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Hexes are the standard unit of measurement in Fallout, Fallout 2, and J.E. Sawyer's Fallout Role-Playing Game. Fallout Tactics and Van Buren also technically used the hex, though the maps were not divided into hexes, and hex distance changed based on stance and Agility score.
The entire game map is made up of hexes. When not in combat, there is free movement across a hex. During combat, though, each hex costs one Action Point to move across. With a Crippled Leg, each hex costs 4 AP to move across, having both legs crippled prevents movement in combat.
A weapon's maximum range is measured out in hexes. A melee weapon or an unarmed weapon usually have a range of one hex, so the attacker need to be right next to something to hit it. A spear or a sledgehammer, though, have a range of two, and can hit the target from a little bit farther distance. Some critters like spore plants have a special flag that allows attacking from two hexes away.
A gun has a range that is somewhat determined by the ammo type and power of the gun. A pipe rifle, for instance, has a range of 20 hexes, while a Colt 6520 has a longer range at 25. The longest range for weapons is 50 hexes, possessed by the DKS-501, the PPK12, and the M72.
In Fallout Tactics, the hex still appears, though not in a literal sense. Moving costs a number of action points based on the distance, and what stance the person is at. Some characters, like deathclaws, will move faster in CTB than in ITB or STB, as well.
In Fallout and Fallout 2, it is not actually possible to scroll the screen far enough to make use of the 50 hex range on the weapons without increasing the screen resolution externally.