40k Dice Calculator

A comprehensive tool to calculate Warhammer 40,000 combat probabilities, including hit, wound, armour save, and damage rolls. Understand your odds and refine your battlefield strategy.

Combat Probability Calculator

Combat Results

Key Assumptions:

Attacks: —

Hit Roll: —

Wound Roll: —

Target Save: —

Target Invuln: —

Save Modifier: —

Damage/Wound: —

Shots/Attack: —

Formula Explanation:
1. Calculate the probability of a single hit (based on Hit Roll).
2. Calculate the probability of a single wound (based on Wound Roll).
3. Calculate the effective save probability (considering base save, invulnerable save, and modifiers).
4. Calculate the probability of a wound succeeding past the save.
5. Multiply probabilities to find the chance of a successful hit, wound, and damage.
6. Total damage is calculated by multiplying the number of successful hits that also succeed wounds and damage rolls by the damage per wound.

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What is the 40k Dice Calculator?

The 40k dice calculator is an essential tool for any Warhammer 40,000 player looking to quantify the effectiveness of their units’ attacks. In the grim darkness of the far future, dice rolls dictate the ebb and flow of battle, and understanding the underlying probabilities is crucial for making informed strategic decisions. This calculator helps you break down the complex sequence of a Warhammer 40k combat engagement – from hitting your target, to wounding them, to them failing their armour or invulnerable save, and finally, dealing damage.

Who should use it?

• New Players: To grasp the fundamental mechanics of combat and avoid common pitfalls.
• Experienced Players: To optimize army builds, identify efficient unit synergies, and plan attack sequences.
• Competitive Players: To fine-tune lists, test hypothetical matchups, and understand optimal deployment and target priority.
• Hobbyists: To settle friendly debates about unit effectiveness or explore theoretical combat scenarios.

Common Misconceptions about 40k Combat:

• “A 3+ to hit is always twice as good as a 4+.” While seemingly intuitive, this isn’t always true when other factors like multiple wounds or specific abilities come into play. The 40k dice calculator shows the precise difference.
• “High Strength weapons always wound easily.” The Strength vs. Toughness (S vs T) table is key. A high S doesn’t guarantee a wound against a very tough target.
• “Invulnerable saves are always better.” Invulnerable saves often have a worse roll requirement (e.g., 5+) than regular armour saves (e.g., 3+). They are specifically useful against weapons that ignore standard armour.
• “Damage output is just the weapon’s Damage stat.” The actual damage dealt depends on a chain of successful rolls: hit, wound, and save. The 40k dice calculator clarifies this dependency.

40k Dice Calculator Formula and Mathematical Explanation

The 40k dice calculator works by calculating the probability of success at each sequential stage of an attack: hitting, wounding, and bypassing the target’s save. These probabilities are then multiplied together to find the overall chance of damage being dealt.

Step-by-Step Calculation:

1. Probability of a Hit: This is determined by the “To Hit” characteristic. A standard roll is on a D6 (six-sided die).
   • Roll of 1 always fails.
   • Roll of 6 often has special results (critical hits), but for basic probability, we consider it a success.
   • Probability = (Number of successful outcomes) / (Total possible outcomes)
   • Example: A 3+ to hit means rolls of 3, 4, 5, 6 are successful. That’s 4 successful outcomes out of 6 total. Probability = 4/6 = 0.667 or 66.7%.
2. Probability of a Wound: This depends on the attacking weapon’s Strength (S) versus the target’s Toughness (T). The game uses a simple table:
   • S = T: 4+ to wound
   • S > T: 3+ to wound
   • S >> T (S is double T): 2+ to wound
   • S < T: 5+ to wound
   • S << T (S is half T): 6+ to wound
   • Similar to hitting, Probability = (Number of successful outcomes) / 6. A 4+ to wound is 3/6 = 0.5 or 50%.
3. Probability of a Successful Save: This is the target’s Armour Save (AS) or Invulnerable Save (IS), potentially modified.
   • The base save roll (e.g., 3+) is the minimum needed.
   • A modifier (e.g., +1) improves the save (making the required roll lower, like 2+). A modifier of -1 makes it worse (e.g., 4+ from a 3+).
   • Invulnerable saves are only used if they are better than the standard armour save after modifiers.
   • The probability is calculated similarly: (7 – Effective Save Roll) / 6. Example: A 3+ save with a +1 modifier becomes a 2+ effective save. Probability = (7 – 2) / 6 = 5/6 = 0.833 or 83.3%.
4. Probability of a Wound Succeeding (Dealing Damage): This is the probability that a wound roll is successful AND the target fails their save.
   • Probability = P(Wound) * P(Save Failure)
   • P(Save Failure) = 1 – P(Save Success)
   • Example: P(Wound) = 50% (0.5). P(Save Success) = 83.3% (0.833). P(Save Failure) = 1 – 0.833 = 0.167 (16.7%).
   • P(Wound Succeeds Past Save) = 0.5 * 0.167 = 0.0835 or 8.35%.
5. Expected Damage Per Attack: This is the sum of probabilities of each possible damage outcome. For simplicity, if damage is fixed:
   • Expected Damage = P(Hit) * P(Wound) * P(Save Failure) * Damage Per Wound
   • Example: P(Hit) = 66.7% (0.667). P(Wound Succeeds Past Save) = 8.35% (0.0835). Damage = 1.
   • Expected Damage Per Attack = 0.667 * 0.0835 * 1 = 0.0557 or 5.57% chance of dealing 1 damage.
6. Total Expected Damage:
   • Total Expected Damage = Expected Damage Per Attack * Number of Attacks * Shots Per Attack
   • Example: 5 Attacks * 1 Shot/Attack * 5.57% = 27.85% average damage. The calculator presents this as a primary result, often rounded or presented as a simplified “average damage dealt” based on the successful number of hits that cause wounds that bypass saves.

Variables Table:

Variable	Meaning	Unit	Typical Range
Attacks	Number of dice rolled for attacks.	Count	1+
Hit Roll	Minimum roll needed to hit target on a D6.	Roll Value (2-6)	2-6
Wound Roll	Minimum roll needed to wound target on a D6 (based on S vs T).	Roll Value (2-6)	2-6
Target Save	Target’s base armour save roll.	Roll Value (2-7)	2-7 (7 = no save)
Invulnerable Save	Target’s invulnerable save roll.	Roll Value (0-7)	0-6 (0 = no invuln save, 7 = no save)
Save Modifier	Modifier applied to the target’s save roll.	Integer	-3 to +3 (common)
Damage	Damage dealt per successful wound.	Count	1+
Shots Per Attack	Number of shots fired per attack action.	Count	1+
Hit Probability	Chance of a single attack hitting.	Percentage	16.7% – 83.3%
Wound Probability	Chance of a single hit wounding the target.	Percentage	16.7% – 83.3%
Save Probability	Chance of the target successfully saving against a wound.	Percentage	0% – 83.3%
Damage Probability	Chance of a successful hit resulting in damage dealt.	Percentage	0% – 83.3%
Average Damage	Expected total damage dealt per full attack sequence.	Value	0+

Practical Examples (Real-World Use Cases)

Let’s see the 40k dice calculator in action with a couple of common scenarios:

Example 1: Space Marines vs. Ork Boyz

Scenario: A unit of 5 Tactical Space Marines (Assault Intercessor equivalent) with Bolt Rifles attacking a unit of 10 Ork Boyz.

• Space Marine Profile: Strength 4, Toughness 4, Armour Save 3+, Invulnerable Save 0 (N/A), Damage 1, Attacks 1 per model.
• Ork Boyz Profile: Toughness 5, Armour Save 6+.
• Weapon: Bolt Rifle (Assault 1, Range 24″, Rapid Fire at 12″). Assume they are within 12″ for Rapid Fire.
• Space Marine Attacks: 5 models * 2 shots (Rapid Fire) = 10 Attacks.
• To Hit: Space Marines are 3+ to hit.
• To Wound: Strength 4 vs Toughness 5 = 5+ to wound.
• Target Save: Ork Boyz 6+.
• Damage: 1 per successful wound.

Inputs for the 40k dice calculator:

• Number of Attacks: 10
• Hit Roll: 3
• Wound Roll: 5
• Target Save: 6
• Invulnerable Save: 0
• Save Roll Modifier: 0
• Damage Per Successful Wound: 1
• Shots Per Attack: 1 (since we already factored in Rapid Fire into total attacks)

Calculator Output:

• Primary Result (Avg Damage): ~3.06 Damage
• Hits Succeeded: ~8.33 Hits
• Wounds Succeeded: ~4.17 Wounds
• Saves Made: ~1.12 Saves
• Damage Dealt: ~3.06 Damage

Interpretation: On average, these 10 Bolt Rifle shots will deal approximately 3 wounds, enough to eliminate 3 Ork Boyz. This helps the Space Marine player understand the expected attrition they can inflict.

Example 2: Necron Warriors vs. Imperial Guardsmen

Scenario: A unit of 10 Necron Warriors with Gauss Reapers attacking Imperial Guardsmen.

• Necron Warrior Profile: Strength 4, Toughness 4, Armour Save 3+, Invulnerable Save 5+, Damage 1.
• Imperial Guardsmen Profile: Toughness 3, Armour Save 5+.
• Weapon: Gauss Reaper (Assault 2, Range 12″). Assume within 12″ for Assault 2.
• Necron Warrior Attacks: 10 models * 2 shots = 20 Attacks.
• To Hit: Necron Warriors are 4+ to hit.
• To Wound: Strength 4 vs Toughness 3 = 3+ to wound.
• Target Save: Guardsmen 5+.
• Damage: 1 per successful wound.

Inputs for the 40k dice calculator:

• Number of Attacks: 20
• Hit Roll: 4
• Wound Roll: 3
• Target Save: 5
• Invulnerable Save: 0
• Save Roll Modifier: 0
• Damage Per Successful Wound: 1
• Shots Per Attack: 1 (Assault 2 factored into total attacks)

Calculator Output:

• Primary Result (Avg Damage): ~11.57 Damage
• Hits Succeeded: ~10 Hits
• Wounds Succeeded: ~6.67 Wounds
• Saves Made: ~3.33 Saves
• Damage Dealt: ~11.57 Damage

Interpretation: The Necron Warriors’ superior firepower (Assault 2) allows them to inflict significant damage, potentially eliminating around 11 Guardsmen. This demonstrates the power of volume of fire and favorable S vs T matchups.

How to Use This 40k Dice Calculator

Using the 40k dice calculator is straightforward. Follow these steps to get accurate probability insights for your Warhammer 40,000 battles:

1. Identify Your Attacking Unit and Weapon: Determine the number of attacks your unit will make, considering any special rules like Rapid Fire or Assault.
2. Note Your “To Hit” Characteristic: This is usually found on the unit’s datasheet or weapon profile (e.g., 3+).
3. Determine “To Wound”: This depends on the weapon’s Strength (S) versus the target’s Toughness (T). Consult the Warhammer 40k S vs T chart or use the calculator’s guidance.
4. Identify Target’s Defenses: Find the target’s Armour Save (AS) characteristic and any Invulnerable Save (IS). Also, note any modifiers to saves that might apply.
5. Determine Damage Per Wound: Check the weapon’s Damage (D) characteristic.
6. Enter Values into the Calculator: Input the numbers gathered above into the corresponding fields: “Number of Attacks,” “Hit Roll,” “Wound Roll,” “Target Save,” “Invulnerable Save,” “Save Roll Modifier,” “Damage Per Successful Wound,” and “Shots Per Attack.”
7. Click “Calculate Probabilities”: The calculator will instantly update with the results.

How to Read Results:

• Primary Highlighted Result (e.g., Average Damage Dealt): This is the most crucial number, representing the expected amount of damage your attack sequence will inflict. Use this to gauge how effectively you’ll destroy enemy units.
• Intermediate Values (Hits Succeeded, Wounds Succeeded, Saves Made): These show the expected number of successes at each stage. They help you understand where potential losses occur (e.g., many hits but few wounds means your weapon might be too weak for the target’s Toughness).
• Key Assumptions: These are the input values you provided. Double-check them to ensure they match your unit and target profiles.
• Formula Explanation: Provides a brief overview of how the probabilities are calculated, reinforcing your understanding.

Decision-Making Guidance:

• High Average Damage: Your unit is performing well against the target.
• Low Average Damage Despite Many Hits: Your “To Wound” roll or target’s save is the bottleneck. Consider using re-rolls or targeting weaker units.
• Low Average Damage Despite Many Wounds: The target’s save is too high. Look for weapons with abilities that ignore saves or reduce the save characteristic.
• Comparing Units: Use the calculator to compare different weapon options or unit choices for the same target. The unit providing the highest average damage output for its points cost is often the more efficient choice. Remember to factor in durability and strategic role beyond raw damage.

Key Factors That Affect 40k Dice Calculator Results

While the 40k dice calculator provides a powerful statistical overview, several real-world factors can influence the actual outcomes in a game. Understanding these is key to adapting your strategy:

1. Unit Abilities and Special Rules: Many units have rules that modify probabilities. Examples include:
   • “Re-roll wound rolls of 1”: This doesn’t change the base probability but increases the reliability.
   • “Ignores Armour Saves”: This bypasses the save roll entirely, drastically increasing damage output against heavily armoured targets.
   • “Critical Hits”: Some weapons deal extra damage or have special effects on a roll of a 6 to hit.
   • “Exploding” Dice: Certain rolls (e.g., hitting on a 6, or wounding on a specific roll) might grant additional hits or attacks.

   The calculator provides the base probability; these rules can significantly swing the odds in your favor.

2. Target Toughness vs. Weapon Strength (S vs T): This is the primary determinant of the “To Wound” roll. A large gap in favor of Strength (e.g., S8 vs T3) makes wounding much easier (2+). Conversely, a large gap favoring Toughness (e.g., S4 vs T8) makes wounding very difficult (6+). The calculator directly uses the resulting wound roll, but understanding the S vs T relationship is fundamental.
3. Target Armour Save vs. Weapon’s Armour Penetration (AP): While this calculator doesn’t directly factor in AP, it’s crucial in determining the *effective* save value. AP reduces the target’s armour save characteristic (e.g., AP -1 makes a 3+ save behave like a 4+). Many players use the calculator assuming base saves and mentally adjust for AP, or use the modifier input if the AP value is known and fixed. For precise calculations involving AP, dedicated AP calculators might be needed, or you must manually calculate the effective save.
4. Dice Variance (RNG – Random Number Generation): The calculator shows *average* or *expected* results. In reality, dice can be streaky. You might roll incredibly well and exceed the average, or suffer a string of bad luck and fall short. Building resilience into your army (e.g., multiple units, re-rolls) helps mitigate variance.
5. Terrain Effects: Cover provides bonuses to saves (e.g., +1 to the roll), making it harder to wound. This directly impacts the “Save Probability” and should be factored into the “Save Roll Modifier” or “Target Save” inputs if applicable.
6. Psychic Powers & Stratagems: Many psychic powers and army-specific stratagems can alter hit rolls, wound rolls, damage, or saves. For example, a stratagem might allow re-rolls of all failed wounds, or a psychic power might reduce a target’s Toughness. These tactical options can drastically improve the effectiveness of an attack sequence beyond base stats.
7. “Feel No Pain” (FNP) Rolls: Some units can ignore a certain amount of damage on a successful dice roll (e.g., “5+ FNP”). This doesn’t stop the wound but reduces the effective damage dealt. This mechanic is not directly calculated here but significantly impacts the final damage output.

Frequently Asked Questions (FAQ)

• What is the difference between Hit Roll, Wound Roll, and Save Roll?
  Hit Roll: Determines if your attack successfully connects with the target. Based on the weapon’s “Ballistic Skill” (BS) for ranged or “Weapon Skill” (WS) for melee.
  Wound Roll: Determines if the hit is strong enough to harm the target. Based on the weapon’s Strength (S) versus the target’s Toughness (T).
  Save Roll: Determines if the target’s armour or inherent resilience prevents the wound from causing damage. Based on the target’s Armour Save (AS) or Invulnerable Save (IS), potentially modified by the weapon’s Armour Penetration (AP).
• How does Armour Penetration (AP) affect the calculation?
  This 40k dice calculator doesn’t directly input AP. However, AP modifies the target’s save roll. For example, AP -1 makes a 3+ save function like a 4+ save. You can manually adjust the “Target Save” or use the “Save Roll Modifier” field to reflect this. A 3+ save with AP -1 becomes effectively a 4+ save, so you’d input ‘4’ into the Target Save field, or ‘0’ to Target Save and ‘-1’ to Modifier.
• What does it mean if Invulnerable Save is 0?
  An Invulnerable Save value of ‘0’ typically means the unit does not have an invulnerable save, or it’s so poor (e.g., 7+) that it’s effectively useless. The calculator prioritizes the standard armour save unless the invulnerable save is better (lower number required). Setting it to 0 ensures it won’t be used unless explicitly better than the armour save.
• Can this calculator handle weapons with multiple damage types (e.g., D3, D6)?
  This specific calculator uses a fixed “Damage Per Successful Wound.” For weapons with variable damage (like D3 or D6), you would need to calculate the average damage for that weapon type (e.g., average D3 is 2, average D6 is 3.5) and input that average value for a general estimate. For precise analysis of variable damage, you’d run the calculator multiple times with different damage inputs.
• How do “Feel No Pain” abilities affect the results?
  “Feel No Pain” (FNP) abilities allow a target unit to ignore a certain amount of damage on a successful dice roll (e.g., a 5+ FNP). This calculator does not directly account for FNP. To approximate its effect, you would need to calculate the expected damage *before* FNP, then calculate the probability of FNP succeeding and reducing the damage. For example, with a 5+ FNP (83.3% chance to ignore damage), you’d multiply your calculated damage by the probability of the FNP *failing* (1 – 0.833 = 0.167).
• What if my unit has special rules for critical hits (e.g., wounds on a 2+ instead of 3+)?
  This calculator uses the base “To Hit” and “To Wound” characteristics. For abilities that alter these rolls on specific outcomes (like critical hits), you’d need to calculate the new overall probability. For example, if a 3+ normally hits, but a 6 to hit also wounds automatically, you’d calculate the probability of hitting on 3, 4, 5 (standard hits) and add the probability of wounding on a 6 (which is 100% assuming it hits). A more advanced calculator or manual calculation is needed for complex critical hit rules.
• Why are my calculated damage numbers different from what I expect in-game?
  Several factors can cause discrepancies:

  • Dice Variance: Real-world rolls can deviate from averages.
  • Unaccounted Rules: Abilities like FNP, special ammunition, critical hits, or modifiers to saves (AP) are not always directly inputted.
  • Targeting Errors: Incorrectly inputting target stats (Toughness, Save) or weapon stats (Strength, AP).
  • Rounding: Minor differences can occur due to rounding in calculations.

  Always double-check your inputs and consider the tactical situation.

• How can I use this calculator to compare two different weapons?
  Simply input the stats for the first weapon and note the results (especially average damage). Then, clear the fields or adjust them for the second weapon and compare the outputs. This allows you to see which weapon is statistically more effective against a specific target profile. Remember to consider factors like range, AP, and special rules beyond raw damage output when making final decisions. The [Warhammer 40k Weapon Comparison Guide](fake-link-1) offers more insights.