The Bekenstein-Hawking formula for the entropy of a black hole suggests that entropy in strong gravity situations should be proportional to bounding area rather than enclosed volume. But we argue that the S and T dualities of string theory suggest an entropy formula that is extensive in the volume, with the area formula appearing as a special case. In particular we find a set of states in string theory that violate the covariant entropy bound, which seeks to extend the area entropy formula to situations like the early Universe.