP of H2 using CH4 as the reference, as this choice cancels out some uncertainties that are common to both H2 and CH4. The GWP for H2 relative to CH4 from fossil fuel sources is 0.35−0.06+0.13 on time horizons beyond 15 years; put differently, we find that relative to an equivalent mass of emission of fossil CH4, hydrogen emission has a climate impact about three times smaller. These global warming potentials underscore that hydrogen leakage does contribute to climate change, emphasizing the importance of limiting both hydrogen and methane leakage if global net-zero greenhouse gas emissions are to be achieved by 2050.