The Coulomb staircase in polymer-covered Pd and Au nanocrystals of varying diameters in the 1.7-6.4 nm has been investigated by employing tunneling conductance measurements. Charging up to several electrons is observed at room temperature in the I-V data. Small nanocrystals show charging steps exceeding 200 mV while the larger ones exhibit smaller steps. Significantly, the charging energies follow a scaling law of the form, U = A + B/d, where d is the diameter of the nanocrystal. Furthermore, the line widths in the derivative spectra also vary inversely with the diameter.