How does Range affect damage in Fallout 4?

A weapon's range value is the maximum range within which a weapon does maximum damage. Exceeding it, the damage output will increasingly decrease until at twice the range and after, the damage output will be halved.

• A weapon's 'Range' (which is likely in in-game meters or (more appropriately) feet) is the distance after which a projectile's speed (or damage) deteriorates, or, in the words of the Fandom page:

  the furthest distance that a particular weapon will deal its maximum damage outside of V.A.T.S. and additionally affect the chance to hit a target when using V.A.T.S.

  It can thus be interpreted as "maximum optimal range".

• According to the Damage Resistance page on Fandom, weapon damage beyond this maximum range will decrease the damage up to 50% when the range is doubled:

  PaperDamage = WeaponBaseDamage x RangeMulti ( x Perk 1 × Perk 2 × ⋯)

  where

  RangeMulti is 1.0 at 100% WeaponRange or closer, 0.5 at 200% of WeaponRange or farther, and scales from 1.0 to 0.5 as range increases from 100% to 200% of WeaponRange.

  This applies to projectile, close-combat, and energy weapons.
  From some point onward, the damage will drop to 0, but this is beyond the vanilla maximum NPC draw distance.

  EDIT: each weapon has an Out-of-Range Multiplier value. It is true that for most weapons this value is 0.5, but some weapons deviate from this (like the Assaultron Laser, which only decreases to 0.8).