# How is ranged damage calculated?

I have a dwarven bow of frost and ancient nord arrows.

Dwarven bow - 20 damage
Frost enchantment - 10 damage
Ancient nord arrows - 10 damage

Would it calculate 20+10 to give each arrow 30 damage (ignoring enchantments for now)? Or does it take an average of them, giving each 15 damage? Or does it take the highest, thus 20 damage?

Is the enchantment calculated afterwards (and would it be affected by the sneak bonus/critical hits)?

• An enchantment is meant to improve a weapon, not make it worse. The same goes for arrows. Nov 14 '11 at 12:54
• Doesn't the game straight-up tell you how much damage they combine to in the inventory? Nov 14 '11 at 17:08

Yes, by using your weapon you make the arrow stronger so you simply add the arrow's damage to the weapon's damage. IF it is the case that the weapon is enchanted then the weapon is even stronger, so

``````total damage = weapon damage + enchantment damage + arrow damage
``````

is the right formula. They don't limit it by the average, because that would make those slow bows rather weak. The highest damage doesn't really make sense as then getting better arrows does in most cases not result in getting better damage...

• I believe the posters question is asking more of: totalDamage=archeryBonus(weaponDmg+enchantDmg)+arrowDmg Which I have no idea if that is the formula. But it likely is much more selective in where bonuses are applied. Don't forget the skill bonuses potions/items can give. Nov 14 '11 at 16:18
• Do skills give bonuses to damage? I've still not been able to find a source that they do. Thought skills might just be for perk access. Nov 16 '11 at 0:03

There are so many factors that go into damage calculation for physical weapons. I'll list the one's that I have found:

(A) Weapon base (for bows: bow damage base + arrow damage base) (B) Damage from weapon enchantments (C) % increase from skill level (D) % increase from perks, enchantments, potions, blessings, ect. (E) % increase from sneak postion (by default: 2x the damage + perk increase, 6x for one-handed = 12x, 3x for bows = 6x, 15x for daggers = 30x) (G) % increase from Mystic Binding perk from Conjuration school (Bound weapons do more damage)

The math involved, while not impossible, can get somewhat complicated, and there is a bit of algebra involved. So please correct me if needed.

A and B are integers and are easily calculated. It's the rest that I'm not sure about how they factor in because they are multipliers. Do they stack and if so in what order? I've noticed that from the sneak position, I can get the message in the corner of the screen that says sneak attack for 30x times damage. Where does that fit into the formula? Imagine it as:

Damage = (A (G*)) (C + D) (E) + B *With bound weapon damage increase

So keeping it simple with small and rounded numbers, if you have:

(A) Sword for 20 damage (B) Sword has enchantment that adds 10 points of fire damage (C) One-handed skill level at 50 (D) Perk adds 40% more damage, enchantment adds 20% more damage, potion adds 10% more damage = 70% more damage total

Then:

20 (1.5 + 1.7) + 10 = 74

So from numerous attempts at figuring this out, here is what I came up with:

For combat: Damage = (Base_Damage*(1 + Current_Effects)) + (Base_Damage*((Skill*(1 + Current_Bonuses))/100))

Where Base_Damage is the weapon's base damage value. Where Current_Effects are anything boosting the effect itself: Bows do 20% more damage, etc... Where Current_Bonuses are anything effecting the Skill itself: Archery is improved by 20%, etc...

Also, the value is either rounded down, or the decimal is not displayed.

Hope that helps.

• ...and damage in this case is the weapon damage. Addition holds true for enchantments and arrows.
– bob
Nov 17 '11 at 0:47