Action Points

Action Points  (or AP) is a game mechanic governing the number of things a character can do during one combat turn in Fallout and Fallout 2. In Fallout 3 and Fallout: New Vegas, Action Points are used to attack in V.A.T.S.. In Fallout 4, Action Points are used to attack in V.A.T.S, sprint, and operate the jetpack.

Fallout, Fallout 2 and Fallout Tactics
Action Points are spent firing a weapon, reloading a weapon, fetching equipment from a character's backpack or moving to a new battlefield hex.


 * $$\text{Initial level}=5+floor\left\lfloor\frac{\text{Agility}}{2}\right\rfloor$$

Example: A starting Agility of 5.


 * $$5+\left\lfloor\frac{5}{2}\right\rfloor=7~\text{Action points}$$

Fallout 3
Action points are used in the V.A.T.S. system to attack opponents, each weapon has it own cost per use and can be found on the weapons page. Unlike in the turn-based games, action points in Fallout 3, Fallout: New Vegas, and Fallout 4 are not accumulated at the end of a turn. Instead, Action Points are regenerated over time.


 * $$\text{Initial level}=65+(2\times\text{Agility})$$

Example: A starting Agility of 5.


 * $$65+(2\times5)=75~\text{Action points}$$

Fallout 3 AP Bonuses
Maximum AP

The maximum figure achievable without chems is 148. Starting AP = 65 + 10 Agility (85) + the Action Boy perk at level 16 (110) + Ledoux's hockey mask (135) + the tribal power armor (148). The +15AP bonus is negated by the -1 Agility penalty which the armor carries. An alternative to negate the -1 Agility is to use the Chinese stealth armor multiple hat glitch/exploit to wear Poplar's hood which has a +1 Agility bonus and stack it with Ledoux's mask for the +30 AP, making the maximum total 150 AP.

The maximum figure achievable with items and chems is a massive 280. (148) + Jet (178) + Ultrajet (218) + Nukalurk meat (228) + Nuka Cola Quantum (248) + Mississippi Quantum pie (268) + alien biogel (278). The -1 Agility/ -2AP penalty carried by the tribal power armor can be negated using either more alien biogel or fire ant nectar (280). An alternative to negate the -1 Agility is to use the Chinese stealth armor multiple hat glitch/exploit to wear Poplar's hood which has a +1 Agility bonus and stack it with Ledoux's mask for the +30 AP.

Fallout: New Vegas
Action Points in New Vegas function mechanically identical to those in Fallout 3, however the agility bonus is multiplied by 3 instead of 2.


 * $$\text{Initial level}=65+(3\times\text{Agility})$$

Example: A starting Agility of 5.


 * $$65+(3\times5)=80~\text{Action points}$$

Notes:
 * Maximum initial base is capped at 95 AP.
 * This limit can be increased with the addition of bonuses (see table below).

Regeneration Rate
A character will take 16.66 seconds to recover their AP bar to full regardless of their AP total, unless their AP is modified by perks. It should be noted that AP gained through perks do NOT count towards regeneration rate. Therefore a player character with 115 AP, 30 of which were gained through Action Boy perks, would actually take over 23 seconds to fully recover their AP bar. Furthermore, the perk Nerves of Steel decreases this regeneration period by 20%, to a potential minimum recovery period of 13.33 seconds.

The exact recovery time can be derived from the GECK variable Action Points Restore Rate, which in Fallout: New Vegas is the inverse of the number of seconds required to fully restore the AP bar. The default value is 0.060 (1/0.06 = 16.66 seconds).

Fallout 4
Action Points in Fallout 4 function mechanically identical to those in Fallout 3 and New Vegas, however the agility bonus is multiplied by 10 instead of 2 or 3.


 * $$\text{Initial level}=60+(10\times\text{Agility})$$

Example: A starting Agility of 5.


 * $$60+(10\times5)=110\text{Action points}$$

Action Points can now be used to sprint. The rate at which they deplete while sprinting relies on Endurance.

Weapon mods, affect the AP cost is V.A.T.S. This video attempts to help explain the affect of some mods, https://www.youtube.com/watch?v=f9gByrm2ukY.