As usual, different sources give different figures, which may or may not include the area of adjacent seas, gulfs, and bays. To further complicate matters, the official boundaries were changed in 2000 when the Southern Ocean was defined by the International Hydrographic Organization. However, the most-cited figure is 68,556,000 sq km (26,463,000 sq mi) from the CIA World Factbook; it excludes the Southern Ocean but includes all adjacent waters.

http://www.lib.utexas.edu/maps/cia01/indian_ocean_sm01.jpg
Source(s):
https://www.cia.gov/library/publications/the-world-factbook/geos/xo.html

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