Hit point

Hit Points (HP) are a game mechanic used to measure the health of a character. During combat, wounded characters lose HP. When a character gains a new level, additional HP is awarded. Should a character be reduced to 0 HP, the character dies. Needless to say, HP is an important character statistic to be monitored during play. HP can be restored using various medical items/food items such as stimpaks and wasteland omelets. HP can also be restored by sleeping or paying a doctor (both of these methods heal crippled limbs, except in hardcore mode in Fallout: New Vegas).

Fallout, Fallout 2

 * $$\text{Initial level}=15+\text{Strength}+(2\times\text{Endurance})$$

The Maximum HP increase per level is
 * $$\left\lfloor\frac{\text{Endurance}}{2}\right\rfloor+2$$

Notes:
 * The Lifegiver perk gives you an additional 4 maximum HP per rank every time you gain a level.
 * The Alcohol Raised hit points and Autodoc Raised Hit Points perks each increase your maximum HP by 2.
 * The Alcohol Raised hit points II and Autodoc Raised Hit Points II perks each increase your maximum HP by 4.
 * The Alcohol Lowered hit points and Autodoc Lowered Hit Points perks each decrease your maximum HP by 2.
 * The Alcohol Lowered hit points II and Autodoc Lowered Hit Points II perks each decrease your maximum HP by 4.

Fallout 3

 * $$\text{Initial level}=100+(\text{Endurance}\times20)+(\text{(Level - 1)}\times10)$$

Example: A starting Endurance of 5 at Level 1
 * $$100+(5\times20)+(0\times10)=200~\text{Hit points}$$

Fallout: New Vegas
Between Fallout 3 and New Vegas, base HPs were changed from 90 to 95. Further, fAVDHealthLevelMult was changed from 10 to 5. The result is starting characters from both games with Endurance 5 will have the same HPs (200) but New Vegas character's HPs scale slower than Fallout 3 characters.
 * $$\text{Initial level}=100+(\text{Endurance}\times20)+(\text{(Level - 1)}\times5)$$

Example: A starting Endurance of 5 at Level 1
 * $$100+(5\times20)+(0\times5)=200~\text{Hit points}$$

Max health of a player without any add-ons, chem boosts, or perks and at max Endurance is 445
 * $$100+(10\times20)+(29\times5)=445~\text{Hit points}$$

Max health of a player with add-ons, chem boosts and perks at max Endurance is 835
 * $$100+(10\times20)+(49\times5)+30^1+60^2+75^3+100^4+25^5=835~\text{Hit points}$$
 * 1 From Life Giver perk. 2 From buffout. 3 From Sierra Madre martini. 4 From Thought You Died perk (if karma is at 1000 points). 5 From Black blood sausage.

Trivia
The sound of a heart beat can be heard when the player is on low health, the sound gets louder (and faster) the lower health the player is on. However, there have been some occasions in which the player's health is so low that their heartbeat actually stops.

Fallout 4

 * $$\text{Initial level}=80+(Endurance*5)+((Level-1)*(2.5+Endurance*0.5))$$

Example: A starting Endurance of 4 at Level 1
 * $$80+(4*5)+(0*(2.5+4*0.5))=100~\text{Hit points}$$

Fallout Tactics

 * $$\text{Initial level}=15+\text{Strength}+(2\times\text{Endurance})$$

The Maximum HP increase per level is
 * $$\left\lfloor\frac{\text{Endurance}}{2}\right\rfloor+3$$

Notes:
 * The Lifegiver perk gives you an additional 4 maximum HP per rank every time you gain a level.
 * The Brutish Hulk perk gives double the normal amount of maximum hit points each time a level is gained(deathclaw only).

Fallout: Brotherhood of Steel

 * The Die Hard skill gives you an additional +20 maximum HP (up to a maximum +200) per rank.
 * The Rad Child skill allows Cain to regenerate health when others would receive radioactive damage.
 * The Sadist skill gives you the ability to regenerate +2 HP for Cain and +5 HP for Nadia (up to regenerate a maximum +25 HP for Nadia and +10 HP for Cain) per rank whenever they kill an enemy.