The Delta-Eddington approximation is a rapid and accurate method for calculating monochromatic radiative fluxes in an absorbing-scattering atmosphere. It combines a Dirac delta function and a two-term approximation to overcome the poor accuracy of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is proportional to the square of the phase function asymmetry factor, distinguishing the Delta-Eddington approximation from others. Comparisons with more exact calculations show typical differences of 0–0.02 and maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo, and phase function asymmetry factor. Delta-Eddington fluxes are in error by no more than 0.5% on average and no more than 2% at maximum. This computationally fast and accurate approximation is useful in applications such as general circulation and climate modeling. The Delta-Eddington approximation approximates the phase function by a Dirac delta function forward scatter peak and a two-term expansion. It is normalized and has the same asymmetry factor as the original phase function. The second moment of the phase function is identical to the original, leading to a specific value for the fraction of scattering into the forward peak. The Delta-Eddington phase function agrees with the Henyey-Greenstein phase function up to three terms, and their difference is shown to decrease as the asymmetry factor approaches 1. The Delta-Eddington approximation is equivalent to the Eddington approximation with transformed parameters. It allows for the transformation of problems with strongly anisotropic phase functions to those with lower asymmetry factors. The approximation is validated against exact solutions, showing errors up to 0.15 in reflectivity and 0.08 in absorptivity for certain conditions. The average error is no more than 0.5% of the incident flux, with errors in flux ratios increasing as the solar zenith angle decreases. The Delta-Eddington approximation provides a physically sound, accurate, and analytically simple parameterization of radiation, replacing empirical methods in general circulation and climate models. It is applicable to homogeneous layers and can be extended to vertical inhomogeneity by concatenating layers. Computer codes are available for monochromatic n-layer cases. The approximation avoids negative reflectivities and transmissivities exceeding 100%, which can occur in the Eddington approximation for large asymmetry factors. The Delta-Eddington approximation is validated for a wide range of parameters and is suitable for practical applications in atmospheric radiation modeling.The Delta-Eddington approximation is a rapid and accurate method for calculating monochromatic radiative fluxes in an absorbing-scattering atmosphere. It combines a Dirac delta function and a two-term approximation to overcome the poor accuracy of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is proportional to the square of the phase function asymmetry factor, distinguishing the Delta-Eddington approximation from others. Comparisons with more exact calculations show typical differences of 0–0.02 and maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo, and phase function asymmetry factor. Delta-Eddington fluxes are in error by no more than 0.5% on average and no more than 2% at maximum. This computationally fast and accurate approximation is useful in applications such as general circulation and climate modeling. The Delta-Eddington approximation approximates the phase function by a Dirac delta function forward scatter peak and a two-term expansion. It is normalized and has the same asymmetry factor as the original phase function. The second moment of the phase function is identical to the original, leading to a specific value for the fraction of scattering into the forward peak. The Delta-Eddington phase function agrees with the Henyey-Greenstein phase function up to three terms, and their difference is shown to decrease as the asymmetry factor approaches 1. The Delta-Eddington approximation is equivalent to the Eddington approximation with transformed parameters. It allows for the transformation of problems with strongly anisotropic phase functions to those with lower asymmetry factors. The approximation is validated against exact solutions, showing errors up to 0.15 in reflectivity and 0.08 in absorptivity for certain conditions. The average error is no more than 0.5% of the incident flux, with errors in flux ratios increasing as the solar zenith angle decreases. The Delta-Eddington approximation provides a physically sound, accurate, and analytically simple parameterization of radiation, replacing empirical methods in general circulation and climate models. It is applicable to homogeneous layers and can be extended to vertical inhomogeneity by concatenating layers. Computer codes are available for monochromatic n-layer cases. The approximation avoids negative reflectivities and transmissivities exceeding 100%, which can occur in the Eddington approximation for large asymmetry factors. The Delta-Eddington approximation is validated for a wide range of parameters and is suitable for practical applications in atmospheric radiation modeling.