40k Dice Calculator

Analyze the probable outcomes of your Warhammer 40,000 attack sequences. This tool helps you understand the average number of hits, wounds, and final damage you can expect from your units, turning complex probability into a clear tactical advantage.

What is a 40k Dice Calculator?

A 40k dice calculator is a specialized statistical tool designed for players of the tabletop wargame Warhammer 40,000. Its primary purpose is to compute the probable outcomes of in-game dice rolls, particularly the complex sequence of an attack. By inputting variables like the number of attacks, weapon skill, weapon strength, target toughness, and various saves, players can get an immediate understanding of how effective an attack is likely to be.

This is invaluable for both list-building and in-game decision-making. Should you shoot your Lascannons at that tank or at those elite infantry? Will your Guardsmen’s flashlights actually manage to damage that monster? A 40k dice calculator removes the guesswork and replaces it with data, allowing you to make informed tactical choices based on probability. It models the “MathHammer” of an attack, showing the expected number of hits, wounds, failed saves, and ultimately, the total damage dealt.

The 40k Dice Calculator Formula and Explanation

The core of any Warhammer 40k attack is a sequence of dice rolls: the Hit roll, the Wound roll, and the Save roll. Our 40k dice calculator models the statistical probability of each step to determine the average outcome.

1. Probability of a Single Roll: All dice in Warhammer 40k are six-sided (d6). The probability of rolling a specific target number ‘X’ or higher (e.g., 3+) is calculated as:

P(Success) = (7 – X) / 6

2. Hit Roll: The initial number of attacks is multiplied by the probability of hitting, which is determined by the attacker’s Ballistic Skill (BS) or Weapon Skill (WS). For example, a BS of 3+ gives a `(7-3)/6 = 4/6` or 66.7% chance to hit per attack.

3. Wound Roll: The number of successful hits becomes the number of dice rolled to wound. The target roll here depends on the weapon’s Strength (S) versus the target’s Toughness (T), as shown in the table below. For an in-depth guide on probabilities, you might check out this {related_keywords} guide.

Strength vs. Toughness Chart

Table showing the required d6 roll to wound a target based on Strength vs. Toughness.

Comparison	Roll Needed to Wound
Strength is double or more than Toughness	2+
Strength is greater than Toughness	3+
Strength is equal to Toughness	4+
Strength is less than Toughness	5+
Strength is half or less than Toughness	6+

4. Save Roll: The number of successful wounds is then passed to the defender. For each wound, the defender rolls a die. A successful save negates the wound. The target number is the model’s Save (Sv), modified by the weapon’s Armour Penetration (AP). For example, a 3+ save against an AP-1 weapon becomes a 4+ save.

5. Final Damage: The number of failed saves is multiplied by the weapon’s Damage (D) characteristic to find the total damage inflicted.

Practical Examples

Let’s see the 40k dice calculator in action with two common scenarios.

Example 1: Intercessors vs. Ork Boyz

A squad of 5 Intercessors (2 attacks each) fires their Bolt Rifles at a unit of Ork Boyz.

• Inputs:
  • Number of Attacks: 10
  • Skill (BS): 3+
  • Weapon Strength: 4
  • Weapon AP: -1
  • Weapon Damage: 1
  • Target Toughness: 5
  • Target Save: 6+
• Results:
  • Expected Hits: 6.67
  • Expected Wounds: 2.22 (S4 vs T5 wounds on a 5+)
  • Expected Unsaved Wounds: 1.85 (A 6+ save modified by AP-1 becomes a 7+, which is impossible)
  • Expected Total Damage: 1.85
• Conclusion: On average, the squad will kill about two Ork Boyz. To optimize this, you might consider using a different tool like an {related_keywords} to see how they’d fare.

Example 2: Leman Russ vs. Chaos Rhino

A Leman Russ Battle Tank fires its Battle Cannon at a Chaos Rhino transport.

• Inputs:
  • Number of Attacks: 7 (Average of D6+1)
  • Skill (BS): 4+
  • Weapon Strength: 10
  • Weapon AP: -1
  • Weapon Damage: 3 (Average of D6)
  • Target Toughness: 9
  • Target Save: 3+
  • Target Invulnerable Save: None
• Results:
  • Expected Hits: 3.50
  • Expected Wounds: 2.33 (S10 vs T9 wounds on a 3+)
  • Expected Unsaved Wounds: 1.17 (A 3+ save modified by AP-1 becomes a 4+)
  • Expected Total Damage: 3.51
• Conclusion: The Battle Cannon is likely to deal a decent chunk of damage, but is unlikely to destroy the Rhino in one shot.

How to Use This 40k Dice Calculator

Using this calculator is simple. Follow these steps to analyze your combat encounters:

1. Enter Attacker Stats: Fill in the number of attacks, the required skill roll (BS/WS), and the weapon’s Strength, AP, and Damage values.
2. Enter Defender Stats: Input the target’s Toughness and its Armour Save.
3. Add Modifiers & Re-rolls: Select any re-rolls for hit or wound rolls. Also, input any Invulnerable or Ward (“Feel No Pain”) saves the target may have. The calculator will automatically use the best save available.
4. Review the Results: The calculator instantly updates. The “Expected Total Damage” is your primary result. You can also see the intermediate values for expected hits, wounds, and unsaved wounds to understand where your attacks are most effective or where they are failing.
5. Analyze the Chart: The bar chart provides a visual representation of your attack’s attrition rate, making it easy to see the drop-off at each stage of the attack sequence.

Key Factors That Affect 40k Dice Outcomes

While luck always plays a part, several key factors consistently influence the results of a 40k dice calculator.

• Skill (BS/WS): This is the first and most critical gate. An improvement from a 4+ to a 3+ to hit is a massive 33% increase in potential output.
• Strength vs. Toughness: Hitting the key breakpoints on the S vs. T chart is vital. Getting to a point where you wound on a 3+ instead of a 4+ provides another significant boost in efficiency.
• Armour Penetration (AP): Reducing the target’s ability to save is one of the most effective ways to push damage through. High AP can render even the best armour useless.
• Volume of Attacks: Sometimes, sheer weight of dice can overcome poor individual stats. Many low-quality shots can be just as effective as a few high-quality ones. A {related_keywords} can often surprise you with its effectiveness.
• Re-rolls: Re-rolls are a powerful way to mitigate bad luck and increase average output. A full re-roll is statistically more powerful than just re-rolling 1s.
• Invulnerable Saves: These saves ignore AP and provide a consistent defense against high-powered weaponry, making them a crucial factor for a target’s durability.
• Damage Characteristic: A high damage weapon can be overkill on single-wound models but is essential for taking down multi-wound elites and vehicles. Consider using a {related_keywords} to manage your army composition effectively.

Frequently Asked Questions (FAQ)

1. What does “Expected Damage” mean?

Expected Damage is the statistical average outcome if you were to repeat the same attack sequence thousands of times. In any single roll, you might get lucky or unlucky, but over the course of a game, your results will tend towards this average.

2. How do re-rolls work in the calculation?

The calculator incorporates the added probability of a successful outcome from a re-roll. For example, re-rolling a failed hit roll gives you a second chance, so the probability of success increases. The formula is `P(original) + P(failure) * P(original)`.

3. What’s the difference between an Armour Save and an Invulnerable Save?

An Armour Save is modified by a weapon’s AP value, while an Invulnerable Save is not. The calculator automatically determines which save is better for the defender to use (e.g., a 3+ armour save against an AP-2 weapon becomes a 5+, so a 4++ invulnerable save would be used instead).

4. What is a Ward Save or “Feel No Pain”?

This is a special type of save that is taken *after* a model fails its Armour or Invulnerable save. For each point of damage inflicted, you get to roll one die. A successful roll negates that point of damage.

5. Why isn’t my result a whole number?

The calculator deals in averages, not certainties. An “Expected Damage” of 4.5 means that over many trials, the average damage would be 4.5. It doesn’t mean you will deal exactly that amount in one go.

6. Can this calculator handle abilities like “Sustained Hits” or “Lethal Hits”?

This version focuses on the core mechanics. For more complex army-specific rules and abilities, you might need a more advanced {related_keywords}, which can simulate specific unit loadouts and stratagems.

7. Does this work for Age of Sigmar?

While the hit/wound/save sequence is similar, Age of Sigmar uses a different “to wound” chart and has its own unique abilities. For best results, use a dedicated {related_keywords}.

8. How accurate is this 40k dice calculator?

The math is based on established principles of probability and accurately reflects the statistical averages of the core rules of Warhammer 40,000 10th Edition. It’s a reliable guide for what to expect on average.