For square contingency tables with nominal categories, Tomizawa (1994) and Tomizawa, Seo and Yamamoto (1998) considered measures that reflect the degree of departure from symmetry. This paper proposes a generalized measure for T-way (T ≥ 3) tables. The proposed measure is expressed by using the power divergence of Cressie and Read (1984) or the diversity index of Patil and Taillie (1982). The measure could be useful for comparing the degrees of departure from symmetry in several multi-way tables. Some examples of analysis using biomedical data are shown.