Remarkably accurate scaling relations are shown to exist between the correlation energy contributions from various excitation levels of the configuration interaction approach, considered as functions of the size of the correlating orbital space. These relationships are used to develop a method for extrapolating a sequence of smaller configuration interaction calculations to the full configuration-interaction energy. Calculations of the neon atom ground state with the Dunning's quadruple zeta basis set demonstrate the ability of the method to obtain benchmark quality results. (C) 2004 American Institute of Physics.