According to the library's 1988 edition of The Oxford companion to ships and the sea, a fathom:
...comes from the old English faedm, to embrace, and is a measurement across the outstretched arms of a man, approximately 6 feet in a man of average size; the length of a nautical fathom is therefore 6 feet.
So how far is "full fathom five?" About 30 feet, or a little over 9 meters.
Lets go all the way back to viking-speak... Norse language: Faðmr - to reach with arms; Used even today in Denmark in the form: "Favn". BTW, it is 1.88m.
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