The Proto-Indo-European root *peth₂- "to spread" in the suffixed o-grade from *pot(h₂)-mo- became Proto-Germanic *faþmaz "the length of two arms stretched out", then Old English fæðm "outstretched arms, embrace". A fathom is 6 feet, about the length of a person's arms outstretched. That was the original meaning of fathom, and then it developed into "take surroundings of" and then to "get to the bottom of".
compass is from Old French compasser "to measure", which is from Latin com plus passus "step". passus is derived from *peth₂-.
It's interesting that encompass also has a meaning similar to "embrace".