Despite reduced insolation in the late Archean, evidence suggests a~warm climate which was likely sustained by a stronger greenhouse effect, the so-called faint young sun problem (FYSP). CO₂ and CH₄ are generally thought to be the mainstays of this enhanced greenhouse, though many other gases have been proposed. We present high accuracy radiative forcings for CO₂, CH₄, and 26 other gases, performing the radiative transfer calculations at line-by-line resolution and using HITRAN 2012 line data for background pressures of 0.5, 1, and 2 bar of atmospheric N₂. For CO₂ to resolve the FYSP alone at 2.8 Gyr BP (80% of present solar luminosity), 0.32 bar is needed with 0.5 bar of atmospheric N₂, 0.20 bar with 1 bar of atmospheric N₂, or 0.11 bar with 2 bar of atmospheric N₂. For CH₄, we find that near-infrared absorption is much stronger than previously thought, arising from updates to the HITRAN database. CH₄ radiative forcing peaks at 10.3, 9, or 8.3 W m⁻² for background pressures of 0.5, 1, or 2 bar, likely limiting the utility of CH₄ for warming the Archean. For the other 26 HITRAN gases, radiative forcings of up to a few to 10 W m⁻² are obtained from concentrations of 0.1–1 ppmv for many gases. For the 20 strongest gases, we calculate the reduction in radiative forcing due to overlap. We also tabulate the modern sources, sinks, concentrations, and lifetimes of these gases and summaries the literature on Archean sources and concentrations. We recommend the forcings provided here be used both as a first reference for which gases are likely good greenhouse gases, and as a standard set of calculations for validation of radiative forcing calculations for the Archean.