An approach to converting HF and DFT energies of molecules, ions, and radicals to standard enthalpies of formation (Delta H(f)degrees) is presented. Employing a combination of atomic equivalents, bond density functions, and corrections for molecular charge and spin multiplicity, this new approach is capable of producing accurate enthalpy estimates for most organic and inorganic compounds of the first- and second-row elements. At the B3LYP/6-311G** level of theory, the average absolute errors in the computed values of (Delta H(f)degrees) amount to 1.6, 2.4, and 3.4 kcal/mol for the sets of 61 CH, 156 CHNOS, and 300 H...Cl species that include systems as small as the Cl- anion and as large as the C-60 fullerene. Computationally inexpensive theoretical predictions of molecular thermochemistry with accuracy rivaling that of calorimetric measurements are now possible for compounds of interest to the broad audience of experimental chemists.