Hit Points

Hit Points (HP) also known as Health 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). HP can also be restored by waiting, at a rate of approximately 2 HP per 3 hours (Fallout: New Vegas).

Fallout and Fallout 2

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

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

Notes:
 * The Lifegiver perk gives a +4 maximum HP per rank for each new level.
 * The Alcohol Raised Hit Points and Autodoc Raised Hit Points perks each increase maximum HP by 2.
 * The Alcohol Raised Hit Points II and Autodoc Raised Hit Points II perks each increase maximum HP by 4.
 * The Alcohol Lowered Hit Points and Autodoc Lowered Hit Points perks each decrease maximum HP by 2.
 * The Alcohol Lowered Hit Points II and Autodoc Lowered Hit Points II perks each decrease maximum HP by 4.

Fallout 3

 * $$\text{Initial level}=90+(\text{Endurance}\times20)+(\text{Level}\times10)$$

Example: A starting Endurance of 5 at Level 1
 * $$90+(5\times20)+(1\times10)=200~\text{Hit Points}$$

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.
 * $$\text{Initial level}=95+(\text{Endurance}\times20)+(\text{Level}\times5)$$

Example: A starting Endurance of 5 at Level 1
 * $$95+(5\times20)+(1\times5)=200~\text{Hit Points}$$

Max health of a player character without any chem boosts, DLC or perks and at max Endurance is 445
 * $$95+(10\times20)+(30\times5)=445~\text{Hit Points}$$

Max health of a player character with DLC, chems and perks at max Endurance is 885
 * $$95+(10\times20)+(50\times5)+30^1+60^2+75^3+100^4+25^5+50^6=885~\text{Hit Points}$$


 * 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. 6 From Battle brew.

Fallout 4
Fallout 4's health scaling formula:
 * $$ 80 + (\text{Endurance} \times 5) + (\text{Level} - 1) \times \left ( \frac{\text{Endurance}}{2} + 2.5 \right )$$


 * Decimals are truncated in the PIPboy.
 * Temporary Endurance bonuses do not add permanent health on level up.
 * Health is retroactive on permanent Endurance increase.

This is a significant change from Fallout 3 and Fallout:New Vegas. The character starts with significantly less health and thus enemies feel much more dangerous. Thankfully, there are unlimited levels and thus an infinite amount of health a character can obtain.

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 +4 maximum HP per rank for each level gained.

Fallout: Brotherhood of Steel

 * The Die Hard skill gives 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 grants 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.