The scaling relation for the classical rate constants on the scaled potential-energy surfaces has been derived using the scaling theorem in classical dynamics reported previously. This applies to the classical rate constants, both for unimolecular and for bimolecular reactions, that can be obtained by the classical trajectory method and the transition state theory. Validity of the theory has been tested for the prototype reactions, H2CO -->H-2 + CO and Cl + H-2--> HCl + H. Exact scaling of the rate constants obtained by the classical trajectory calculations has been demonstrated. The rate-energy relations for the former reaction calculated with the statistical Rice-Ramsperger-Kassel-Marcus theory also displayed excellent scaling in the high-energy limit. The scaling relation does not hold rigorously near the reaction threshold due to the quantum mechanical zero-point energy effect. Regardless, the order of magnitude prediction of the threshold rate constant by scaling was possible even in extreme cases. The present method may allow reliable prediction of the classical rate constant by using potential energy data obtained at moderately high levels of electronic structure calculation.