40k Damage Calculator

An essential tool for Warhammer 40,000 players to forecast average damage and optimize strategy.

0.00Average Damage Dealt

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Calculation based on sequential probability analysis.

Damage Probability Analysis

A visual breakdown of the attack sequence attrition.

What is a 40k Damage Calculator?

A 40k Damage Calculator is a tool for players of the Warhammer 40,000 tabletop game to estimate the average damage output of an attack. This practice, often called “Math-hammer,” uses probability to forecast the outcome of the game’s core dice-rolling sequence: hitting, wounding, saving, and damage infliction. While the luck of the dice determines any single outcome, understanding the statistical average helps players make more informed decisions.

This calculator is for anyone from a new player trying to understand how weapon stats interact, to a competitive tournament-goer fine-tuning their army list. By inputting the characteristics of an attacking weapon and a defending target, you can quickly see how effective that attack is likely to be, helping you choose the right tool for the right job on the battlefield. It removes the guesswork and provides a solid, data-driven foundation for your tactical choices. For more on improving your game, see our guide to advanced Warhammer tactics.

The 40k Damage Formula and Explanation

The core of damage calculation in Warhammer 40,000 is a sequence of probabilities. Each step of an attack acts as a filter, reducing the number of potential successes from the previous step. The general formula for average damage is:

Expected Damage = Attacks × P(Hit) × P(Wound) × P(Failed Save) × Average Damage per Weapon × P(Failed FNP)

Where ‘P(…)’ denotes the probability of that event occurring. For example, a “3+” to hit means you succeed on a 3, 4, 5, or 6, which is a 4-in-6 chance, or a probability of ~66.7%.

Calculation Variables

Variable	Meaning	Unit / Type	Typical Range
Attacks	The number of dice rolled to hit.	Count (unitless)	1 – 30
BS / WS	The target number needed on a D6 to score a hit.	X+ (D6 roll)	2+ to 6+
Strength (S)	The power of the weapon.	Value (unitless)	1 – 20
Toughness (T)	The resilience of the target.	Value (unitless)	1 – 20
Armour Penetration (AP)	Reduces the target’s Armour Save roll.	Modifier (unitless)	0 – 6
Damage	Damage inflicted per failed save.	Value / Dice (e.g., d6)	1 – 12

Practical Examples

Example 1: Intercessors vs. Ork Boyz

A standard squad of 5 Intercessors fires their Bolt Rifles at a unit of Ork Boyz.

• Inputs: 2 Attacks each (Rapid Fire range) for 10 total attacks, BS 3+, S 4, AP -1, Damage 1.
• Target: Ork Boyz are T 5 with a 6+ Save.
• Calculation: The Intercessors need 3+ to hit. With S4 vs T5, they need 5+ to wound. The Ork’s 6+ save is modified by AP-1 to a 7+, meaning it’s impossible.
• Result: This results in an average of 2.22 damage, which should eliminate 2 Ork Boyz on average. To better understand this interaction, check our hit and wound rolls explained guide.

Example 2: Lascannon vs. Leman Russ Tank

A single Devastator Marine fires a Lascannon at a Leman Russ Battle Tank.

• Inputs: 1 Attack, BS 3+, S 12, AP -3, Damage D6.
• Target: A Leman Russ is T 11 with a 2+ Save.
• Calculation: The Lascannon hits on a 3+. Strength 12 is greater than Toughness 11, so it wounds on a 3+. The tank’s 2+ save is modified by AP-3 to a 5+. The average damage of a D6 is 3.5.
• Result: This single shot has an average damage output of 1.56 damage against the tank’s hull. This highlights how even powerful single shots can be unreliable without support. For more on this, see our article on choosing the right weapon.

How to Use This 40k Damage Calculator

Using this tool is straightforward. Follow these steps to get an accurate damage forecast:

1. Enter Attacker Stats: Fill in the number of attacks, the skill required to hit (BS/WS), the weapon’s Strength (S), its Armour Penetration (AP), and its Damage characteristic.
2. Enter Defender Stats: Input the target’s Toughness (T), Armour Save (Sv), and any Invulnerable or Feel No Pain saves they may have.
3. Select Modifiers: Check any boxes for re-rolls that apply to the attack. This significantly impacts the final probability and is a key part of an effective strategy for re-rolls.
4. Review the Results: The calculator will instantly update, showing the final average damage, as well as the intermediate values for expected hits, wounds, and failed saves. The chart provides a visual representation of how the initial attacks are reduced at each stage.
5. Interpret the Output: The “Average Damage Dealt” is the most important number. It tells you, over many trials, the statistical outcome of this attack. Use this to compare different weapons or decide which enemy unit to target for maximum efficiency.

Key Factors That Affect 40k Damage Output

Several key factors can dramatically swing the outcome of an attack. Understanding them is crucial for effective “Math-hammer.”

• Hit & Wound Rolls: The core of any attack. A small “+1 to hit” bonus can increase hits by 16.7% and is often more valuable than re-rolls. The Strength vs. Toughness chart is another critical breakpoint; increasing Strength to be equal to, greater than, or double the target’s Toughness provides massive boosts to wounding probability.
• Armour Penetration (AP): AP is vital for taking down heavily armored targets. An attack with high AP can render a target’s primary defense useless. Our AP guide has more details.
• Invulnerable Saves: These saves are powerful because they are unaffected by AP. A target with a good invulnerable save can be highly resilient to attacks that would otherwise slice through their armor.
• Number of Attacks: Volume of fire is often more reliable than a single powerful shot. More attacks mean more chances to get past the defender’s layers of dice rolls, leading to more consistent, predictable damage.
• Damage Characteristic: A high damage weapon is great, but only if it can get through. Damage is the final multiplier; a D6 damage weapon that never wounds is useless. Random damage (like D3 or D6) also adds variance; for average calculations, values like 3.5 (for D6) and 2 (for D3) are used.
• Re-rolls: Re-rolling dice is one of the most powerful mechanics in the game. Re-rolling all failed hits, for instance, provides a significant percentage increase in successful hits, cascading through the entire damage formula.

Frequently Asked Questions (FAQ)

What does ‘X+’ mean?

In Warhammer 40,000, ‘X+’ refers to the target number on a six-sided die (D6). For example, a Ballistic Skill of 3+ means you need to roll a 3, 4, 5, or 6 to succeed.

How does Strength (S) vs. Toughness (T) work?

The wound roll is determined by comparing the weapon’s Strength to the target’s Toughness. If S equals T, you wound on a 4+. If S is higher, 3+. If S is double T, 2+. If S is lower, 5+. If S is half of T or less, 6+.

What’s the difference between Armour Save and Invulnerable Save?

An Armour Save is modified by the Armour Penetration (AP) of a weapon. An Invulnerable Save is not. If the modified Armour Save would be worse than the Invulnerable Save, you use the Invulnerable Save instead.

How do you handle random damage like ‘D6’ in a 40k damage calculator?

For calculating averages, we use the statistical mean of the dice roll. A D6 has an average value of 3.5, and a D3 has an average of 2. This calculator automatically converts dice notation into its average value.

Is average damage guaranteed?

No. The calculator shows the statistical average over many trials. In any single roll of the dice, you could do much more or much less damage. However, over the course of a full game, your results will tend towards the averages calculated here.

Which is better: re-rolling 1s or getting +1 to hit?

It depends on your starting skill. A +1 to hit is almost always better. For example, moving from a 4+ to a 3+ to hit increases your success chance from 50% to 66.7%. Re-rolling 1s on a 4+ only increases it from 50% to ~58.3%.

How does this calculator handle Feel No Pain (FNP)?

Feel No Pain is a final step. After a wound is inflicted and unsaved, the target gets to roll a die for each point of damage. An FNP of 5+ means that for every point of damage, there’s a 2-in-6 chance (33.3%) to ignore it. This calculator applies this as a final reduction to the total damage.

Why isn’t my high-damage weapon showing a high output?

A weapon’s final damage is only one part of the equation. If its low number of attacks, poor skill, or low strength prevents it from getting hits and wounds through, the high damage value will rarely get a chance to be applied. A balanced profile is often better than one that is exceptional in only a single area.