Warhammer Damage & Probability Calculator
Analyze combat effectiveness and predict battle outcomes for Warhammer 40k & Age of Sigmar.
The ‘A’ characteristic of the attacking weapon profile.
The required roll to hit (e.g., 3+).
The ‘S’ characteristic of the weapon.
The ‘AP’ of the weapon (e.g., -1, -2). Use 0 for none.
The ‘D’ characteristic of the weapon.
The ‘T’ characteristic of the target model.
The target’s save characteristic (e.g., 3+).
The target’s invulnerable save (e.g., 5++). Select ‘None’ if not applicable.
Applies common re-roll abilities for hit rolls.
Applies common re-roll abilities for wound rolls.
Expected Outcome
Expected Damage Dealt
Successful Hits
Successful Wounds
Failed Saves
| Damage Threshold | Probability |
|---|
What is a Warhammer Calculator?
A warhammer calculator, often called a “Math-hammer” tool, is a specialized statistical calculator used by players of tabletop wargames like Warhammer 40,000 and Warhammer: Age of Sigmar. Its primary purpose is to predict the average outcome of a combat interaction between two units. By inputting the core statistics of the attacking unit and the defending unit, the calculator processes the probabilities at each stage of the game’s combat sequence: hitting, wounding, saving, and inflicting damage. This allows players to make more informed strategic decisions, compare the effectiveness of different units, and understand the likely results of their choices before committing to a move on the tabletop. It is an essential tool for anyone interested in {related_keywords} and competitive play.
The Warhammer Calculator Formula and Explanation
The core of a warhammer calculator relies on a sequence of probability calculations. The average damage is not a simple formula but a chain of expected values. The basic calculation is:
Expected Damage = (Number of Attacks) × P(Hit) × P(Wound) × P(Failed Save) × (Damage per Wound)
Each probability (P) is determined by the specific stats and dice roll requirements. For example, P(Hit) for a unit with a 3+ Ballistic Skill is 4/6 (since rolls of 3, 4, 5, or 6 succeed). Re-rolls and other abilities add layers to this calculation, which this tool automatically handles. Understanding {related_keywords} is key to mastering the game.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Attacks (A) | The number of dice rolled by the attacker. | Unitless count | 1 – 30 |
| Skill (BS/WS) | The target number for a successful hit roll. | Dice roll (X+) | 2+ to 6+ |
| Strength (S) | The power of the attack. | Unitless value | 1 – 20 |
| Toughness (T) | The resilience of the target. | Unitless value | 1 – 20 |
| Armour Penetration (AP) | Reduces the target’s Armour Save. | Modifier | 0 to -6 |
| Save (Sv) | The target number for a successful armour save. | Dice roll (X+) | 2+ to 6+ |
| Damage (D) | The amount of damage inflicted per failed save. | Wounds | 1 – 12 |
Practical Examples
Example 1: Space Marines vs. Ork Boyz
Imagine 5 Intercessors (a standard Space Marine unit) firing their Bolt Rifles at a squad of 10 Ork Boyz.
- Inputs: 10 Attacks (Rapid Fire), 3+ Skill, Strength 4, AP -1, Damage 1.
- Defender Inputs: Toughness 5, 6+ Save.
- Results: This warhammer calculator would show an expected ~2.22 total damage. This helps a player quickly gauge that this volley is unlikely to wipe out more than two Ork Boyz on average, which is crucial for target prioritization.
Example 2: Anti-Tank Weapon vs. Vehicle
A Leman Russ Battle Tank fires its main cannon at an enemy transport.
- Inputs: 6 Attacks (hypothetical), 4+ Skill, Strength 8, AP -2, Damage 3.
- Defender Inputs: Toughness 7, 3+ Save, No Invulnerable Save.
- Results: The calculator would process the higher strength vs. toughness, the modified save, and the multi-damage profile to predict a significant amount of damage, likely around 5-6 wounds. This confirms the weapon is a good choice for this target. For more detailed analysis, see our guide on {related_keywords}.
How to Use This Warhammer Calculator
Using this tool is straightforward and designed for quick analysis during list-building or even during a game.
- Enter Attacker Stats: Fill in the fields for the attacking unit, including Number of Attacks, Skill (BS/WS), Strength, Armour Penetration (AP), and Damage.
- Enter Defender Stats: Input the target’s Toughness, Armour Save, and any Invulnerable Save they may have. If a model has no invulnerable save, leave it as ‘None’.
- Apply Modifiers: Select any applicable re-roll abilities for hits or wounds from the dropdown menus. These significantly affect the outcome.
- Review Results: The calculator instantly updates. The primary result shows the total expected damage. The intermediate values break down how many hits, wounds, and failed saves are expected on average.
- Analyze Advanced Data: Use the chart to visualize the damage flow and the probability table to understand the chances of dealing specific amounts of damage, which is vital for risk assessment. Proper use of a warhammer calculator is a cornerstone of advanced strategy.
Key Factors That Affect Damage
Several key relationships dictate the results of a warhammer calculator. Mastering them is key to effective play.
- Strength vs. Toughness: This is the most crucial breakpoint. If S is double T, you wound on a 2+. If S is greater than T, you wound on a 3+. If S equals T, it’s a 4+. Understanding these tiers is fundamental.
- Armour Penetration (AP): High AP can completely negate a target’s armor, making it a vital stat against heavily armored elites. An AP of -3 turns a 2+ save into a 5+ save.
- Volume of Attacks: Sometimes, many low-quality shots (low S, low AP) can be more effective against weak targets than a few high-quality shots. This tool helps you compare.
- Re-rolls: The ability to re-roll failed dice is one of the most powerful in the game. Re-rolling all failed hits is mathematically superior to a +1 to hit modifier in most cases. Our resources on {related_keywords} delve deeper into this.
- Invulnerable Saves: These saves are not affected by AP, making them a powerful defense against high-AP weaponry. A model will always use its Invulnerable Save if it’s better than its modified Armour Save.
- Damage Characteristic: A high damage weapon (e.g., D6 damage) is inefficient against single-wound models due to “wasted” damage. This calculator helps quantify that efficiency.
Frequently Asked Questions (FAQ)
1. What is “Math-hammer”?
“Math-hammer” is the community term for using probability and statistics to analyze Warhammer. This warhammer calculator is a prime example of a Math-hammer tool.
2. How does the calculator handle re-rolls?
It calculates the probability of success on the first roll, then adds the probability of failing the first roll multiplied by the probability of succeeding on the second (re-rolled) attempt.
3. What’s the difference between an Armour and Invulnerable Save?
An Armour Save is modified by the AP of an attack. An Invulnerable Save is not. This calculator automatically determines which save the defender would use.
4. Why is the result a decimal? You can’t deal 3.5 damage.
The result is a statistical average or “expected value.” Over many identical trials, the average damage dealt would approach this number. It represents the most likely trend, not a guaranteed outcome in a single roll.
5. Does this work for Warhammer: Age of Sigmar (AoS)?
Yes. While the terminology is slightly different (e.g., “Rend” instead of “AP”), the core mechanics of rolling to hit, wound, and save are identical, making this calculator perfectly suitable for AoS.
6. How do I input a D6 number of attacks?
For a variable number of attacks (like D6), it’s standard practice to use the average value. The average of a D6 roll is 3.5. For a D3, it’s 2. Enter that average into the “Number of Attacks” field.
7. Can this calculator handle abilities like “Feel No Pain”?
This specific version calculates damage inflicted up to the failed save step. A “Feel No Pain” roll is a subsequent step that would further reduce the damage taken. For example, a 5+ FNP would reduce incoming damage by 1/3 on average.
8. How accurate are these predictions?
The mathematical predictions of average outcomes are very accurate. However, the dice are random. The calculator shows the most probable outcome, but extreme results (rolling all sixes or all ones) are always possible in a real game.