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.)
Smaller world: 576 square miles. (About the size of Oahu.)
Small world: 2,234 square miles. (About the size of Delaware.)
Medium world: 8,802 square miles. (About the size of Wales.)
Large world: 34,935 square miles. (About the size of Maine.)
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.
This is impossible to know because (at least) at this moment, dwarf fortress is very inconsistent. I used the walking speed of a df game human, and compared with real life human average walking speed to find the tile size (forgot the result I got), I assumed the walking speed of the game was realistic. I found the tile size was X meters, but other many gameplay feature stuff would be nonsensical (more unrealistic than you would imagine dwarf fortress developer would want his game to be) if you assume the size is x meters, this show its impossible to know the tile size right now (a thing needed to find the size of the map)
Anyway, all this I said also show something about dwarf fortress. That dwarf fortress really need to decide on a tile size and turn the game into a multi tile game, to be able to be better designed in a way that reduce inconsistencies.