We present a parameter-free mass–radius relation for compact objects, derived directly from a Planck-scale thermodynamic damping law for null orbits. The derivation uses only fundamental constants and predicts a linear relation between mass and radius with a fixed energy increment per unit radius independentof object type or mass scale. Unlike the tautological Schwarzschild formula, the relation here is obtained without using mass to determine the radius, enabling a nontrivial test against independently inferred radii. We validate the law across regimes from neutron stars to supermassive black holes, including a fully worked example for the GW150914 remnant. The combined statistical analysis (goodness-of-fit,weighted residuals, and zero-intercept slope test) shows agreement well within 1σ, and modest dataset expansion achieves >5σ discovery significance. A companion submission to Classical and Quantum Gravity develops the related photon-ring closure effect and the mapping from imaged rings to geodesic radii, providing a direct bridge between classical and quantum gravity.