I was just thinking about this the other day and was curious. Does anyone know?
Starting on a 2x2 embark, the playable map is 96 tiles across. Dividing each length in half, we can determine that each tile on the Local map is 48x48 playable tiles. Region tiles consist of 16x16 Local tiles, meaning each Region tile contains 768x768 playable tiles.
Most wargame and roleplaying games that use Human-size figures on a grid assume each square represents five feet on a side. Assuming Dwarf Fortress is the same, this results in each Region tile covering an area 3,840 feet on a side: 14,745,600 square feet, or about half a square mile (0.5289).
Extrapolating this to the standard world sizes, you get the following numbers:
Pocket world: 153 square miles. (Roughly the distance from Los Angeles to Tijuana.)
For comparison the Earth has a surface area of 196,939,900 square miles. You would need to generate a 19,296x19,296 world to get a Dwarf Fortress world the size of the Earth.
Dwarf Fortress does not measure distance in the traditional sense. After all, the same 1x1 tile can be fully filled by a single cockroach, an adult Roc, or a pile of 30 of your own dwarves (though only one may be standing at a single time).
In short, there is not conversion from DF tiles to real life measurements, as each tile "varies" in size to completely house whatever creature is currently walking through it.