Scaling

Scaling determines how much additional damage a weapon deals.

The additional damage is based on the weapon's stat bonus, base damage and your strength, dexterity, faith and intelligence stats.
The weapon's stat bonus is indicated by a letter grade of S/A/B/C/D/E or as - which means no scaling for that stat.

Calculating bonus damage

Each weapon has a base bonus value for each stat, for example the Butcher Knife has a strength bonus of 104
This bonus gets multiplied by a scalar value dependent on the upgrade level. For any weapon maximally upgraded this scalar value is 1.4.
The result of this multiplication is divided by 100 and then multiplied by a value dependent on your strength stat. This gets multiplied by the weapon damage.
This calculation is done for every stat the weapon has a bonus for and then these values get added together to form the bonus damage.

Example
My character uses a Butcher Knife+10 with a strength bonus of 104 and 190 weapon damage.
It is a +10 weapon so the scalar value is 1.4.
My character has 25 strength, at 25 strength the stat's modifier is 0.4342289734.

$Bonus damage = 104 * 1.4 / 100 * 0.4342289734 * 190$

This gives us a bonus damage of ~120.13 or 120.

*I haven't tested with intelligence or faith*

Weapon upgrade bonus scalars

Upgrade Type +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10
Titanite Shard 1.0 1.05 1.1 1.15 1.2 1.23 1.26 1.29 1.32 1.35 1.4
Titanite Scale /
Twinkling Titanite
1.0 1.08 1.16 1.24 1.32 1.4 - - - - -

Strength/Dex Modifiers

Level Scalar
1 0.0
18 0.25
40 0.75
60 0.85
99 1.0

Weapon Base Bonuses

Weapon Str Bonus Dex Bonus Int Bonus Fth Bonus
Carthus Curved Greatsword 41 55 0 0
Exile Greatsword 40 45 0 0
Murakumo 42 53 0 0
Old Wolf Curved Sword 21 72 0 0

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