Dice Calculator 40k

Utilize this advanced Dice Calculator 40k to precisely determine the expected outcomes of your unit’s attacks in Warhammer 40,000. Input your unit’s stats, apply modifiers and rerolls, and instantly see the probabilities for hits, wounds, and the total damage dealt. Perfect for tactical planning, list building, and understanding unit effectiveness.

Dice Calculator 40k

Detailed Probability Breakdown

Stage	Target Roll	Base Probability	Reroll 1s	Reroll Failed	Final Probability
Hit	N/A	N/A	N/A	N/A	N/A
Wound	N/A	N/A	N/A	N/A	N/A
Save	N/A	N/A	N/A	N/A	N/A

What is a Dice Calculator 40k?

A Dice Calculator 40k is an essential digital tool designed for players of Warhammer 40,000 to accurately predict the statistical outcomes of dice rolls during combat. In a game as complex and dice-heavy as Warhammer 40k, understanding probabilities is key to strategic decision-making, army list optimization, and evaluating unit effectiveness. This calculator takes into account various factors like the number of attacks, Ballistic Skill (BS) or Weapon Skill (WS), Strength (S) vs. Toughness (T) comparisons, Armor Penetration (AP), Save (Sv) characteristics, and crucial modifiers and rerolls.

Who should use it?

• Competitive Players: To fine-tune army lists, understand damage output against specific target units, and make informed tactical choices during a game.
• List Builders: To compare the efficiency of different weapon options or unit compositions before committing to a build.
• New Players: To grasp the underlying mechanics of the game’s combat system and demystify dice probabilities.
• Hobbyists: To simply satisfy curiosity about how certain unit interactions play out statistically.

Common Misconceptions:

• “It’s just luck”: While individual dice rolls are random, the cumulative effect over many dice follows predictable statistical patterns. A Dice Calculator 40k helps reveal these patterns.
• “Only for math-hammer”: While it’s a powerful “math-hammer” tool, its purpose is practical. It translates complex rules into actionable insights, making the game more understandable and enjoyable for everyone.
• “It tells me what will happen”: The calculator provides expected outcomes, not guarantees. It shows what is most likely to happen on average, over many repetitions, not necessarily what will happen in a single turn of a single game.

Dice Calculator 40k Formula and Mathematical Explanation

The core of any Dice Calculator 40k lies in calculating the probability of success at each stage of the attack sequence: hitting, wounding, and saving. These probabilities are then chained together to determine the overall chance of inflicting damage.

Step-by-step Derivation:

1. Probability of Success on a Single Die (P_success):

   For a standard D6 roll needing a target value (X+), the probability of success is (7 - X) / 6. For example, a 3+ roll has a (7 - 3) / 6 = 4/6 = 0.667 probability. If X <= 1, probability is 1 (always succeeds). If X >= 7, probability is 0 (always fails).

2. Hit Probability (P_hit):
   • Base Target: Determined by the unit's Ballistic Skill (BS) or Weapon Skill (WS).
   • Modifiers: Any + or - modifiers to hit are applied to the target roll. A +1 to hit means you need one less on the die (e.g., 3+ becomes 2+), effectively reducing the target roll. A -1 to hit increases the target roll. The effective target roll is clamped between 2 and 6.
   • Rerolls:
     • Reroll 1s: If a 1 is rolled (and it would have failed), it's rerolled. The probability of success becomes P_initial + (1/6) * P_initial.
     • Reroll Failed: If any roll fails, it's rerolled. The probability of success becomes P_initial + (1 - P_initial) * P_initial. If both reroll options are present, "Reroll Failed" typically takes precedence as it's more general.
   • Final P_hit: The calculated probability after all modifiers and rerolls.
3. Wound Probability (P_wound):
   • Base Target: Determined by comparing the attacking weapon's Strength (S) to the defending unit's Toughness (T):
     • S ≥ 2T: 2+ to wound
     • S > T: 3+ to wound
     • S = T: 4+ to wound
     • S < T: 5+ to wound
     • S ≤ 0.5T: 6+ to wound
   • Modifiers: Similar to hit rolls, modifiers to wound adjust the target roll, clamped between 2 and 6.
   • Rerolls: Similar logic to hit rerolls (Reroll 1s, Reroll Failed).
   • Final P_wound: The calculated probability after all modifiers and rerolls.
4. Save Probability (P_save):
   • Base Target: Determined by the defending unit's Save (Sv) characteristic.
   • Armor Penetration (AP): The attacking weapon's AP value modifies the defender's save roll. A weapon with AP -1 makes a 3+ save into a 4+ save. The effective save target is clamped between 2 and 6.
   • Modifiers: Any modifiers to save (e.g., from cover) adjust the target roll.
   • Final P_save: The calculated probability after all modifiers. (Rerolls are rare for saves in 40k).
5. Expected Outcomes:
   • Expected Hits: Number of Attacks * P_hit
   • Expected Wounds: Expected Hits * P_wound
   • Expected Failed Saves: Expected Wounds * (1 - P_save) (These are the wounds that successfully bypass the save).
   • Expected Total Damage: Expected Failed Saves * Damage per Attack

Variables Table:

Variable	Meaning	Unit	Typical Range
Number of Attacks (A)	Total attacks made by the unit/weapon	Count	1 - 20+
BS/WS	Ballistic Skill / Weapon Skill (target to hit)	Roll (X+)	2 - 6
Modifier to Hit	Adjusts the hit roll target	Integer	-1 to +1 (or more)
Reroll 1s to Hit	Option to reroll dice that rolled a 1	Boolean	True/False
Reroll Failed Hits	Option to reroll all failed hit dice	Boolean	True/False
Strength (S)	Attacker's Strength characteristic	Value	1 - 14+
Toughness (T)	Defender's Toughness characteristic	Value	1 - 14+
Modifier to Wound	Adjusts the wound roll target	Integer	-1 to +1 (or more)
Reroll 1s to Wound	Option to reroll dice that rolled a 1	Boolean	True/False
Reroll Failed Wounds	Option to reroll all failed wound dice	Boolean	True/False
Armor Penetration (AP)	Weapon's ability to reduce save	Value	0 to -5+
Defender Save (Sv)	Defender's armor or invulnerable save target	Roll (X+)	2 - 7 (or N/A)
Modifier to Save	Adjusts the save roll target	Integer	-1 to +1 (or more)
Damage per Attack (D)	Damage inflicted by each successful wound	Value	1 - 6+

Practical Examples (Real-World Use Cases)

Understanding how to use a Dice Calculator 40k with practical scenarios can significantly enhance your strategic thinking in Warhammer 40,000.

Example 1: Intercessors vs. Chaos Space Marines

Let's calculate the expected damage from a squad of 5 Intercessors (Bolt Rifles) shooting at a squad of Chaos Space Marines.

• Attacker: 5 Intercessors
• Weapon: Bolt Rifle (Rapid Fire 1, S4, AP-1, D1)
• Target: Chaos Space Marines (T4, Sv3+)

Inputs for Dice Calculator 40k:

• Number of Attacks: 10 (5 models * 2 shots at 12" range)
• BS/WS: 3 (for Space Marines)
• Modifier to Hit: 0
• Rerolls to Hit: None (assume no Captain nearby)
• Attacker Strength (S): 4
• Defender Toughness (T): 4
• Modifier to Wound: 0
• Rerolls to Wound: None
• Armor Penetration (AP): -1
• Defender Save (Sv): 3
• Modifier to Save: 0
• Damage per Attack (D): 1

Expected Outputs:

• Probability to Hit: 66.67% (3+ roll)
• Probability to Wound: 50.00% (S4 vs T4 = 4+ roll)
• Probability to Save: 50.00% (3+ save modified by AP-1 becomes 4+ roll)
• Expected Hits: 6.67
• Expected Wounds: 3.33
• Expected Failed Saves: 1.67
• Expected Total Damage: 1.67 Damage

Interpretation: On average, 5 Intercessors firing Bolt Rifles will inflict approximately 1.67 damage against a standard Chaos Space Marine squad. This helps you gauge if this unit is effective for clearing infantry or if you need more specialized anti-infantry weapons.

Example 2: Lascannon vs. Leman Russ Battle Tank

Let's calculate the expected damage from a single Lascannon shot against a Leman Russ Battle Tank.

• Attacker: Vehicle with Lascannon
• Weapon: Lascannon (Heavy 1, S9, AP-3, D D6)
• Target: Leman Russ Battle Tank (T8, Sv3+)

Inputs for Dice Calculator 40k:

• Number of Attacks: 1
• BS/WS: 3 (for many Imperial Guard vehicles)
• Modifier to Hit: 0 (assume no penalties for moving Heavy weapon)
• Rerolls to Hit: Yes, Reroll 1s to Hit (e.g., from a nearby Tank Commander)
• Attacker Strength (S): 9
• Defender Toughness (T): 8
• Modifier to Wound: 0
• Rerolls to Wound: None
• Armor Penetration (AP): -3
• Defender Save (Sv): 3
• Modifier to Save: 0
• Damage per Attack (D): 3.5 (average of D6)

Expected Outputs:

• Probability to Hit: 77.78% (3+ roll with reroll 1s)
• Probability to Wound: 66.67% (S9 vs T8 = 3+ roll)
• Probability to Save: 16.67% (3+ save modified by AP-3 becomes 6+ roll)
• Expected Hits: 0.78
• Expected Wounds: 0.52
• Expected Failed Saves: 0.43
• Expected Total Damage: 1.51 Damage (0.43 * 3.5)

Interpretation: A single Lascannon shot, even with reroll 1s to hit, is expected to deal about 1.5 damage to a Leman Russ. This highlights that even powerful anti-tank weapons require multiple shots or combined fire to reliably take down tough vehicles. This Dice Calculator 40k helps you understand the statistical reality behind your unit choices.

How to Use This Dice Calculator 40k

Our Dice Calculator 40k is designed for ease of use, allowing you to quickly get the statistical insights you need for your Warhammer 40,000 games. Follow these steps to get the most out out of the tool:

Step-by-step Instructions:

1. Input Number of Attacks (A): Enter the total number of attacks your unit will make. Remember to account for abilities like Rapid Fire, Assault, or extra attacks from special rules.
2. Set Ballistic/Weapon Skill (BS/WS): Input the target roll needed to hit (e.g., '3' for a 3+ BS/WS).
3. Apply Modifier to Hit: If your unit has abilities that modify hit rolls (e.g., +1 to hit, -1 to hit from cover), enter the modifier. A +1 to hit is entered as -1 in the calculator (as it reduces the target roll), and a -1 to hit is entered as +1.
4. Select Rerolls to Hit: Check the appropriate boxes if your unit benefits from rerolling 1s to hit or rerolling all failed hit rolls.
5. Enter Attacker Strength (S): Input the Strength characteristic of the attacking weapon or unit.
6. Enter Defender Toughness (T): Input the Toughness characteristic of the target unit.
7. Apply Modifier to Wound: Similar to hit modifiers, enter any adjustments to the wound roll target.
8. Select Rerolls to Wound: Check the appropriate boxes for rerolling 1s to wound or all failed wound rolls.
9. Input Armor Penetration (AP): Enter the AP value of the attacking weapon. Remember to input negative values as they appear on datasheets (e.g., -1, -2).
10. Set Defender Save (Sv): Input the target roll for the defender's save. This could be their armor save or an invulnerable save if it's better.
11. Apply Modifier to Save: Enter any modifiers to the save roll (e.g., from cover or special rules).
12. Enter Damage per Attack (D): Input the damage value for each successful wound. For D3 or D6 weapons, use the average (2 for D3, 3.5 for D6).
13. View Results: The calculator updates in real-time as you adjust inputs. The primary result, "Expected Total Damage Dealt," is highlighted.
14. Reset and Copy: Use the "Reset" button to clear all inputs to default values. Use "Copy Results" to easily transfer the calculated outcomes to a document or chat.

How to Read Results:

• Probability to Hit/Wound/Save: These percentages show the chance of success at each individual stage.
• Expected Hits/Wounds/Failed Saves: These are the average number of successful outcomes you can expect at each stage, given your inputs.
• Expected Total Damage Dealt: This is the most crucial metric, representing the average total damage your attack sequence is likely to inflict on the target.

Decision-Making Guidance: Use these results to compare different weapon profiles, evaluate the effectiveness of buffs/debuffs, and make informed decisions about which units to target or which strategies to employ in your games of Warhammer 40,000. This Dice Calculator 40k is a powerful ally in your tactical arsenal.

Key Factors That Affect Dice Calculator 40k Results

The outcome of your attacks in Warhammer 40,000, as reflected by the Dice Calculator 40k, is influenced by a multitude of interacting factors. Understanding these can help you optimize your strategies.

1. Number of Attacks (A): This is often the most straightforward factor. More attacks generally lead to more hits, wounds, and ultimately, more damage. Units with high attack counts, even with weaker profiles, can be surprisingly effective due to sheer volume.
2. Ballistic Skill (BS) / Weapon Skill (WS): A lower BS/WS value (e.g., 2+ instead of 4+) dramatically increases the probability of hitting. Improving this skill, or choosing units with better inherent skills, is a direct path to higher damage output.
3. Strength (S) vs. Toughness (T) Comparison: The ratio between your weapon's Strength and the target's Toughness dictates the base wound roll. Wounding on 2+ or 3+ is significantly more reliable than 5+ or 6+. Prioritizing targets where your Strength is high relative to their Toughness is crucial.
4. Armor Penetration (AP): AP directly reduces the effectiveness of the target's save. High AP values (e.g., AP-3, AP-4) can turn strong armor saves into weak ones, leading to many more failed saves and thus more damage. This is especially critical against heavily armored units.
5. Damage Characteristic (D): The damage value per successful wound determines the lethality of your attacks. High damage weapons (e.g., D3, D6, or flat 3+) are essential for taking down multi-wound models like vehicles and monsters. The average damage for variable damage weapons (D3=2, D6=3.5) is often used in calculations.
6. Rerolls (to Hit/Wound): Reroll abilities (e.g., reroll 1s, reroll all failed) are incredibly powerful force multipliers. They provide a "second chance" for dice that would have failed, significantly increasing the overall probability of success at that stage. Full rerolls are often considered one of the strongest buffs in the game.
7. Modifiers (+/- to Hit/Wound/Save): These can come from various sources like unit abilities, psychic powers, or terrain. A +1 to hit or wound is a substantial boost, while a -1 to hit or save can severely cripple an opponent's offensive or defensive capabilities. Always account for these when using the Dice Calculator 40k.
8. Invulnerable Saves: While not a direct input in the standard save field (you'd just enter the invulnerable save value if it's better than the armor save), invulnerable saves are a critical defensive factor. They ignore AP, making them incredibly resilient against high-AP weapons and often requiring a different approach to damage calculation.
9. Cover: Units in cover often gain a +1 to their armor save, effectively making them tougher to wound. This is factored into the "Modifier to Save" input.

By carefully considering and inputting these factors into the Dice Calculator 40k, players can gain a profound understanding of their units' true combat potential and make more strategic decisions on the battlefield.

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

Q: Why is my expected damage not a whole number?

A: The Dice Calculator 40k provides statistical averages. While you can't deal "0.75 damage" in a single instance, over many games or many similar attacks, the average outcome will trend towards these fractional values. It represents the likelihood of success.

Q: How do I input D3 or D6 damage values?

A: For variable damage, use the average value. For D3, use 2 (average of 1, 2, 3). For D6, use 3.5 (average of 1, 2, 3, 4, 5, 6). This gives the most accurate expected damage from the Dice Calculator 40k.

Q: What if my unit has multiple weapon profiles?

A: You'll need to run the Dice Calculator 40k separately for each weapon profile and then sum the expected damage if they are fired simultaneously. For example, a tank firing a main gun and a heavy bolter would require two separate calculations.

Q: How do "reroll 1s" and "reroll failed" interact?

A: In this Dice Calculator 40k, if "Reroll Failed" is selected, it takes precedence and overrides "Reroll 1s" for that stage (hit or wound). This is because rerolling all failed dice inherently includes rerolling any 1s that failed.

Q: Can this calculator account for abilities like "Mortal Wounds on 6s to hit"?

A: This specific Dice Calculator 40k focuses on standard damage. Abilities that generate Mortal Wounds on specific rolls (like 6s to hit or wound) are separate mechanics and would require a more specialized calculator or manual addition to the total expected damage.

Q: Why is my save value sometimes capped at 2+ or 6+?

A: In Warhammer 40,000, a natural roll of 1 always fails, and a natural roll of 6 always succeeds (unless otherwise specified). This means the best possible save is 2+ (you can't save on a 1), and the worst possible save is 6+ (you can't fail on a 6). The calculator reflects these game rules.

Q: How does this help with list building?

A: By using the Dice Calculator 40k, you can compare the damage output of different units or weapon loadouts against common enemy threats. This allows you to build a more balanced and effective army list tailored to your playstyle and expected meta.

Q: Is this calculator suitable for all editions of Warhammer 40k?

A: This Dice Calculator 40k is primarily designed for the current (10th) edition ruleset, which features a consistent attack sequence and modifier application. While the core dice mechanics are similar across editions, specific rules for rerolls, modifiers, and wound charts might vary, so always cross-reference with your edition's rulebook.

Related Tools and Internal Resources

Enhance your Warhammer 40,000 experience with these other helpful tools and articles:

• Warhammer 40k Unit Builder: Design and optimize your custom units with detailed stat tracking.
• 40k Army List Optimizer: Fine-tune your army composition for competitive play.
• Wargame Terrain Generator: Create balanced and engaging battlefields for your games.
• 40k Mission Planner: Strategize your objectives and deployment for various mission types.
• Dice Roll Simulator: Practice your luck and understand random outcomes.
• Combat Resolution Tool: A broader tool for resolving complex combat scenarios in wargames.