A semiquantitative Li-Mn-O phase diagram is proposed to analyze the relationship between the capacity and rechargeability of spinel Li1+2Mn2-nO4 (-0.11 less than or equal to chi less than or equal to 0.33, 0 less than or equal to y less than or equal to 0.33) as a 4 V cathode for lithium-ion batteries. Each compound on the LiMn2O4-Li4Mn5O12-Li2Mn4O9 triangle can be prepared directly by solid-solid reaction techniques. The chemical formula for each compound is expressed as Li8n/(n+m)Mn8/(n+m)O-4 (0.5 less than or equal to n less than or equal to 0.8, 3.5 less than or equal to m less than or equal to 4.0) through knowledge of the Li/Mn molar ratio, n, and the average Mn valence, m. Each compound has an initial capacity of 1184 x (4 - m)/(m + n) mAh/g. The capacity decreases with increases in both Lithium content and vacancy rate along one sheet of the hyperboloid, while the rechargeability improves. The synthesis conditions for preparation of an optimal spinel with a large capacity and an ideal rechargeability can be estimated.