The low-temperature electrical conductance through correlated quantum dots provides a sensitive probe of the physics (e. g., of Fermi-liquid versus non-Fermi-liquid behavior) of such systems. Here, we investigate the role of level asymmetry (gate voltage) and local Coulomb repulsion (charging energy) on the low-temperature and low-field scaling properties of the linear conductance of a quantum dot described by the single-level Anderson impurity model. We use the numerical renormalization group to quantify the regime of gate voltages and charging energies where universal Kondo scaling may be observed and also quantify the deviations from this universal behavior with increasing gate voltage away from the Kondo regime and with decreasing charging energy. We also compare our results with those from a recently developed method for linear and nonlinear transport, which is based on renormalized perturbation theory using dual fermions, finding excellent agreement at particle-hole symmetry and for all charging energies and reasonable agreement at small finite level asymmetry. Our results could be a useful guide for detailed experiments on conductance scaling in semiconductor and molecular quantum dots exhibiting the Kondo effect. DOI: 10.1103/PhysRevB.87.165132