Estimates of Earth’s clear-sky longwave feedback from climate models and observations robustly give a value of approximately -2 W/m^2/K, suggesting that this feedback can be estimated from first principles. Here we derive an analytical model for Earth’s clear-sky longwave feedback based on a novel spectral decomposition that splits the feedback into components from surface emission, CO2, H2O, and the H2O continuum. Analytic expressions are given for each of these terms based on their underlying physics, and the model can also be framed in terms of Simpson’s Law and deviations therefrom. We validate the model by reproducing line-by-line radiative transfer calculations across a wide range of climates, as well as the spatial dependence of the clear-sky feedback from radiative kernels. The latter result motivates us to estimate the spatial pattern of Earth’s clear-sky longwave feedback from reanalysis data, which shows good agreement with climate model data. Together, these results show that Earth’s clear-sky longwave feedback, its spatial variations, and its state-dependence across past and future climates can be successfully understood from only a handful of physical principles.