General Formulas

There are three general formulas used all over the game.

Base Scaling Formula

As you level up, most numbers in the game tend to get bigger. The base values for all these numbers all eventually come from the Base Scaling Formula.
For convience, other pages refer to this formula by β.
BL2TPS
β = 1.13 ^ Level β = 1.10 ^ Level

Attribute Bonus Formula

Any attribute in the game uses this formula to calculate it's final value from it's various bonuses. Some stats are comprised of multiple attributes, this is not always the final value.
FINAL = (BASE + PreAdd) × (1 + Positive Scale)÷(1 - Negative Scale) + PostAdd
Any bonus falls into one of these four modifier types, and all bonuses of a type are summed together before being applied. The detailed calculation pages colour code bonuses based on their modifier type.
Note that the game only distingishes between positive and negative scale values based on the final value of the bonus. This means that if a scale bonus is based on some complex formula, it will be treated differently if the formula resolves to a positive value than if it resolves to a negative.

Grade Bonus Formula

Weapons and Items use a concept called Grades. Each part can add or remove grades of a particular name, and if the weapon or item has defined a grade bonus using that name it gets converted into a standard bonus.
Grades are defined by three things: their modifier type, their base value, and a per-grade multiplier.
BONUS = BASE + PERGRADE×Grades
The detailed calculation pages again colour code grade bonuses.