Warhammer Math Calculator

Optimize your army performance with the definitive Warhammer math calculator for probabilistic outcomes.

Metric	Calculation Result	Efficiency Ratio

What is a Warhammer Math Calculator?

A Warhammer math calculator is an essential tool for players of Warhammer 40,000, Age of Sigmar, and other tabletop wargames that rely on D6 dice mechanics. Often referred to by the community as “MathHammer,” this process involves using probability theory to determine the average or “expected” outcome of any given combat interaction. By using a Warhammer math calculator, players can remove the guesswork from their tactical decisions, allowing them to understand whether a unit is capable of destroying a specific target before they commit to a charge or a shooting phase.

Who should use it? Competitive players use it to build optimal lists, while casual players find it helpful to understand why certain units feel “underpowered” or “overpowered.” A common misconception is that a Warhammer math calculator predicts the future perfectly. In reality, it provides the mathematical mean; actual dice rolls will vary, but over dozens of games, your results will converge toward these calculated averages.

Warhammer Math Calculator Formula and Mathematical Explanation

The core logic of a Warhammer math calculator follows a chain of independent probabilities. Each step in the attack sequence—hitting, wounding, and saving—acts as a filter, reducing the initial number of attacks to the final damage tally.

The fundamental formula for expected damage (E) is:

E = A × P(H) × P(W) × P(S) × D

Variable	Meaning	Unit	Typical Range
A	Number of Attacks	Count	1 – 100+
P(H)	Probability of Hitting	Decimal	0.16 (6+) – 0.83 (2+)
P(W)	Probability of Wounding	Decimal	0.16 – 0.83
P(S)	Probability of Failed Save	Decimal	0 (No pen) – 1.0 (Auto)
D	Damage Characteristic	Value	1 – 12+

When calculating rerolls, the Warhammer math calculator adjusts the probability. For example, “Reroll 1s” adds a (1/6) chance to roll again, effectively increasing a 3+ hit rate from 66.6% to 77.7%.

Practical Examples (Real-World Use Cases)

Example 1: Space Marine Intercessors vs. Orks

Imagine 10 Intercessors firing Bolt Rifles (20 shots) at a unit of Orks. Intercessors hit on 3+ and wound Orks (T4) on 4+. The Orks have a 6+ save, but the Bolt Rifle has AP -1. Using the Warhammer math calculator, we input: 20 attacks, 3+ hit, 4+ wound, 6+ save with AP 1 (making the save impossible). The calculator shows an expected 6.67 wounds, likely wiping out a significant portion of the mob.

Example 2: Anti-Tank Firepower

A Lascannon (1 shot, 3+ hit, 3+ wound vs Light Tank, AP -3, D6+1 damage). Without a Warhammer math calculator, you might rely on luck. With the tool, you see the expected damage is roughly 3.11. If the tank has 6 wounds remaining, you know you need at least two Lascannons to have a reliable chance of destruction.

How to Use This Warhammer Math Calculator

1. Enter Attacks: Input the total number of dice you are rolling for the specific weapon or unit.
2. Select Skill: Choose the target number required to hit (e.g., BS 3+).
3. Apply Rerolls: Select if you have buffs allowing rerolls of 1s or all failures.
4. Determine Wound Roll: Compare your Strength to the enemy Toughness and select the appropriate 2+ through 6+ value.
5. Input Save and AP: Select the target’s base save and your weapon’s Armor Penetration. The Warhammer math calculator automatically computes the modified save.
6. Enter Damage: Put in the flat damage value of the weapon.

The results will update instantly, showing the average performance. Use these metrics to decide whether to split fire or concentrate your units on a single objective.

Key Factors That Affect Warhammer Math Calculator Results

• Volume of Fire: Increasing the number of attacks is the most reliable way to overcome poor dice luck.
• Reroll Auras: Rerolls drastically shift the bell curve, making high-risk maneuvers much more consistent.
• Armor Penetration (AP): High AP is critical against elite infantry. A Warhammer math calculator shows that AP -2 can double your effective damage against targets with 3+ saves.
• Invulnerable Saves: These ignore AP, creating a “floor” for how much damage an enemy can mitigate, regardless of your weapon’s power.
• Damage Characteristic: Multi-damage weapons (D2, D3) are far more efficient against multi-wound models like Terminators, but “waste” damage on 1-wound infantry.
• Feel No Pain (FNP): This secondary save layer adds another calculation step, further reducing the final unsaved wounds.

Frequently Asked Questions (FAQ)

What does “MathHammer” mean?

MathHammer is the slang term for using a Warhammer math calculator to analyze unit statistics and determine the most efficient tactical choices based on mathematical averages.

Does the calculator account for exploding sixes?

Standard calculators focus on base outcomes. “Exploding 6s” (scoring extra hits on a roll of 6) requires adding 16.6% to the hit probability for each extra hit generated.

Why did my unit do 0 damage when the calculator said 5?

The Warhammer math calculator provides the mean result over infinite rolls. Individual variance (luck) can always result in extremes, but the average helps you plan for the most likely outcome.

How do I calculate Strength vs Toughness?

If S > 2xT (2+), S > T (3+), S = T (4+), S < T (5+), S < 1/2T (6+). Input these results into the Warhammer math calculator wound field.

What is the benefit of rerolling 1s vs rerolling all failures?

Rerolling 1s provides a smaller but often cheaper boost. Rerolling all failures (especially on a 4+ or 5+ skill) provides a massive increase in consistency and output.

Does AP affect Invulnerable Saves?

No. Invulnerable saves are fixed. When using the Warhammer math calculator, ensure you use the better of the two saves (modified armor save vs invulnerable save).

Can this calculator be used for Age of Sigmar?

Yes! The logic for To Hit, To Wound, and Save is identical in Age of Sigmar, though the names of statistics might vary slightly.

Is more damage always better?

Not always. A Warhammer math calculator might show high damage, but if that damage comes from a single shot, it is vulnerable to a single “1” on the dice. High volume (many shots) is usually more stable.