A relationship between the dipolar and the chemical-shift scaling factors of cyclic radio-frequency irradiation schemes is introduced. This scaling factor theorem is derived analytically using Average Hamiltonian Theory, and its validity is illustrated numerically with homonuclear dipolar decoupling sequences generated randomly, and with the analysis of existing sequences. While derived for a static sample, the theorem provides insight into homonuclear dipolar decoupling schemes that combine radio-frequency irradiation with fast rotation of the sample at the magic-angle with respect to the static magnetic field. (C) 2011 Elsevier Inc. All rights reserved.