Madian Khabsa and C. Lee Giles mail have published "The Number of Scholarly Documents on the Public Web" in PLOS ONE.
Here's an excerpt:
The number of scholarly documents available on the web is estimated using capture/recapture methods by studying the coverage of two major academic search engines: Google Scholar and Microsoft Academic Search. Our estimates show that at least 114 million English-language scholarly documents are accessible on the web, of which Google Scholar has nearly 100 million. Of these, we estimate that at least 27 million (24%) are freely available since they do not require a subscription or payment of any kind. In addition, at a finer scale, we also estimate the number of scholarly documents on the web for fifteen fields: Agricultural Science, Arts and Humanities, Biology, Chemistry, Computer Science, Economics and Business, Engineering, Environmental Sciences, Geosciences, Material Science, Mathematics, Medicine, Physics, Social Sciences, and Multidisciplinary, as defined by Microsoft Academic Search. In addition, we show that among these fields the percentage of documents defined as freely available varies significantly, i.e., from 12 to 50%.