Warhammer 40,000 Dice Calculator

Utilize our advanced dice calculator 40k to predict combat outcomes in Warhammer 40,000. This tool helps you understand the probabilities of hitting, wounding, and dealing damage, giving you a strategic edge on the battlefield.

Dice Calculator 40k

Detailed Wound Probability Table

Wounds Dealt	Probability of Exactly X Wounds	Probability of At Least X Wounds

What is a Dice Calculator 40k?

A dice calculator 40k is an essential digital tool for players of Warhammer 40,000, a popular tabletop wargame. It allows players to quickly and accurately determine the statistical probabilities of various combat outcomes, such as the number of successful hits, wounds, and total damage dealt by a unit’s attacks. Instead of relying on intuition or complex mental math, a dice calculator 40k provides concrete expected values, helping players make informed tactical decisions.

Who Should Use a Dice Calculator 40k?

• Competitive Players: To optimize unit loadouts, predict damage output, and understand the statistical advantage of different strategies.
• New Players: To grasp the core combat mechanics and how different stats (BS/WS, S, T, AP, Sv, FNP) interact.
• List Builders: To evaluate the effectiveness of units and weapons before a game, ensuring a balanced and potent army.
• Hobbyists: To satisfy curiosity about specific combat scenarios or to settle debates about dice odds.

Common Misconceptions about Dice Calculator 40k

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

• It doesn’t guarantee outcomes: Probability is about averages over many trials. In a single game, dice can be “hot” or “cold.” The calculator provides the *expected* result, not a guaranteed one.
• It doesn’t account for all special rules: Basic calculators focus on the core hit, wound, save, and FNP sequence. Complex rules like “Sustained Hits,” “Lethal Hits,” “Devastating Wounds,” or specific unit abilities often require manual adjustment or more specialized tools.
• It’s not a substitute for game knowledge: Understanding the numbers is crucial, but knowing when and where to apply that knowledge on the battlefield comes from experience and strategic thinking.

Dice Calculator 40k Formula and Mathematical Explanation

The calculations performed by a dice calculator 40k follow a sequential probability model, where the outcome of one roll influences the next. Here’s a step-by-step breakdown:

Step-by-Step Derivation

1. Probability to Hit (P_Hit):
   • Base Probability: (7 - BS/WS) / 6 (e.g., for 3+, it’s (7-3)/6 = 4/6). A roll of 1 always fails.
   • Re-roll 1s: If a 1 is rolled, it’s re-rolled. The probability of hitting on the re-roll is added. P_Hit = ( (7 - BS/WS) / 6 ) + ( (1/6) * ( (7 - BS/WS) / 6 ) )
   • Re-roll All Misses: If a roll fails, it’s re-rolled. P_Hit = ( (7 - BS/WS) / 6 ) + ( (1 - (7 - BS/WS) / 6) * ( (7 - BS/WS) / 6 ) )
2. Expected Hits: Expected Hits = Number of Attacks * P_Hit
3. Probability to Wound (P_Wound):
   • Determine Wound Roll (WR) based on S vs T:
     • S ≥ 2T: 2+ (WR = 2)
     • S > T: 3+ (WR = 3)
     • S = T: 4+ (WR = 4)
     • S < T: 5+ (WR = 5)
     • S ≤ 0.5T: 6+ (WR = 6)
   • Base Probability: (7 - WR) / 6. A roll of 1 always fails.
   • Re-roll 1s: Similar to hits. P_Wound = ( (7 - WR) / 6 ) + ( (1/6) * ( (7 - WR) / 6 ) )
   • Re-roll All Failed: Similar to hits. P_Wound = ( (7 - WR) / 6 ) + ( (1 - (7 - WR) / 6) * ( (7 - WR) / 6 ) )
4. Expected Wounds (before saves): Expected Wounds = Expected Hits * P_Wound
5. Probability to Fail Save (P_FailSave):
   • Modified Save (MS): Defender Save - AP.
   • Effective Save (ES): min(MS, Invulnerable Save). If Invulnerable Save is ‘None’ (value 7), then ES = MS.
   • A roll of 1 always passes. A roll of 6 always fails (unless modified). The target roll for save is ES. So, P_FailSave = (ES - 1) / 6. If ES is 1 or less, P_FailSave is 5/6 (only 1 passes). If ES is 7 or more, P_FailSave is 0.
6. Expected Failed Saves: Expected Failed Saves = Expected Wounds * P_FailSave
7. Probability to Fail Feel No Pain (P_FailFNP):
   • If FNP is ‘None’ (value 7), P_FailFNP = 1.
   • Otherwise, P_FailFNP = (FNP - 1) / 6. A roll of 1 always passes.
8. Expected Wounds (after FNP): Expected Wounds (after FNP) = Expected Failed Saves * P_FailFNP
9. Expected Total Damage: Expected Total Damage = Expected Wounds (after FNP) * Damage per Wound

Variable Explanations and Table

Understanding the variables is key to using any dice calculator 40k effectively.

Key Variables for Dice Calculator 40k

Variable	Meaning	Unit	Typical Range
A	Number of Attacks	Count	1 – 200+
BS/WS	Ballistic Skill / Weapon Skill	Target Roll (e.g., 3+)	2+ to 6+
S	Attacker Strength	Numeric Value	1 – 14+
T	Defender Toughness	Numeric Value	1 – 14+
AP	Armor Penetration	Modifier (e.g., -1)	0 to -5+
Sv	Defender Save	Target Roll (e.g., 3+)	2+ to 6+
Invuln	Invulnerable Save	Target Roll (e.g., 4+)	2+ to 6+ (or None)
FNP	Feel No Pain	Target Roll (e.g., 5+)	2+ to 6+ (or None)
Damage	Damage per Wound	Numeric Value	1 to 6+ (or D3, D6 averages)

Practical Examples (Real-World Use Cases)

Let’s look at how a dice calculator 40k can be applied to common 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) are shooting at a unit of Ork Boyz (T5, Sv5+, no Invuln, no FNP).

• Inputs:
  • Number of Attacks: 10
  • BS/WS: 3+
  • Re-roll Hits: None
  • Attacker Strength: 4
  • Defender Toughness: 5
  • Re-roll Wounds: None
  • Armor Penetration: -1
  • Defender Save: 5+
  • Invulnerable Save: None
  • Feel No Pain: None
  • Damage per Wound: 1
• Outputs (from dice calculator 40k):
  • Expected Hits: 6.67
  • Expected Wounds (before saves): 3.33 (S4 vs T5 requires 5+ to wound)
  • Expected Failed Saves: 2.22 (Modified Save is 5+ – (-1) = 4+. Probability to fail 4+ save is 3/6 = 0.5)
  • Expected Wounds (after FNP): 2.22
  • Expected Total Damage: 2.22
• Interpretation: On average, 5 Intercessors will kill about 2 Ork Boyz. This helps a player decide if this unit is efficient for clearing hordes or if they should target something else.

Example 2: Custodian Guard vs. Tyranid Carnifex

Scenario: 3 Custodian Guard (9 attacks total) with Guardian Spears (S6, AP-2, D2) are attacking a Carnifex (T9, Sv2+, Invuln4+, FNP5+).

• Inputs:
  • Number of Attacks: 9
  • BS/WS: 2+
  • Re-roll Hits: 1s (e.g., from a Captain nearby)
  • Attacker Strength: 6
  • Defender Toughness: 9
  • Re-roll Wounds: None
  • Armor Penetration: -2
  • Defender Save: 2+
  • Invulnerable Save: 4+
  • Feel No Pain: 5+
  • Damage per Wound: 2
• Outputs (from dice calculator 40k):
  • Expected Hits: 7.88 (2+ with re-roll 1s)
  • Expected Wounds (before saves): 3.94 (S6 vs T9 requires 5+ to wound)
  • Expected Failed Saves: 1.31 (Modified Save is 2+ – (-2) = 0+, but capped at 2+. Invuln is 4+. Effective Save is 4+. Probability to fail 4+ save is 3/6 = 0.5)
  • Expected Wounds (after FNP): 0.87 (FNP 5+ means 2/6 = 0.33 probability to fail FNP)
  • Expected Total Damage: 1.74
• Interpretation: Even with powerful attacks, a Carnifex is very resilient. The Custodians are expected to deal less than 2 damage, highlighting the need for more attacks or higher damage weapons to take down such a tough target. This dice calculator 40k helps manage expectations.

How to Use This Dice Calculator 40k

Using this dice calculator 40k is straightforward, designed for quick and accurate results.

Step-by-Step Instructions

1. Enter Number of Attacks: Input the total number of attacks your unit will make.
2. Select BS/WS: Choose the Ballistic Skill or Weapon Skill required to hit (e.g., 3+).
3. Choose Re-roll Hits: Indicate if you have any abilities that allow you to re-roll hit dice (e.g., re-roll 1s, re-roll all misses).
4. Enter Attacker Strength (S): Input the Strength characteristic of your weapon or unit.
5. Enter Defender Toughness (T): Input the Toughness characteristic of the target unit.
6. Choose Re-roll Wounds: Indicate if you have any abilities that allow you to re-roll wound dice.
7. Enter Armor Penetration (AP): Input the AP value of your weapon (e.g., -1, -2).
8. Select Defender Save (Sv): Choose the normal Save characteristic of the target unit.
9. Select Invulnerable Save (Invuln): Choose the Invulnerable Save of the target unit, if any. Select “None” if they don’t have one.
10. Select Feel No Pain (FNP): Choose the Feel No Pain ability of the target unit, if any. Select “None” if they don’t have one.
11. Enter Damage per Wound: Input the average damage each successful wound inflicts (e.g., 1 for D1, 2 for D3, 3.5 for D6).
12. View Results: The calculator will automatically update the “Calculation Results” section as you change inputs.

How to Read Results

• Expected Hits: The average number of attacks that will successfully hit the target.
• Expected Wounds (before saves): The average number of hits that will successfully wound the target, before any saves are made.
• Expected Failed Saves: The average number of wounds that the defender fails to save.
• Expected Wounds (after FNP): This is the primary result, representing the average number of wounds that successfully bypass all defenses, including Feel No Pain. This is often the most critical number for assessing damage.
• Expected Total Damage: The average total damage dealt to the target, calculated by multiplying Expected Wounds (after FNP) by the Damage per Wound.
• Probability Chart and Table: These show the likelihood of achieving specific numbers of wounds, providing a deeper insight beyond just the average.

Decision-Making Guidance

The dice calculator 40k empowers you to:

• Compare Units: Quickly assess which of your units is more effective against a specific enemy target.
• Optimize Strategy: Decide whether to focus fire, charge, or fall back based on predicted damage output.
• Manage Expectations: Understand the statistical reality of your attacks, reducing frustration from “bad dice” and appreciating “good dice.”
• Identify Key Synergies: See how re-rolls, buffs to S/AP, or debuffs to T/Sv impact the final damage, helping you identify powerful unit combinations.

Key Factors That Affect Dice Calculator 40k Results

Several factors significantly influence the outcomes generated by a dice calculator 40k. Understanding these can help you manipulate the odds in your favor.

1. Number of Attacks (A): This is the most direct factor. More attacks mean more opportunities to hit and wound, linearly increasing expected damage. Even low-strength attacks can be effective in high volume.
2. Ballistic Skill / Weapon Skill (BS/WS): A lower target number (e.g., 2+ vs 4+) dramatically increases hit probability. Improving BS/WS is often one of the most impactful buffs.
3. Attacker Strength (S) vs. Defender Toughness (T): This comparison dictates the wound roll. Achieving S ≥ 2T (2+ wound) or S > T (3+ wound) is highly desirable. Even a small difference here can halve or double your wound output.
4. Armor Penetration (AP): AP directly reduces the defender’s save characteristic. High AP weapons can bypass strong armor, forcing saves on worse numbers or even denying them entirely if the save is pushed to 7+. This is crucial against heavily armored targets.
5. Defender Save (Sv) & Invulnerable Save (Invuln): These are the primary defensive layers. A good save (e.g., 2+ or 3+) makes a unit resilient. Invulnerable saves are particularly strong as they ignore AP, making them vital against high-AP weapons. The dice calculator 40k helps determine which save is more likely to be failed.
6. Feel No Pain (FNP): This ability provides a final chance to ignore wounds that have already bypassed all other defenses. Even a 6+ FNP can significantly reduce incoming damage over many attacks, making units surprisingly durable.
7. Re-rolls: Re-rolling 1s (for hits or wounds) provides a consistent, small boost to probability. Re-rolling all failed rolls offers a much larger boost, effectively giving you a second chance on a significant portion of your dice. These abilities are powerful force multipliers.
8. Damage per Wound: While not a probability factor, the average damage per wound directly scales the final damage output. High damage weapons are essential for taking down multi-wound models, and the dice calculator 40k helps quantify this impact.

Frequently Asked Questions (FAQ) about Dice Calculator 40k

Q: How accurate is this dice calculator 40k?

A: This dice calculator 40k is mathematically accurate for the core dice mechanics it simulates. It provides the statistically expected average outcome over a large number of trials. For any single game, actual dice rolls can vary due to randomness, but over time, results will trend towards these averages.

Q: Can this calculator account for all special rules in Warhammer 40,000?

A: No, this calculator focuses on the fundamental hit, wound, save, and Feel No Pain sequence. Complex special rules like “Sustained Hits,” “Lethal Hits,” “Devastating Wounds,” or specific unit abilities that modify dice rolls in unique ways are not directly integrated. For such rules, you might need to perform separate calculations or use more specialized tools.

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

A: For variable damage, you should input 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 will give you the expected average total damage.

Q: Why do my in-game results sometimes differ from the calculator?

A: Dice rolls are random! The calculator shows the *expected* outcome. In any given turn, you might roll exceptionally well (“hot dice”) or poorly (“cold dice”). The law of large numbers dictates that over many games and many rolls, your results will converge towards the calculator’s predictions. Don’t confuse a single game’s variance with inaccuracy of the dice calculator 40k.

Q: How does the calculator handle a 1 always failing and a 6 always succeeding (for hits/wounds)?

A: The calculator inherently accounts for this. For hit/wound rolls, a 1 always fails, and a 6 always succeeds (unless a specific rule overrides it, which this calculator doesn’t model). For save rolls, a 1 always passes, and a 6 always fails (unless modified). The probability calculations are adjusted accordingly.

Q: What is the difference between a normal save and an invulnerable save?

A: A normal save (Sv) can be modified (worsened) by Armor Penetration (AP). An Invulnerable Save (Invuln) ignores AP entirely. If a unit has both, they use the better of the two after AP has been applied to the normal save. This dice calculator 40k automatically determines the effective save.

Q: Can I use this calculator for other dice-based games?

A: While the core probability concepts are universal, this calculator is specifically tailored for Warhammer 40,000’s sequential hit-wound-save-FNP system. Other games might have different mechanics (e.g., opposed rolls, different re-roll rules, exploding dice) that this calculator would not accurately model.

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

A: Analyze which stage of the attack sequence is the weakest. If you’re getting few hits, look for ways to improve BS/WS or get re-rolls. If wounds are low, seek Strength buffs or target lower Toughness units. If saves are the problem, increase AP. If FNP is soaking too much, focus on high damage per wound to overwhelm it. The dice calculator 40k helps pinpoint these bottlenecks.

Related Tools and Internal Resources

• Warhammer 40k Dice Probability Explained: Dive deeper into the mathematical underpinnings of dice rolls in 40k.
• 40k Wound Calculator Examples: See more practical applications of wound calculations.
• Factors Affecting 40k Damage Calculator: Understand all the variables that impact your damage output.
• Warhammer 40,000 Dice Odds FAQ: Get answers to common questions about dice probabilities.
• How to Use a 40k Combat Calculator: Step-by-step guide to maximizing your combat predictions.
• Understanding Your Warhammer 40k Dice Calculator: A foundational guide to what this tool offers.