An index of rotatability is suggested that will enable the experimenter to obtain an immediate appreciation of the overall shape of specified variance contours for symmetrical second-order designs. Values of the index are tabulated for the central composite designs for two to eight factors. Three designs of Roquemore (1976) are assessed via the index. Comparisons are made with an entirely different index suggested by Khuri (1988). It is concluded that both indexes are useful and sensibly consistent.