Dice Calculator 40k
Master your tabletop strategy with our advanced dice calculator 40k. Calculate expected wounds, hit probabilities, and damage variance for Warhammer 40,000.
Total number of dice being rolled for the attack.
The required roll on a D6 to score a hit.
Based on Strength vs Toughness comparison.
The opponent’s final armor or invulnerable save.
Flat damage (e.g., 2) or use 2 for D3, 3.5 for D6.
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Expected Hits
Expected Wounds
Unsaved Wounds
Formula: Attacks × P(Hit) × P(Wound) × P(Failed Save) × Damage.
Efficiency Pipeline: Total Attacks vs Expected Result Path
What is a Dice Calculator 40k?
A dice calculator 40k is an essential mathematical tool used by tabletop wargamers to determine the statistical probability of various outcomes in the Warhammer 40,000 universe. Whether you are leading a legion of Space Marines or a swarm of Tyranids, understanding the average damage output of your units is the difference between a crushing victory and a tactical defeat.
Tactical players use a dice calculator 40k to evaluate which units are most efficient against specific targets. By calculating the “Expected Value” (EV) of an attack sequence, players can mitigate the inherent randomness of D6 rolls and make decisions based on mathematical certainty rather than gut feeling.
Common misconceptions include the “Gambler’s Fallacy,” where players believe a string of bad rolls makes a good roll more likely. A dice calculator 40k grounds your strategy in objective reality, accounting for rerolls, modifiers, and high-volume fire.
Dice Calculator 40k Formula and Mathematical Explanation
The core of the dice calculator 40k logic follows a chain of independent probabilities. Each step in the “To Hit,” “To Wound,” and “Save” process reduces the initial volume of attacks.
The mathematical derivation for the sequence is as follows:
Expected Damage = [A * P(H) * P(W) * P(S) * D]
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| A | Number of Attacks | Integer | 1 – 100+ |
| P(H) | Probability of Hitting | Percentage | 16.6% (6+) to 83.3% (2+) |
| P(W) | Probability of Wounding | Percentage | 16.6% to 83.3% |
| P(S) | Probability of Failed Save | Percentage | 0% to 100% |
| D | Damage per Hit | Integer/Avg | 1, 2, 3, D3 (2), D6 (3.5) |
Practical Examples (Real-World Use Cases)
Example 1: Space Marine Intercessors vs. Ork Boyz
Imagine 10 Intercessors firing Bolt Rifles at a squad of Orks.
- Inputs: 20 Attacks, BS 3+, To Wound 4+, Save 6+, Damage 1.
- Using the dice calculator 40k:
- Hits: 20 * (4/6) = 13.33
- Wounds: 13.33 * (3/6) = 6.67
- Unsaved: 6.67 * (5/6) = 5.56
- Result: 5.56 Expected Wounds. You can reliably expect to remove 5 Ork models.
Example 2: Tank Commander vs. Chaos Knight
A Leman Russ Battle Cannon firing at a high-toughness target.
- Inputs: D6+3 Attacks (Avg 6.5), BS 4+, To Wound 5+, Save 5+, Damage D6 (Avg 3.5).
- Calculation: 6.5 * 0.5 * 0.33 * 0.66 * 3.5 = 2.5 damage.
- Interpretation: Against such a heavy target, the Tank Commander is relatively inefficient without buffs like “Order: Take Aim.”
How to Use This Dice Calculator 40k
- Enter Attacks: Look at the “A” characteristic on your unit’s datasheet. If rapid firing or using special rules, ensure you enter the total count.
- Select To Hit: Choose the Ballistic Skill (BS) or Weapon Skill (WS). Account for modifiers like Heavy or Stealth.
- Reroll Rules: Select if you have “Reroll 1s” (common for Auras) or “Reroll All” (from Stratagems).
- Calculate Wound: Compare Strength vs. Toughness. If S > 2xT, it’s 2+. If S > T, it’s 3+. If S = T, it’s 4+. If S < T, it's 5+. If S < 0.5xT, it's 6+.
- Target Save: Input the enemy save after applying Armor Penetration (AP). If the enemy has a 3+ save and your AP is -2, the target roll is 5+.
- Damage: Enter the damage value. For D3, enter 2. For D6, enter 3.5. For D6+2, enter 5.5.
Key Factors That Affect Dice Calculator 40k Results
Understanding the math is just the start. Several battlefield factors will influence your dice calculator 40k outcomes:
- Ballistic Skill Modifiers: Moving with Heavy weapons or being hit by “Stealth” modifiers can shift your P(H) significantly.
- Critical Hits: Rules like “Lethal Hits” or “Sustained Hits” (Exploding 6s) drastically increase the efficiency of high-volume fire.
- Invulnerable Saves: These ignore your AP, creating a “floor” for how low an opponent’s save can go.
- Damage Mitigation: Abilities like “Feel No Pain” or “-1 Damage” rules require a second stage of calculation not shown in basic formulas.
- Cover: Benefit of Cover improves a save by 1, which can cut incoming damage by 16.6% to 50% depending on the original save.
- Reroll Efficiency: Rerolling “To Wound” is often more mathematically valuable than rerolling “To Hit” because wound rolls are usually harder (4+ or 5+).
Frequently Asked Questions (FAQ)
What is the average of a D6 roll?
The average of a single D6 is 3.5. This is calculated by (1+2+3+4+5+6)/6. Our dice calculator 40k uses these averages for damage rolls.
How does “Reroll 1s” affect the probability?
Rerolling 1s adds (1/6 * P) to your success chance. For a 3+ roll (4/6), it increases the success rate from 66.6% to approximately 77.7%.
Why use a 40k probability tool instead of rolling?
A dice calculator 40k is used during army list building and tactical planning to understand the “math-hammer” behind your units, ensuring you bring the right tools for the job.
Does this calculator handle “Mortal Wounds”?
Mortal wounds skip the “Save” step. To calculate them, set the Target Save to “No Save” (or 7+) in our dice calculator 40k.
What are “Devastating Wounds”?
In the current edition, a Critical Wound roll with Devastating Wounds ignores saves. This is a massive boost to damage against high-armor targets.
What is the best way to calculate D3 damage?
The average of a D3 (which is D6/2 rounded up) is exactly 2. Enter 2 in the damage field of the dice calculator 40k.
How do I calculate “Twin-Linked” weapons?
Twin-linked usually grants a full reroll to wound. Select “Reroll All” in the wound reroll dropdown.
Can modifiers make a roll impossible?
In 10th Edition, an unmodified 1 is always a fail and an unmodified 6 is always a success, regardless of modifiers.
Related Tools and Internal Resources
- Warhammer 40k Math Guide – A deep dive into the statistics of the 41st millennium.
- Expected Damage Calculator – Advanced damage modeling for multi-weapon profiles.
- Probability of Hitting Mastery – How to maximize your hit rolls with modifiers and buffs.
- Wound Roll Odds Explained – Understanding the Strength vs Toughness table for maximum efficiency.
- Armor Save Calculator – Calculate how much punishment your units can take before they fall.
- Mortal Wound Distribution – Math for psychic attacks and devastating weaponry.