The electronegativities of 82 elements in different valence states and with the most common coordination numbers have been quantitatively calculated on the basis of an effective ionic potential defined by the ionization energy and ionic radius. It is found that for a given cation, the electronegativity increases with increasing oxidation state and decreases with increasing coordination number. For the transition-metal cations, the electronegativity of the low-spin state is higher than that of the high-spin state. The ligand field stabilization, the first filling of p orbitals, the transition-metal contraction, and especially the lanthanide contraction are well-reflected by the relative values of our proposed electronegativity. This new scale is useful for us to estimate some quantities (e.g., the Lewis acid strength for the main group elements and the hydration free energy for the first transition series) and predict the structure and property of materials.