Sneak Attack Critical

A Sneak Attack Critical occurs in Fallout 3, Fallout: New Vegas, Fallout 4, and Fallout 76 when attacking while [HIDDEN]. Successfully hitting the target will result in a guaranteed critical strike (unless the weapon does not allow critical hits), while at the same time doubling (ranged) or quintupling (melee/unarmed) total damage.

(Loud) silent kills

 * It is possible to kill an enemy without alerting those around them if the "sneak" critical is also a one-hit-kill, even with loud weapons like the assault rifle.
 * Doesn't work in Fallout: New Vegas.
 * Additional attacks after the first will not be treated as sneak attacks if queued in V.A.T.S. They will reveal the attacker's location to the target and possibly other enemies. This can happen with all weapons except silent weapons like the silenced 10mm pistol, dart gun, BB gun, Perforator or infiltrator which have a reduced chance to alert opponents.
 * Two weapons suggested for this kind of situation are the Victory rifle or the Gauss rifle. Because the hit was a critical, the opponent will be knocked down and immobilized for a few seconds, giving a chance to quickly deliver a few headshots or follow up with something powerful and then hide until the others stop searching.

(Silent) silent kills

 * It has been reported that all melee attacks are considered silent. However, in the intimate proximity required to deliver a melee attack, the transition to [CAUTION] almost instantly proceeds to [DANGER] as the opponent is programmed to turn around and start moving in the direction of where the attack came from, looking for the enemy in [CAUTION] mode. The instant the enemy spots the attacker, it goes directly into [DANGER] mode which alerts all nearby creatures, even its own enemies. Occasionally, this will result in the enemy that spotted the attacker being attacked by another that was formerly unaware of the first enemy's presence.
 * Still, it is possible to get in 2-3 melee attacks without alerting the whole room. If the stalker sneaks up in back of one of the more lumbering creatures, it is possible it will not turn around fast enough. Note: It will take a Stealth Boy, Chinese stealth armor or the Silent Running perk with maxed skill to get that close.
 * This is quite unlike sneak attacks with a dart gun, with which someone can dart an enemy three times in one use of V.A.T.S. and then just sit still, hiding in the dark a good distance away, only under a temporary [CAUTION] while the enemy searches (slowly, with crippled legs) and then hopefully drops dead from poison, its death setting the status back to [HIDDEN]. Enemies shot with a silent weapon still have some clue as to what direction the shot came from, and will search for the source.
 * The behavior of enemies seems to follow this pattern: if a noise is heard (e.g. dart impacting a wall), they will run to that location, patrol briefly then go back to [HIDDEN]. If the enemy is hit directly, they run to the attacker's location and briefly patrol the general area unless the location is quite a bit away, in which case they will go for a short jog in that direction then return to [HIDDEN]. There is only one exception to the noise-rule: if it is made by an approaching grenade, the enemy will be alerted unless V.A.T.S. is engaged, in which case the enemy in question will scream about the grenade but it WILL count as a sneak attack (this has no effect however as grenades do not have critical damage). Sometimes, enemies remain in [CAUTION] for quite long even if the offender vacates the area.
 * In Fallout: New Vegas, some of the enemies (mostly wildlife) can become repeatedly alerted by the presence of recently killed bodies in their sight, even if the kills are made with a silenced weapon, which renders repeated sneak attacks difficult.

Sneak Criticals & slow projectiles
Certain weapons, like the microwave emitter, have relatively slow projectiles. Outside of V.A.T.S., this may sometimes give away the attacker's position before the shot reaches the target, nullifying the Sneak Attack Critical bonus. For that reason, it is important to be close to the target before trying to Sneak Attack Critical, if using these weapons.

Choice weapons
The best weapons for sneak attacks are the ones with the highest critical damage bonus (affected by +50% damage Better Criticals perk). Here is a number of weapons from Fallout 3 with big bonuses. The number marked in bold is the critical damage when the Better Criticals perk is taken.
 * Alien blaster +100/150 (+120/180'')^
 * A3-21's plasma rifle +50/75
 * Blackhawk +45/67.5
 * Firelance +80/120 (+120/96/144)^ (+180/144/216)"
 * Scoped Gauss rifle +50/75
 * Hunting rifle +25/37.5
 * Lincoln's repeater +50/75
 * Microwave emitter +100/150
 * Plasma rifle +44/66
 * Scoped .44 Magnum +35/52.5
 * Sniper rifle +40/60
 * The Terrible Shotgun +40/60 ( +360/540 )

^ Damage calculated with Xenotech Expert

" Damage calculated with the perks Pyromaniac/Xenotech Expert/Both

Damage calculated if the weapon is fired outside of V.A.T.S., and all pellets make contact. (See below).

Sneak Attack targeting in V.A.T.S.
For most creatures in the game, a sneak attack headshot, along with the Better Criticals perk, can be an instant one-shot kill on Normal difficulty or lower. Even the low-damage dart gun can kill raiders with one sneak attack headshot. In some cases, however, it may not be possible to line up a headshot on a target, due to the target facing an unfavorable position or an obstructed line of fire.

In these cases, even a sneak attack critical on an arm or leg can prove fatal to the target. Though results may vary based on the player character's skills and perks, it is possible to shoot off a target's limb (an instant kill) with one shot from a sniper rifle.

Multi-shot weapons
Weapons that fire several "shots" at the same time, such as combat shotguns (and The Terrible Shotgun), Metal Blaster (from The Pitt), Protectron's Gaze, the tri-beam laser rifle (from Broken Steel), and Paulson's revolver (from Mothership Zeta) are some of the most effective weapons for sneak attacks (when done outside of V.A.T.S.). This is due to the fact that outside of V.A.T.S., each of the weapons' shots' critical damage is calculated individually. This aspect makes these weapons very effective in sneak attacks (and regular critical hits). With the right addition of perks, such as Better Criticals and Finesse, these weapons will be able to deal large damage consistently.

Calculating the weapon's damage
The Terrible Shotgun is the best example for this concept. While in perfect condition, and with a Small Guns skill of 100, the weapon deals 80 damage, with an extra 40 damage for critical hits. However, this weapon fires 9 pellets. Because of this, when the weapon is fired outside of V.A.T.S. and scores a critical hit, the critical hit for each pellet is counted individually. This means that (if all pellets make contact), the weapon will deal 440 damage (80 base damage, plus 9 extra 40 critical damages). While sneaking, this damage is doubled, increasing it to 880 points of damage. In addition, if the attacker has the Better Criticals perk, the damage will increase to 1,240. If the damage is further increased via a headshot, then that damage doubles again to 2,480. High enough to instantly kill almost anything in the game with a single shot.

In Fallout: New Vegas
In Fallout: New Vegas, most multi-shot weapons have had their crit damage significantly reduced. As mentioned, in Fallout 3, The Terrible Shotgun has a base damage of 80 and a crit damage of 40. Compare to the riot shotgun in Lonesome Road, base 75 damage, but only 10 crit damage. Thus, on a full 7-pellet-hit SAC, the total damage is 75 base + 70 critical = 145 total x 2 SAC multiplier = 290. This is still enough to kill most enemies outright, but is significantly less than the previously illustrated 880 from the Terrible Shotgun.

However, this also has the side-effect of lowering non-SAC critical damage, and more significantly V.A.T.S. criticals and SACs with multi-shot weapons. Because each pellet will only add 10 damage if it crits, in V.A.T.S., a regular crit will only do 75 + 10 = 85 for a normal crit, or 170 SAC damage. These changes make crit % increases somewhat under-valued for characters using multi-shot weaponry.