This study investigates the natural processes that control concentration of detrital minerals and consequently chemical elements in river sand. The novelty of our approach consists in the systematic integration of detailed textural, petrographical, mineralogical and chemical data, and in the quantitative description and modeling of relationships among mineralogical and chemical variables for each sample and each grain-size class in each sample. Bed sediment in transit in the largest sedimentary system on Earth chiefly consists of fine-grained lithofeldspathoquartzose sand including rich amphibole–epidote–garnet suites, mixed with minor very-fine-grained-sand to silt subpopulations containing less heavy minerals and representing intermittent suspension. Mineralogical and particularly chemical differences between Ganga and Brahmaputra bedload are orders of magnitude less than both intersample variability associated with selective-entrainment effects and intrasample variability associated with settling-equivalence effects. Any provenance interpretation of mineralogical, chemical, or detrital-geochronology datasets therefore requires quantitative understanding of hydraulically controlled compositional variability. Mineralogical and chemical, intrasample and intersample variability can be deduced with simple equations and numerical solutions. The underlying assumptions on the chemical composition of detrital minerals, as well as the possible pitfalls, uncertainties and approximations involved are discussed. Principal results include calibration of rare REE-bearing ultradense minerals, ill-determined by optical analyses but crucial in both detrital-geochronology and settling-equivalence studies, and assessment of progressively changing concentration for any detrital component with increasing intensity of selective-entrainment effects. Contributions by each mineral group to the chemical budget were inferred with sufficient precision and accuracy. Although complex because of diverse controlling factors including provenance, weathering and anthropogenic pollution, mineralogical and consequently chemical variability of fluvial sediments can be quantitatively predicted. This path, difficult because of insufficient information but far from hopeless, shall eventually lead to more accurate calculation of sediment fluxes and chemical budgets, as well as to a deeper understanding of sedimentary geochemistry and fluvial sedimentology.