We propose a versatile formula that describes action spectra for vibrationally mediated reactions of single molecules with a scanning tunneling microscope. Spectral fitting of the formula to experimental results of CO hopping on Pd(110) and rotation/hopping of propene on Cu(211) enables us to determine the vibrational energy, reaction order, rate constant and effective vibrational broadening. The formula proposed here is general and easy to apply to any vibrationally mediated motion and reaction of single molecules. Quantitative analysis of the spectra provide theoretical background for determining vibrational energy more precisely than conventional manner. The analysis of the spectra are considered plausible because our assignment of vibrational signals follow the propensity rule that was previously proposed.