Abstract Surveys have looked for Hα emission from accreting gas giants but found very few objects. Analyses of the detections and nondetections have assumed that the entire gas flow feeding the planet is in radial freefall. However, hydrodynamical simulations suggest that this is far from reality. We calculate the Hα emission from multidimensional accretion onto a gas giant, following the gas flow from Hill sphere scales down to the circumplanetary disk (CPD) and the planetary surface. We perform azimuthally symmetric radiation hydrodynamics simulations around the planet and use modern tabulated gas and dust opacities. Crucially, contrasting with most previous simulations, we do not smooth the gravitational potential but do follow the flow down to the planetary surface, where grid cells are 0.01 Jupiter radii small. We find that roughly only 1% of the net gas inflow into the Hill sphere directly reaches the planet. As expected for ballistic infall trajectories, most of the gas falls at too large a distance on the CPD to generate Hα. Including radiation transport removes the high-velocity subsurface flow previously seen in hydrodynamics-only simulations, so that only the free planet surface and the inner regions of the CPD emit substantial Hα. Unless magnetospheric accretion, which we neglect here, additionally produces Hα, the corresponding Hα production efficiency is much smaller than usually assumed, which needs to be taken into account when analyzing (non)detection statistics.