How is critical hit damage calculated?

Weapons

Critical hits multiply the weapon's damage by two factors: first, the critical multiplier of the weapon type; second, the sum of all bonuses to critical hit damage (usually from abilities, but also from sniper rifles and a few weapon parts).

CriticalDamage = CardDamage × CriticalMultiplier × (100% + BonusA + BonusB + BonusC + ···)

Example: If Zer0 has five ranks in Headsh0t (+20% Critical Hit Damage) and is using a Jakobs sniper rifle (+160% Critical Hit Damage) that is listed as dealing 150 damage, then a critical hit will deal 150 × 2 × (280%) = 840 damage before being modified by elemental effects.

Weapons with the effect "Deals Bonus Elemental Damage" apply their bonus damage after the critical hit damage is calculated. That is: bonus elemental damage is not multiplied on a critical hit.

Weapon parts that contribute to increased critical hit damage:

• Pistols: The Hyperion barrel increases the critical multiplier by 0.15 (totaling to 2.65 for Jakobs pistols, 2.15 for all others).
• Shotguns: The "Critikal Hit," "Critical," "Doc's," "Royal," and "Juicy" prefixes all correspond to an accessory that grants +50% critical hit damage.
• Sniper rifles: The "Night," "Venture," "Tumtum," "Gentleman's," and "Razrez" prefixes all correspond to an accessory that grants +20% critical hit damage (totaling to +180% for Jakobs sniper rifles, +120% for all others).

When a weapon card says "+X% Critical Hit Damage," that value indicates the total effective multiplier. For example, a non-Jakobs pistol that says "+8% Critical Hit Damage" is actually reflecting the increase from a Hyperion barrel; the multiplier of 2.15 corresponds to a total effective increase of 7.5% (rounded to 8%); the weapon doesn't actually have a built-in critical hit damage bonus (like sniper rifles do). Similarly, if a Jakobs sniper rifle says "+180% Critical Hit Damage," that means the total bonus is +180%, not 180% on top of the base 160% that all Jakobs sniper rifles have.

Melee

Critical hits in melee inflict ×2 damage. Weapon or skill critical hit bonuses do not increase this any further.
_{Source: Borderlands wiki, "Critical Hit (Borderlands 2)" article}

More detailed reading: Comprehensive Guide on How Critical Hit Damage Works in Borderlands 2 (Gearbox Software Forums post)

I have done some of my own math, and I got base damage figured out, but critical damage is being a little trickster right now. I looked around and I heard you also have to calculate in "how critical was the hit". What I get from that is that each critical point on each enemy gives a different bonus. I came to this site from Google to find the answer to my/your question, but maybe we can help each other. Here is the info that I wrote down and maybe from my info you can do further calculations to figure it out. First to make sure I even knew what the hell I was doing I ran a simple test with base damage. Here is what I got.

Zero was my character. Weapon - Callipeen - 883 damage I had to make sure I looked at all my stats: Class mods, skill trees and badass points. the only modifiers I had towards gun damage were: +6.0% from badass points and +8% from the Vel0city skill. Then I had to see if the damage was compounded or just added on. It's just added, the game would be too beast if it was compounded but here is the calculation:

883 + 883 * (.06+) + 883 * (.08)=1006.62. (I don't know how good you are with math but don't forget to revert the percentages to decimals. I'm not insulting or anything, just being sure and since I'm a math major in college this is my real formula below).

883 * (1+0.14) = 1006.62. (0.14 is the 6% + 8%)

The game rounds up but I was completely correct. I had to take in account that one of Zero's skills adds damage the longer you aim down the sights. So in general here is a formula for finding your base damage

Base damage of weapon * (1+ (sum percentages that deal with gun damage/100)).

Also I sort of disproved the idea that each company or each type of weapon has a hidden damage. There still may be a hidden crit. damage but I don't know yet.

Having encountered Sniper Rifles with stats like "+120% Critical Hit Damage" that seemed too good to be true, I was wondering the same thing, so I decided to run some tests.

Platform: XBox 360

Methodology: I took an alt (level 15 Zer0), respecced him to ensure that talents did not influence his numbers, and turned off his Badass boosts. All damage testing was done at Marcus's shop in Sanctuary on the firing range Bandit (also level 15). Zer0 was using a Turtle shield and a Professional class mod (no weapon or critical damage effects on either). I took two body shots and two head shots with each gun (Each pair was identical, so did not take further confirmation shots. May be worth doing in the future.). I noted three different damage ratings for each rifle: the listed damage, the center mass damage, and the head shot critical damage.

Assumption: Shooting a bandit in the head automatically has a critical multiplier which is added to the weapon's critical multiplier. This total multiplier is than multiplied by the weapon's damage. This is based on enemies who have multiple critical locations taking different damage on some of them (shooting a loader's arm off does less critical damage than shooting the same loader in the eye).

Results: My spreadsheet Note the H column in particular.

Conclusions*: Jacobs sniper rifles have massive critical damage multipliers (5.2). Maliwan corrosive and fire rifles do extra damage to flesh, but use a lower crit factor (3 instead of 4). It's worth noting that having a 120% critical damage multiplier on a Maliwan rifle or a Hyperion shock rifle seems to add 10% to the total crit multiplier (column H). This leads me to suspect that the 120% critical damage boost means the weapon's critical multiplier is increased by 20%... and then that the weapon's critical factor is responsible for half the total critical multiplier. In turn this means that the bandit's headshot factor is 1.5, the Maliwan rifle's factor is (1.5 x 1.2) 1.8 for a total of 3.3.

*All critical multipliers refer to the combined target and weapon multipliers