What do distance units mean?

In XCOM configuration files, distances are expressed in some obscure units, that do not translate to grid cells easily.

Example values:

• unit vision radius: 27
• most weapons range: 27
• sniper rifle range: 100
• soldier (and most enemies) run distance: 12
• thin man run distance: 15
• cryssalid run distance: 20

A soldier definitely does not run 12 meters/grid cells straight.

So, what are distance units in grid cells, and how distances are calculated diagonally?