Every binary word with at least four letters contains a square. A.~Fraenkel and J.~Simpson \cite{FraenkelSimpson95} showed that three {\em distinct squares} are necessary and sufficient to construct an infinite binary word. We study the following complementary question: how many {\em square occurrences} must a binary word contain? We show that this quantity is, in the limit, a constant fraction of the word length, and prove that this constant is $0.55080...$.