40k Dice Calculator: Master Your Warhammer 40,000 Combat Rolls

Unlock the power of “mathhammer” with our comprehensive 40k Dice Calculator.
Accurately predict the expected damage output of your units against any target,
factoring in Ballistic Skill, Weapon Skill, Strength, Toughness, Armor Penetration, Saves, Invulnerable Saves, and Feel No Pain.
Optimize your army lists and tactical decisions with precise probability calculations.

Warhammer 40,000 Combat Predictor

Detailed Probability Breakdown

Stage	Target Roll (X+)	Probability	Expected Successes

What is a 40k Dice Calculator?

A 40k Dice Calculator is an essential tool for any Warhammer 40,000 player looking to gain a strategic edge. It’s a digital utility designed to simulate the complex dice rolls involved in the game’s combat system, providing players with statistical predictions of damage output. Instead of relying on guesswork, a 40k Dice Calculator allows you to input specific unit and weapon profiles, along with target characteristics, to determine the average number of hits, wounds, and ultimately, the total damage you can expect to inflict.

This tool is invaluable for understanding the true effectiveness of your units, comparing different weapon options, and making informed tactical decisions on the battlefield. It translates the often-random nature of dice rolls into predictable averages, helping you build more efficient army lists and execute more successful strategies.

Who Should Use a 40k Dice Calculator?

• Competitive Players: To fine-tune army lists, identify optimal unit matchups, and understand damage thresholds.
• List Builders: To compare weapon loadouts and unit compositions for maximum efficiency.
• New Players: To quickly grasp the impact of different stats (Strength, Toughness, AP, Saves) without extensive in-game experience.
• Hobbyists: To satisfy curiosity about specific combat scenarios or “what if” questions.
• Content Creators: To analyze unit performance for articles, videos, or podcasts.

Common Misconceptions about the 40k Dice Calculator

While incredibly useful, it’s important to understand what a 40k Dice Calculator does and doesn’t do:

• It’s not a guarantee: The calculator provides *expected* outcomes, which are averages over many rolls. Any single game or dice roll can deviate significantly due to pure chance.
• It doesn’t account for all rules: Most calculators focus on the core attack sequence. Special rules like re-rolls, modifiers, mortal wounds, or specific unit abilities might need manual adjustment or a more advanced calculator.
• It’s not a substitute for game knowledge: While it helps with math, understanding terrain, mission objectives, and opponent strategies remains crucial.

40k Dice Calculator Formula and Mathematical Explanation

The core of any 40k Dice Calculator lies in its sequential probability calculations. Each stage of the attack sequence reduces the number of successful outcomes from the previous stage. Here’s a step-by-step breakdown:

Step-by-Step Derivation:

1. Hit Probability:
   • A D6 roll must equal or exceed the attacker’s Ballistic Skill (BS) or Weapon Skill (WS).
   • Probability = (7 – Skill Value) / 6. (e.g., for 3+, it’s (7-3)/6 = 4/6 = 0.667)
   • Expected Hits = Number of Attacks × Hit Probability.
2. Wound Probability:
   • This depends on the comparison between Attacker Strength (S) and Target Toughness (T).
   • If S ≥ 2T: 5/6 chance to wound.
   • If S > T: 4/6 chance to wound.
   • If S = T: 3/6 chance to wound.
   • If S < T: 2/6 chance to wound.
   • If S ≤ 0.5T: 1/6 chance to wound.
   • Expected Wounds (Pre-Save) = Expected Hits × Wound Probability.
3. Save Probability:
   • The target rolls a D6, aiming to equal or exceed their modified Save (Sv) characteristic.
   • Effective Save = Max(Target Save + AP Value, Target Invulnerable Save). If no Invulnerable Save, it’s just Target Save + AP Value. The minimum roll needed is 2+.
   • Probability of Failing Save = (Effective Save – 1) / 6. (e.g., for a 4+ save, it’s (4-1)/6 = 3/6 = 0.5)
   • Expected Wounds Taken (Pre-FNP) = Expected Wounds (Pre-Save) × Probability of Failing Save.
4. Feel No Pain (FNP) Probability:
   • If the target has a FNP ability, they roll a D6 for each wound taken, aiming to equal or exceed their FNP value.
   • Probability of Failing FNP = (FNP Value – 1) / 6. (e.g., for a 5+ FNP, it’s (5-1)/6 = 4/6 = 0.667)
   • Expected Wounds Dealt = Expected Wounds Taken (Pre-FNP) × Probability of Failing FNP.
5. Total Expected Damage Output:
   • Total Expected Damage = Expected Wounds Dealt × Damage per Wound.

Variable Explanations and Table:

Understanding the variables is key to using any 40k Dice Calculator effectively.

Variable	Meaning	Unit	Typical Range
Number of Attacks	The total number of attacks a unit makes.	Attacks	1 – 100+
Skill Value (BS/WS)	The D6 roll needed to hit (e.g., 3+).	+	2 – 6
Attacker Strength (S)	The attacking unit’s Strength characteristic.	S	1 – 14
Target Toughness (T)	The defending unit’s Toughness characteristic.	T	1 – 14
Armor Penetration (AP)	The weapon’s ability to reduce target’s save.	AP	0 to -5 (or more)
Damage (D)	The damage inflicted by each successful wound.	D	1 – 6 (or D3, D6 average)
Target Save (Sv)	The defending unit’s normal armor save.	+	2 – 7 (7+ means no save)
Invulnerable Save (Invuln)	The defending unit’s special save that ignores AP.	+	2 – 7 (0 or 7+ means no invuln)
Feel No Pain (FNP)	The defending unit’s ability to ignore wounds.	+	2 – 7 (0 or 7+ means no FNP)

Practical Examples Using the 40k Dice Calculator

Let’s put the 40k Dice Calculator to the test with some real-world Warhammer 40,000 scenarios.

Example 1: Space Marine Intercessors vs. Ork Boyz

Scenario: 5 Intercessors (10 attacks total) with Bolt Rifles (S4, AP-1, D1) shooting at a unit of Ork Boyz (T5, Sv6+, no Invuln, no FNP). Intercessors hit on 3+.

• Inputs:
  • Number of Attacks: 10
  • Skill Value (BS/WS): 3
  • Attacker Strength (S): 4
  • Target Toughness (T): 5
  • Armor Penetration (AP): -1
  • Damage (D): 1
  • Target Save (Sv): 6
  • Invulnerable Save (Invuln): 0
  • Feel No Pain (FNP): 0
• Expected Outputs (using the 40k Dice Calculator):
  • Expected Hits: 10 * (4/6) = 6.67
  • Expected Wounds (Pre-Save): S4 vs T5 is 4/6 to wound. 6.67 * (4/6) = 4.44
  • Effective Save: 6 (base) + (-1 AP) = 5+. No invuln. So, 5+ save. Probability of failing 5+ save = (5-1)/6 = 4/6. 4.44 * (4/6) = 2.96
  • Expected Wounds Dealt: 2.96 (no FNP)
  • Expected Total Damage Output: 2.96 * 1 = 2.96
• Interpretation: On average, 5 Intercessors will inflict almost 3 wounds on Ork Boyz. This helps determine if they are an efficient target or if another unit should engage.

Example 2: Custodian Guard vs. Tyranid Carnifex

Scenario: A Custodian Guard (3 attacks) with a Guardian Spear (S6, AP-3, D2) charging a Carnifex (T7, Sv2+, Invuln4+, no FNP). Custodian hits on 2+.

• Inputs:
  • Number of Attacks: 3
  • Skill Value (BS/WS): 2
  • Attacker Strength (S): 6
  • Target Toughness (T): 7
  • Armor Penetration (AP): -3
  • Damage (D): 2
  • Target Save (Sv): 2
  • Invulnerable Save (Invuln): 4
  • Feel No Pain (FNP): 0
• Expected Outputs (using the 40k Dice Calculator):
  • Expected Hits: 3 * (5/6) = 2.5
  • Expected Wounds (Pre-Save): S6 vs T7 is 3/6 to wound. 2.5 * (3/6) = 1.25
  • Effective Save: Base 2+ + (-3 AP) = -1. This is worse than the 4+ Invulnerable Save. So, the target uses their 4+ Invulnerable Save. Probability of failing 4+ save = (4-1)/6 = 3/6. 1.25 * (3/6) = 0.625
  • Expected Wounds Dealt: 0.625 (no FNP)
  • Expected Total Damage Output: 0.625 * 2 = 1.25
• Interpretation: A single Custodian Guard can expect to inflict about 1.25 damage on a Carnifex. This highlights the resilience of the Carnifex and the importance of multiple attacking models or higher damage weapons. This 40k Dice Calculator helps confirm that even powerful units need support against tough targets.

How to Use This 40k Dice Calculator

Our 40k Dice Calculator is designed for ease of use, allowing you to quickly get the combat predictions you need. Follow these simple steps:

Step-by-Step Instructions:

1. Input Number of Attacks: Enter the total number of attacks your unit will make.
2. Set Skill Value (BS/WS): Input the Ballistic Skill (for shooting) or Weapon Skill (for melee) your unit needs to hit. For example, if they hit on a 3+, enter ‘3’.
3. Enter Attacker Strength (S): Provide the Strength characteristic of your attacking weapon or unit.
4. Enter Target Toughness (T): Input the Toughness characteristic of the enemy unit you are attacking.
5. Specify Armor Penetration (AP): Enter the AP value of your weapon. Remember, AP-1 is entered as ‘-1’. Enter ‘0’ if your weapon has no AP.
6. Define Damage (D): Input the damage value of your weapon. For D3, use 2; for D6, use 3.5 (average values).
7. Set Target Save (Sv): Enter the normal armor save of the target unit. If they have no save, enter ‘7’.
8. Input Invulnerable Save (Invuln): If the target has an invulnerable save, enter its value. Enter ‘0’ if they do not have one.
9. Specify Feel No Pain (FNP): If the target has a Feel No Pain ability, enter its value. Enter ‘0’ if they do not have one.
10. Calculate: Click the “Calculate Expected Damage” button. The results will update automatically.
11. Reset: Click “Reset” to clear all fields and return to default values.
12. Copy Results: Use the “Copy Results” button to quickly grab the key outputs for sharing or record-keeping.

How to Read Results:

• Expected Wounds Dealt (Primary Result): This is the most crucial number, representing the average number of wounds that will successfully bypass all defenses.
• Expected Hits: The average number of successful hits.
• Expected Wounds (Pre-Save): The average number of wounds inflicted before the target attempts any saves.
• Expected Wounds Taken (Pre-FNP): The average number of wounds that successfully bypassed armor and invulnerable saves, but before any Feel No Pain rolls.
• Expected Total Damage Output: The final average damage inflicted, considering all stages and the weapon’s damage characteristic.
• Probability Breakdown Table: Provides a detailed view of probabilities and expected successes at each stage of the attack sequence.
• Dynamic Chart: Visualizes how your expected wounds change against varying target Toughness and Save values, offering quick comparative insights.

Decision-Making Guidance:

The 40k Dice Calculator empowers you to make better decisions:

• Target Prioritization: Quickly see which of your units are most effective against specific enemy threats.
• Weapon Choice: Compare different weapon options for a unit to determine which is optimal for a given target.
• Army List Optimization: Identify gaps in your army’s damage output or resilience.
• Strategic Planning: Understand how many units or attacks are typically needed to eliminate a specific enemy unit.

Key Factors That Affect 40k Dice Calculator Results

The outcome of any combat calculation in Warhammer 40,000, and thus the results from a 40k Dice Calculator, are influenced by several interconnected factors. Understanding these helps you manipulate the odds in your favor.

1. Number of Attacks: Fundamentally, more attacks mean more chances to hit and wound. This is often the easiest factor to increase through unit size, abilities, or stratagems.
2. Skill Value (BS/WS): A lower skill value (e.g., 2+ vs 4+) dramatically increases hit probability. Improving this through re-rolls or modifiers is incredibly potent.
3. Strength vs. Toughness Differential: The relationship between your unit’s Strength and the target’s Toughness is critical for wounding. Weapons that are S double T (e.g., S8 vs T4) are devastating, while those half T (e.g., S3 vs T6) are largely ineffective.
4. Armor Penetration (AP): High AP values directly reduce the opponent’s armor save, forcing them onto worse saves or even their invulnerable save. AP-3 or more can often negate standard armor entirely.
5. Damage Characteristic: While not affecting the chance to wound, a higher damage value (D2, D3, D6) means each successful wound has a greater impact, especially against multi-wound models.
6. Target’s Defensive Saves (Sv, Invuln, FNP): These are the final layers of defense. A good armor save, a reliable invulnerable save, or a Feel No Pain ability can drastically reduce incoming damage, making a unit much harder to remove. Understanding which save is best to target (e.g., ignoring AP with an invulnerable save) is key.
7. Re-rolls and Modifiers: While not directly input into this basic 40k Dice Calculator, abilities that grant re-rolls (to hit, to wound, to save) or modifiers (e.g., +1 to hit, -1 to wound) significantly alter probabilities and are crucial for optimizing combat.
8. Mortal Wounds: Some attacks inflict mortal wounds, which bypass the entire save sequence. These are extremely valuable against highly durable units and are not typically factored into standard dice calculators.

Frequently Asked Questions (FAQ) about the 40k Dice Calculator

Q: How accurate is this 40k Dice Calculator?

A: This 40k Dice Calculator provides statistically accurate *expected* outcomes based on the probabilities of dice rolls. It’s highly accurate for predicting averages over many attacks. However, individual dice rolls in a single game can always deviate due to random chance.

Q: Can this calculator account for re-rolls (e.g., re-roll 1s to hit)?

A: This specific 40k Dice Calculator focuses on base probabilities. To account for re-rolls, you would typically adjust the “Number of Attacks” or “Skill Value” based on the increased probability. For example, re-rolling 1s to hit on a 3+ effectively changes the hit probability from 4/6 to (4/6) + (1/6 * 4/6) = 28/36 = 7/9. More advanced calculators might have specific re-roll inputs.

Q: What if my weapon has variable damage (e.g., D3 or D6)?

A: For variable damage, it’s best to use the average damage value. For D3, use 2 (average of 1, 2, 3). For D6, use 3.5 (average of 1, 2, 3, 4, 5, 6). This 40k Dice Calculator uses a fixed damage input for simplicity.

Q: How does the calculator handle modifiers to hit or wound?

A: Modifiers (like +1 to hit or -1 to wound) should be applied to the “Skill Value” or the effective “Strength” / “Toughness” comparison before inputting. For example, if you hit on 3+ but have a -1 modifier, you effectively hit on 4+, so you would input ‘4’ for Skill Value in the 40k Dice Calculator.

Q: Why is my effective save sometimes worse than my invulnerable save?

A: The game rules state that a unit uses the better of its normal save (modified by AP) or its invulnerable save. If your normal save becomes very high (e.g., 2+ with AP-3 becomes 5+) and you have a 4+ invulnerable save, the 4+ invulnerable save is better and will be used. Our 40k Dice Calculator automatically accounts for this.

Q: Can I use this 40k Dice Calculator for other dice-based games?

A: While the underlying probability principles are universal, this 40k Dice Calculator is specifically tailored to Warhammer 40,000’s attack sequence (Hit, Wound, Save, FNP). Other games might have different mechanics, so direct application might not be accurate without understanding their specific rules.

Q: What are the typical ranges for Strength and Toughness?

A: In Warhammer 40,000, Strength and Toughness typically range from 1 (e.g., Gretchin) to 14 (e.g., some super-heavy vehicles or monsters). Most infantry are T3-T5, while vehicles and monsters are T6-T12+.

Q: How can I improve my unit’s damage output based on the calculator’s results?

A: Analyze which stage is causing the most failures. If you’re missing hits, look for +1 to hit buffs or re-rolls. If you’re failing wounds, seek higher Strength weapons or +1 to wound buffs. If saves are the issue, increase your AP. The 40k Dice Calculator helps pinpoint these bottlenecks.

Related Tools and Internal Resources

Enhance your Warhammer 40,000 experience further with these related tools and guides:

• 40k Unit Builder: Design and customize your ideal units with all their wargear and abilities.
• 40k Army List Optimizer: Craft competitive army lists by balancing points, power, and tactical roles.
• 40k Terrain Rules Guide: Master the impact of different terrain types on line of sight, movement, and combat.
• 40k Mission Tactics: Learn strategies for scoring objectives and winning various mission types.
• 40k Stratagem Guide: A comprehensive database and tactical breakdown of key stratagems for popular factions.
• 40k Faction Guides: Deep dives into the lore, playstyles, and competitive strategies for each Warhammer 40,000 faction.