40k Damage Calculator

Accurately determine the offensive output of your Warhammer 40,000 units and optimize your battlefield strategy.

Unit Offensive Output Calculator

Calculation Results

Formula Explanation: Damage is calculated by determining the probability of hits, then the probability of wounding with those hits, and finally the probability of the target failing its save. The average damage per target is the product of these probabilities multiplied by the weapon’s base damage.

Damage Breakdown Table

Probability Breakdown per Attack

Metric	Probability	Calculation
To Hit Roll (Success)	—	—
To Wound Roll (Success)	—	—
Target Save Roll (Fail)	—	—
Effective Damage Per Successful Hit	—	—

Damage Output Over Range

What is a 40k Damage Calculator?

A 40k Damage Calculator is a specialized tool designed for players of the tabletop wargame Warhammer 40,000. It helps players quantify the offensive effectiveness of their units by calculating the average amount of damage a weapon or unit can inflict on a target. In the complex strategic environment of 40k, understanding your damage output is crucial for effective army building, tactical deployment, and making informed in-game decisions.

Who should use it? Any Warhammer 40,000 player looking to optimize their army’s performance. This includes:

• Competitive Players: To fine-tune army lists and predict match outcomes.
• Hobbyists: To understand the capabilities of different units and weapons for narrative play or general enjoyment.
• New Players: To grasp the fundamental mechanics of combat resolution in 40k.

Common Misconceptions:

• “It’s just about high Damage stat”: While the Damage characteristic is important, it’s only one piece of the puzzle. Hit probability, wound probability, and the target’s defensive characteristics (Toughness, Save, Invulnerable Save) all play significant roles.
• “Calculators always give the perfect result”: These calculators provide an *average* output. Dice rolls introduce variance, and specific game situations (e.g., cover saves, modifiers, special abilities) can alter outcomes.
• “It only applies to shooting”: While often used for shooting, the core principles apply to melee combat as well, with Weapon Skill (WS) replacing Ballistic Skill (BS).

40k Damage Calculator Formula and Mathematical Explanation

The 40k Damage Calculator works by breaking down the combat sequence into a series of probabilistic steps. Each step’s success probability is multiplied to determine the overall chance of dealing damage.

Step-by-Step Derivation:

1. Hit Roll: The first step is determining if an attack successfully hits. This depends on the attacker’s Ballistic Skill (BS) or Weapon Skill (WS) and the target’s characteristics. Modifiers like cover or special rules can adjust this.
2. Wound Roll: If the attack hits, the next step is determining if it wounds the target. This is based on comparing the weapon’s Strength (S) to the target’s Toughness (T). A table dictates the roll needed to wound (e.g., S=4 vs T=4 needs a 4+, S=4 vs T=8 needs a 6+). Modifiers can also apply here.
3. Target Save Roll: If the attack successfully wounds, the target gets to make a Save (Sv) roll. This is modified by the weapon’s Armour Penetration (AP) value (e.g., AP -1 reduces the target’s 3+ save to a 4+). If the target fails its save, it takes damage.
4. Damage Application: If the save is failed, the weapon’s Damage (D) characteristic is applied. Some weapons have variable damage (e.g., D3, D6+1), which adds another layer of probability. For simplicity, this calculator uses the base Damage value.

Variable Explanations and Formula:

The core calculation for average damage per successful hit involves:

Probability of Hitting = (BS/WS roll needed to hit) / 6 + Modifiers

Probability of Wounding = (S vs T roll needed to wound) / 6 + Modifiers

Probability of Target Failing Save = (Target Save roll modified by AP) / 6 + Modifiers

Average Damage Per Attack = (Probability of Hitting) * (Probability of Wounding) * (Probability of Target Failing Save) * (Weapon Damage)

Average Damage Per Target = Average Damage Per Attack * (Number of Attacks)

The calculator uses these probabilities, accounting for potential rerolls.

Variables Table:

Input Variable Definitions

Variable	Meaning	Unit	Typical Range
Weapon Skill (WS) / Ballistic Skill (BS)	Roll needed on a D6 to hit the target.	D6 Value (Lower is better)	1-7 (1+ is impossible, 7+ automatic miss)
Attacks (A)	Number of dice rolled for attacks.	Count	1+
Strength (S)	Offensive characteristic of the weapon.	Characteristic Value	1+
Target Toughness (T)	Defensive characteristic of the target.	Characteristic Value	1+
Weapon Armour Penetration (AP)	Reduces target’s Save roll.	Modifier (Negative Integer)	0 to -5
Target Save (Sv)	Base roll needed to make a successful saving throw.	D6 Value (Higher is better)	0-7 (0+ impossible, 7+ automatic fail)
Weapon Damage (D)	Amount of damage dealt if a save is failed.	Damage Value / Dice	1+
Reroll Misses / Wounds	Boolean flag for reroll capabilities.	Yes/No	0 or 1
Auto-Hit	Flag for attacks that automatically hit.	Yes/No	0 or 1

Practical Examples (Real-World Use Cases)

Let’s explore how the 40k Damage Calculator can be applied in practical scenarios.

Example 1: Astartes Bolter vs. Infantry

Scenario: A Tactical Marine fires his Bolter at a squad of Guardsmen.

Inputs:

• Weapon Skill / Ballistic Skill: 3+
• Attacks: 2
• Weapon Strength: 4
• Target Toughness: 4
• Weapon AP: 0
• Target Save: 3+
• Weapon Damage: 1
• Reroll Misses: No
• Reroll Wounds: No
• Auto-Hit: No

Calculation & Interpretation:

The calculator will determine that the Bolter has a good chance to hit (4+ roll needed, so 3/6 = 50% probability). Against Toughness 4, Strength 4 wounds on a 4+ (50% probability). A 3+ save is common for infantry, and with AP 0, it remains a 3+ (33.3% chance to fail). The damage is 1.

Average Damage per Attack ≈ 0.50 (Hit) * 0.50 (Wound) * 0.333 (Save Fail) * 1 (Dmg) ≈ 0.083 damage.

With 2 attacks, the Average Damage per Target ≈ 0.083 * 2 ≈ 0.166 damage.

Financial Interpretation (in game terms): This low average damage suggests that a single Bolter is unlikely to eliminate a Guardsman quickly. It’s best used against numerous, low-Toughness targets or to chip away at tougher units over time. Multiple Marines firing in unison would be needed for significant impact.

Example 2: Ork Power Klaw vs. Space Marine Terminator

Scenario: An Ork Nob charges a Terminator bodyguard.

Inputs:

• Weapon Skill: 3+
• Attacks: 1
• Weapon Strength: 8
• Target Toughness: 5
• Weapon AP: -2
• Target Save: 2+
• Weapon Damage: 3
• Reroll Misses: No
• Reroll Wounds: Yes (e.g., via a special rule)
• Auto-Hit: No

Calculation & Interpretation:

WS 3+ means a 50% hit chance. Strength 8 vs Toughness 5 wounds on a 3+ (66.7% probability). The Power Klaw’s AP -2 turns the Terminator’s 2+ save into a 4+ (50% chance to fail). Crucially, the reroll wounds mechanic significantly boosts the wound probability.

Base Wound Probability = 0.667. With rerolls, the chance of success is much higher.

Average Damage per Attack ≈ 0.50 (Hit) * [1 – (0.333 * 0.333)] (Wound w/ Reroll) * 0.50 (Save Fail) * 3 (Dmg) ≈ 0.50 * 0.889 * 0.50 * 3 ≈ 0.667 damage.

With 1 attack, the Average Damage per Target ≈ 0.667 damage.

Financial Interpretation (in game terms): Even with rerolls for wounds, the average damage isn’t sky-high due to the Terminator’s good save. However, the high base damage (3) means that *if* the wound and save are successful, it’s a significant chunk of a Terminator’s health (Terminators often have 3 Wounds each).

How to Use This 40k Damage Calculator

Using the 40k Damage Calculator is straightforward. Follow these steps to get accurate damage estimations:

1. Identify Your Unit and Weapon: Determine the specific unit and weapon you want to calculate the damage for. Note its relevant characteristics.
2. Identify the Target Unit: Determine the characteristics of the unit you are attacking (Toughness, Save).
3. Input Base Stats: Enter the core stats into the calculator:
   • Weapon Skill (WS) / Ballistic Skill (BS): The roll needed to hit.
   • Attacks (A): The number of attacks made.
   • Weapon Strength (S): The weapon’s Strength.
   • Target Toughness (T): The target’s Toughness.
   • Weapon Armour Penetration (AP): The weapon’s AP value.
   • Target Save (Sv): The target’s base Save characteristic.
   • Weapon Damage (D): The weapon’s base Damage.
4. Input Modifiers and Special Rules: Select ‘Yes’ for:
   • Reroll Misses: If any failed hit rolls can be rerolled.
   • Reroll Wounds: If any failed wound rolls can be rerolled.
   • Auto-Hit: If the weapon automatically hits (use with caution regarding Blast).
5. Click ‘Calculate Damage’: The calculator will update instantly.

How to Read Results:

• Primary Result (Average Damage per Target): This is the most important number. It represents the expected total damage your unit will inflict across all its attacks against a single target.
• Intermediate Values: These show the average number of hits, wounds, and damage dealt per attack before multiplying by the total attacks. They help understand where the damage output comes from.
• Probability Breakdown Table: This table details the probabilities of each step (hitting, wounding, failing save) and the expected damage per successful hit. It’s useful for understanding the nuances of the calculation.
• Chart: Visualizes how damage scales with the number of attacks or potentially other variables (like distance for shooting).

Decision-Making Guidance:

Use the results to make strategic choices:

• Target Priority: Allocate your high-damage units against the most threatening enemy units based on their defensive stats.
• Army Building: Ensure your army has a balanced mix of anti-infantry, anti-elite, and anti-tank firepower.
• Stratagem Usage: Decide when to spend Command Points on rerolls or buffs to maximize damage against critical targets.

Key Factors That Affect 40k Damage Results

While the calculator provides a solid estimate, several factors in a game of Warhammer 40k can significantly influence actual damage output:

1. Dice Variance: The most significant factor. You might roll exceptionally well or poorly, deviating from the average calculated. This is the core randomness of tabletop gaming.
2. Cover Saves: Enemy units in cover gain a bonus to their Save characteristic (e.g., a +1 to save). This directly reduces the chance of wounds succeeding and increases the overall damage reduction.
3. Invulnerable Saves: Some units have Invulnerable Saves (e.g., 5++), which cannot be modified by AP. This makes them much harder to damage with weapons that have high AP.
4. Target Unit Size & Remaining Models: The ‘Attacks’ characteristic of some weapons (especially Blast weapons) can change based on the number of models remaining in the target unit. This calculator assumes a full-strength unit unless specified otherwise.
5. Specific Unit/Weapon Abilities: Many units and weapons have unique rules (e.g., “Sustained Hits,” “Lethal Hits,” “Critical Wounds”) that modify hit, wound, or damage rolls in ways not captured by standard modifiers.
6. Buffs and Debuffs: Auras from nearby characters, psychic powers, or army-specific abilities can grant bonuses (like +1 to hit/wound) or penalties to either the attacker or defender, drastically altering probabilities.
7. Terrain Effects: Certain terrain pieces might offer defensive benefits or penalize movement and shooting.
8. Psychic Phase Interference: Enemy psychic powers could potentially deny buffs or inflict mortals wounds before the shooting or fighting phase even begins.

Frequently Asked Questions (FAQ)

What is the difference between WS and BS in 40k?

Weapon Skill (WS) is used for melee attacks, while Ballistic Skill (BS) is used for ranged attacks. Both function identically in the calculator: a lower number indicates a better chance to hit (e.g., WS 3+ or BS 3+).

How do I input AP values like -2?

Enter the negative number directly into the Weapon Armour Penetration (AP) field (e.g., -2). The calculator will correctly adjust the target’s save roll.

My weapon has D3+1 damage. How do I use the calculator?

For simplicity, this calculator uses the base ‘flat’ damage value. For D3+1, you’d typically calculate for ‘2’ or ‘3’ damage and consider the average yourself, or use a more advanced calculator. The current tool focuses on the core hit-to-wound-to-save mechanics.

What does “Auto-hit” mean and when does it apply?

Auto-hit means the attack automatically hits regardless of BS/WS. It’s common for some psychic powers or the Blast weapon rule *if* the unit has 5 or more models. If your unit has fewer than 5 models, Blast weapons do NOT auto-hit.

Can this calculator handle multiple target units with different saves?

No, this calculator is designed to assess damage against a single target profile at a time. For army-wide calculations against mixed targets, you would need to run the calculator multiple times or use a more complex simulation.

What is the S vs T chart in the rulebook?

The Strength vs Toughness (S vs T) chart in the Warhammer 40,000 rules dictates the roll needed to wound. Generally, if S is double T, you wound on a 2+. If S equals T, you wound on a 4+. If T is double S, you wound on a 6+. The calculator implements this standard chart.

How do rerolls affect the damage calculation?

Rerolls significantly increase the probability of success. For example, rerolling a miss (4+ needed) means you only fail if you roll two misses in a row (0.5 * 0.5 = 0.25 chance of failure), drastically improving the hit probability. The calculator accounts for this by adjusting the probabilities.

Is the calculator still useful if I don’t have rerolls?

Absolutely. The calculator provides the baseline average damage output even without rerolls. This is crucial for understanding a unit’s inherent capabilities and for planning against targets that don’t offer reroll opportunities.