40k Damage Calculator
Master the Mathhammer: Optimize Your Unit Efficiency
Total shots or swings
Die roll needed to hit
Weapon Strength value
Enter as positive number (e.g., 1 for AP -1)
Damage per successful wound
Target’s Toughness value
Target’s base armor save
Maximum save regardless of AP
Final chance to ignore damage
Expected Total Damage
6.67
3.33
2.78
Calculation: Hits (3+) → Wounds (S4 vs T4) → Save (3+ vs AP1) → Total Damage
Damage Profile vs. Various Toughness
Shows how your weapon performs against T3 through T12 targets
Comparative Performance Table
| Target Type | Toughness | Save | Expected Damage | Efficiency |
|---|
What is a 40k Damage Calculator?
A 40k damage calculator is an essential tool for Warhammer 40,000 players, commonly referred to as “Mathhammer.” This utility allows players to determine the statistical average of how much damage a specific unit will deal to a target under various conditions. By inputting variables such as the number of attacks, Ballistic Skill (BS), Weapon Strength, Armor Penetration (AP), and the defender’s Toughness and Armor Save, the 40k damage calculator provides a reliable prediction of outcome.
Who should use it? Competitive players use it to optimize their army lists, while casual players find it helpful for understanding why certain units consistently underperform or overperform on the tabletop. A common misconception is that a 40k damage calculator guarantees results; in reality, it provides the “expected value,” while actual dice rolls will fluctuate due to variance.
40k Damage Calculator Formula and Mathematical Explanation
The math behind the 40k damage calculator follows a sequential probability chain. Since each step in a Warhammer 40k attack sequence depends on the previous success, we multiply the probabilities of each stage.
The Core Equation:
Expected Damage = Attacks × P(Hit) × P(Wound) × P(Failed Save) × Damage Characteristic × P(Failed FNP)
Variable Breakdown
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Attacks (A) | Number of dice rolled for the attack | Integer | 1 – 40+ |
| BS / WS | The roll needed to score a hit | Target Number | 2+ to 6+ |
| Strength (S) | The power of the weapon | Integer | 2 – 20 |
| Toughness (T) | The resilience of the target | Integer | 3 – 14 |
| AP | Armor Penetration reducing the save | Modifier | 0 to -6 |
Practical Examples (Real-World Use Cases)
Example 1: Space Marine Intercessor vs. Ork Boy
An Intercessor unit fires 10 Bolt Rifle shots. S4, AP-1, D1. The Ork Boy is T5 with a 5+ save. Using the 40k damage calculator:
- Hits: 10 shots on 3+ = 6.67 hits.
- Wounds: S4 vs T5 requires 5+ = 2.22 wounds.
- Saves: 5+ save becomes 6+ due to AP-1. Failed saves = 83.3%.
- Result: 1.85 total damage.
Example 2: Lascannon vs. Rhino Tank
A single Lascannon shot: S12, AP-3, D d6+1 (Average 4.5). Target Rhino is T9, Sv 3+.
- Hit: 1 shot on 3+ = 0.67 hits.
- Wound: S12 vs T9 requires 3+ = 0.44 wounds.
- Save: 3+ save becomes 6+ due to AP-3. Failed saves = 83.3%.
- Damage: 0.37 unsaved wounds × 4.5 damage = 1.66 total damage.
How to Use This 40k Damage Calculator
- Enter Attacker Stats: Fill in the number of attacks and the skill required to hit (e.g., 3+).
- Set Weapon Power: Input the Strength and AP. Note that AP should be entered as a positive number (if it’s AP-2, enter 2).
- Target Selection: Input the defender’s Toughness and their base Armor Save.
- Advanced Defense: If the target has an Invulnerable save or Feel No Pain, select those from the dropdowns.
- Analyze Results: View the “Expected Total Damage” and use the SVG chart to see how the weapon scales against different toughness brackets.
Key Factors That Affect 40k Damage Calculator Results
- Weapon Strength vs. Toughness: This is the most critical threshold. A weapon with S8 is twice as effective against T4 (wounds on 2+) as it is against T8 (wounds on 4+).
- Armor Penetration (AP): AP values are massive force multipliers. Reducing a 3+ save to a 5+ save doubles the amount of damage that gets through.
- Invulnerable Saves: These create a “damage floor.” No matter how high your AP is, an invulnerable save ensures the defender always has a specific chance to survive.
- Damage Variance: Weapons with random damage (like D6) are riskier. Our 40k damage calculator uses averages, but in-game variance can be swingy.
- Feel No Pain (FNP): This is a secondary layer of defense that reduces damage after saves are failed. It is particularly effective against high-damage weapons.
- Volume of Fire: High attack counts (A) reduce the impact of “bad dice” by increasing the sample size, making the 40k damage calculator more accurate in practice.
Frequently Asked Questions (FAQ)
1. Why does the calculator show decimals like 2.78?
Because it calculates the statistical mean (average). You can’t roll 0.78 of a wound, but over 100 games, this unit will average that amount of damage per turn.
2. Does this 40k damage calculator account for rerolls?
This basic version uses raw stats. To account for rerolls (like “Reroll 1s”), you would adjust the probability of hitting or wounding manually by roughly 16%.
3. How does AP affect Invulnerable Saves?
AP does not affect Invulnerable Saves. The 40k damage calculator automatically chooses the better of the two saves for the defender.
4. Is Toughness 12 much better than Toughness 10?
Yes, especially against S6 weapons. S6 wounds T10 on a 5+, but T12 on a 6+, doubling the defensive efficiency.
5. What is “Mathhammer”?
Mathhammer is the application of probability theory to Warhammer 40,000 to determine the most efficient units for their point cost.
6. Can this calculator handle “Mortal Wounds”?
Mortal wounds bypass hit/wound/save sequences. You can calculate them separately and add them to the total expected damage.
7. How does the “Feel No Pain” mechanic work?
FNP is rolled for every point of damage taken. If you take 3 damage and have a 5+++, you roll 3 dice and ignore each 5 or 6.
8. Why use a 40k damage calculator instead of rolling dice?
The calculator helps in the list-building phase to ensure your army has answers for various threats like heavy tanks or hordes.
Related Tools and Internal Resources
- Army List Efficiency Guide – Learn how to balance your points vs damage output.
- Unit Stat Database – Compare base stats for all major 10th edition factions.
- Dice Probability Charts – A deep dive into the math of 2D6 and 3D6 rolls.
- Competitive Meta Analysis – See which units are currently dominating tournaments.
- Points per Wound Calculator – Calculate the defensive value of your units.
- Weapon Optimization Tool – Find the best weapon loadouts for your squads.