A quick detour via Google seems to suggest that the constant in the Excel formula is wrong, or at least debatable, it should be something like 3963 for miles, or 6378.8 for kilometers. Another source has 3959.98 for miles or 6372.797 for kilometers. Apparently, it (also) depends on how far from the equator you are.

See also Unit 014 - Latitude and Longitude