Unfolded states of proteins and native states of intrinsically disordered proteins (IDPs) populate heterogeneous conformational ensembles in solution. The average sizes of these heterogeneous systems, quantified by the radius of gyration (R G ), can be measured by small-angle X-ray scattering (SAXS). Another parameter, the mean dye-to-dye distance (R E ) for proteins with fluorescently labeled termini, can be estimated using single-molecule Förster resonance energy transfer (smFRET). A number of studies have reported inconsistencies in inferences drawn from the two sets of measurements for the dimensions of unfolded proteins and IDPs in the absence of chemical denaturants. These differences are typically attributed to the influence of fluorescent labels used in smFRET and to the impact of high concentrations and averaging features of SAXS. By measuring the dimensions of a collection of labeled and unlabeled polypeptides using smFRET and SAXS, we directly assessed the contributions of dyes to the experimental values R G and R E . For chemically denatured proteins we obtain mutual consistency in our inferences based on R G and R E , whereas for IDPs under native conditions, we find substantial deviations. Using computations, we show that discrepant inferences are neither due to methodological shortcomings of specific measurements nor due to artifacts of dyes. Instead, our analysis suggests that chemical heterogeneity in heteropolymeric systems leads to a decoupling between R E and R G that is amplified in the absence of denaturants. Therefore, joint assessments of R G and R E combined with measurements of polymer shapes should provide a consistent and complete picture of the underlying ensembles.single-molecule FRET | intrinsically disordered proteins | denatured-state ensemble | protein folding | polymer theory Q uantitative characterizations of the sizes, shapes, and amplitudes of conformational fluctuations of unfolded proteins under denaturing and native conditions are directly relevant to advancing our understanding of the collapse transition during protein folding. These types of studies are also relevant to furthering our understanding of the functions and interactions of intrinsically disordered proteins (IDPs) in physiologically relevant conditions (1). Polymer physics theories provide the conceptual foundations for analyzing conformationally heterogeneous systems such as IDPs and unfolded ensembles of autonomously foldable proteins (2-4). Specifically, order parameters in theories of coil-toglobule transitions and analytical descriptions of conformational ensembles (5, 6) are based on ensemble-averaged values of radii of gyration (R G ) and amplitudes of fluctuations measured by end-toend distances (R E ).Estimates of R G are accessible through small-angle X-ray scattering (SAXS) measurements because scattering intensities are directly related to the global protein size (Fig. 1) (7, 8). At finite concentrations, assuming the absence of intermolecular interactions, R G is proportional to the square root o...