Critical Hit

Critical Hits are hits which cause extra damage, or other side effects. If a hit is successful, it may become a critical hit if it passes Critical Chance. The effect of the hit is determined by the another roll, on the critical hit table. Effect depends on the area hit, and various unknown variables. The effect of a critical hit can be modified by the Perk Better Criticals.

Note that the chance for a critical hit is determined by Critical Chance, and is not the same as critical effect. See Aimed Shot in the Combat section for more info.

Example
The following example is a bit tricky: you might want to open another window with reference material Situation: Alvin York (S5, P9, E5, C3, I5, A10, L10) is carrying a Hunting Rifle and has a Small Guns skill of 150%, and one of his traits is Finesse. He spies an armored gentleman, wearing Metal Armor some distance (8 hexes) away, and decides to make an aimed shot for the eyes. This is what happens:

Alvin's base to hit is (150 - 30) + (8 * 9) + (No penalty) - (15 + 5) + 4 - 60 = 112%, a definite hit! Alvin's critical chance is (1 * 10) + (10) + (a mysterious number) = Critical hit! Alvin rolls 1d100 for the critical effect table, and gets 85. His damage is (0.7 * 20 * 3) - (armor ignored) = 42

Mr. Metal Man loses 42 of his 70 hp, and staggers around blindly. With his remaining 4 of 10 action points, Alvin advances closer to Mr. Metal Man, who lost his responding turn as a result of the critical.

Alvin fires at the eyes again. BTH is the same, and CC is successful. CE rolls a 95.

Mr Man screams in agony, as a round of ammunition pierces his visor, blinding him. He falls slowly to his knees, bewildered and overcome. Bleeding from his helmet, he keels over, killed by the 56 damage AND the "instant kill" effect. With his remaining 4 action points, Alvin York marries Gracie Williams, has seven children, and dies at the age of 76.

Fallout 3
In Fallout 3, the critical hit feature is simplified from Fallout and Fallout 2. When a weapon is fired, it has a predefined, specific percentage chance of getting a critical hit (with a few exceptions, see below), which is essentially just added damage to the original base damage (the damage that will be dealt if the PC does not score a critical hit). This obviously sounds much simpler than the system of the first two games, but it is still more complex than it sounds.

Modifiers of Critical Chance
The PC's initial critical chance is determined by the Luck S.P.E.C.I.A.L. statistic. Each point of Luck adds one percent of critical chance. For example, if you have 7 points of Luck you have a 7% chance to deal a critical strike with a weapon of a x1 critical multiplier (explained in the below paragraph). In addition to the Luck stats, there are various perks that add to the PC's critical chance (see the main article for details). With the maxing out of all perks, it is possible to achieve a base critical chance of 18% with ranged weapons, or 33% with unarmed and melee weapons (due to the Ninja perk). Also, a critical chance of +15% is added to all strikes in V.A.T.S.

Each weapon in the game has a critical multiplier that is combined with the PC's critical chance. For example, the Scoped .44 Magnum has a multiplier of x2, so if the PC has a critical chance of 7% and is using a Magnum, he/she has a 14% chance to score a non-V.A.T.S. critical hit (29% with V.A.T.S). A majority of the weapons have a x1 critical multiplier (such as the Hunting Rifle). There are a few weapons that have a x0 multiplier (like the Sawed-Off Shotgun), and that makes it impossible to score a critical hit; Sneak Attack Criticals do not add any damage due to the 0 critical damage. Very rarely, you can get a non-sneak attack critical hit on a x0 multiplier weapon (tested on The Kneecapper), but because the critical damage is set at 0, it makes it useless. Because automatic weapons have so many bullets, the actual critical multiplier is much lower than the critical multiplier associated with the weapons. For example, the Chinese Assault Rifle has a rate of fire of 8 bullets a second. The multiplier is displayed as x1, but if each bullet was actually x1, there would be way too many critical strikes. The actual multiplier for each bullet is x0.125. So in practical use, the multiplier acts as x1. The critical multiplier for each weapon is between x0 and x5 (save for one acceptation). There are only a few weapons with a x5 critical multiplier: 

Sneak Attack Critical
A Sneak Attack Critical occurs when sucessfully attacking an opponent while being by using one's Sneak skill. Successfully hitting the target will result in a guaranteed critical strike. This more specialized critical strike doubles the damage generally done with a non-sneak attack critical. For example, Lincoln's Repeater has a base damage of 50 (yours might be different with perks, weapon condition, and skill) and a critical damage of 50, so a basic critical hit would do 100 damage (unless you have the Better Criticals perk). When a sneak attack critical dealt, the damage completely doubles, so the Sneak Attack Critical gives a whopping 200 damage (250 with Better Criticals).