We report the rapid separation and purification of lead halide perovskite quantum dots (QDs) in a nonpolar solvent by using a convenient and efficient differential separation method. Size-selective precipitation effectively separates the perovskite QDs from larger aggregates and provides direct evidence for strong quantum confinement in the photoluminescence (PL). Significantly, the size-selected perovskite QDs are readily well-dispersed in a nonpolar solvent and remain stable in ambient air (humidity > 60%) for >20 days. These enable measurement of the electronic band structure of versatile perovskite QDs as a function of size for the first time. Despite a clear blue-shift of the optical bandgap, the lowest unoccupied molecular orbital (LUMO) readily moves towards the vacuum level while the highest occupied molecular orbital (HOMO) changes slightly, in good agreement with that observed in the quantum size effect tuning of quasi-2D perovskites and colloidal semiconductor QDs. The results demonstrate the possibility of utilizing differential centrifugation as a novel method to attain size-dependent tunability for property-specific perovskite-QD based optoelectronic applications. We introduce differential separation as an efficient method for preparing monodisperse fractions of versatile halide perovskite quantum dots with tunable sizes, enabling investigations of their size-dependent electronic band structure properties.