40k Calculator

Advanced Mathhammer Combat Simulator for Warhammer 40,000

What is a 40k Calculator?

A 40k calculator, often referred to by the community as a “Mathhammer” tool, is an essential resource for Warhammer 40,000 players. It utilizes probability theory to predict the outcome of combat sequences. Whether you are playing the latest 10th edition or older versions, understanding the statistical likelihood of your attacks succeeding is crucial for tactical dominance.

Competitive players use a 40k calculator to evaluate unit efficiency, decide which targets to prioritize, and determine if a specific charge or shooting phase is worth the risk. By breaking down the complex dice-rolling sequence into mathematical averages, the tool eliminates guesswork and highlights the raw power of different weapon profiles.

Common misconceptions include the idea that “math doesn’t matter because dice are random.” While dice are indeed random, the law of large numbers ensures that over the course of a tournament or even a single game, results will gravitate toward the averages provided by a high-quality 40k calculator.

40k Calculator Formula and Mathematical Explanation

The core of the 40k calculator relies on a sequential probability chain. Every attack follows a specific hierarchy: Hit Roll -> Wound Roll -> Saving Throw -> Damage Allocation.

The mathematical derivation for expected damage (E) is:

E = A × P(Hit) × P(Wound) × P(Fail Save) × D

Variable	Meaning	Unit	Typical Range
A	Number of Attacks	Dice	1 – 100+
BS/WS	Ballistic/Weapon Skill	Dice Face	2+ to 6+
S vs T	Strength vs Toughness	Ratio	0.5x to 2x
AP	Armor Penetration	Modifier	0 to -6
Sv / Inv	Armor/Invulnerable Save	Dice Face	2+ to 6+

Practical Examples (Real-World Use Cases)

Example 1: Space Marine Intercessors vs. Ork Boyz

Suppose a unit of Intercessors fires 10 Bolt Rifle shots (S4, AP-1, D1) at a unit of Ork Boyz (T5, Sv 5+). Using the 40k calculator:

• Hits: 10 shots at BS 3+ = 6.67 hits.
• Wounds: S4 vs T5 requires a 5+ = 2.22 wounds.
• Saves: Ork 5+ save becomes 6+ due to AP-1. Failed save chance is 5/6.
• Result: 1.85 total damage (roughly 1-2 dead Orks).

Example 2: Anti-Tank Lascannon vs. Rhino

A Lascannon (S12, AP-3, Dd6+1) fires at a Rhino (T9, Sv 3+). Let’s assume an average damage of 4.5.

• Hits: 1 shot at BS 3+ = 0.67 hits.
• Wounds: S12 vs T9 requires 3+ = 0.44 wounds.
• Saves: Rhino 3+ save becomes 6+ due to AP-3. Failed save chance is 5/6.
• Result: 0.37 wounds failing saves × 4.5 damage = 1.67 expected damage.

How to Use This 40k Calculator

1. Input Attacks: Enter the number of shots or melee swings your unit makes.
2. Select Skill: Pick the Weapon Skill (WS) for melee or Ballistic Skill (BS) for shooting.
3. Compare S and T: Enter the Strength of the weapon and the Toughness of the target. The 40k calculator automatically determines the required wound roll.
4. Apply AP: Enter the Armor Penetration value as a positive integer.
5. Set Saves: Choose the target’s best armor and invulnerable saves. The tool will automatically use the better value after modifiers.
6. Analyze Results: View the expected damage and breakdown to make your tactical decision.

Key Factors That Affect 40k Calculator Results

Several financial-like variables influence the “efficiency” of an attack in Warhammer 40,000:

• Volume vs. Quality: High attack counts (A) can overcome poor accuracy (BS/WS), acting like a diversified investment portfolio.
• Strength-Toughness Breakpoints: Small increases in Strength can drastically change the “Return on Investment” (ROI) if they hit a breakpoint (e.g., S5 vs T4).
• AP Saturation: High AP is useless against targets with strong Invulnerable saves, much like how high-cost services aren’t valued by all market segments.
• Damage Waste: If a weapon does 3 damage but the target has only 1 wound, the “Cash Flow” of damage is inefficient.
• Re-rolls: Re-rolling 1s or all failed rolls significantly boosts the reliability of the 40k calculator projections.
• Keywords: Rules like “Lethal Hits” (auto-wound on 6s) or “Devastating Wounds” (bypass saves) provide “tax-free” damage that ignores certain defensive layers.

Frequently Asked Questions (FAQ)

Does this 40k calculator work for 10th Edition?

Yes, the math for hit, wound, and save rolls remains consistent across 10th edition and previous iterations, provided you input the correct S, T, and AP values.

How do I handle D6 damage?

For variable damage like D6, use the average result (3.5) in the damage field. For D3, use 2.

What does AP-0 mean for the calculator?

Enter “0” in the AP field. This means the target will use its base armor save without modification.

Is a higher Toughness always better?

Mathematically, yes, but only if it crosses a breakpoint relative to the enemy’s Strength. Going from T4 to T5 is a huge jump against S4 weapons.

What is “Mathhammer”?

Mathhammer is the slang term for using a 40k calculator to determine the statistical efficiency of units in the game.

Can I calculate Mortal Wounds?

Mortal wounds bypass the Save step. To calculate them, you can set the target save to 7+ (None) or manually account for them as guaranteed damage after the wound roll.

How accurate is the “Expected Damage”?

It is the mathematical mean. In reality, dice follow a binomial distribution, so you may roll higher or lower in a single instance.

Why is AP so important?

AP reduces the opponent’s chance to save. A jump from AP-1 to AP-2 can effectively double the damage against a 3+ save target.

Related Tools and Internal Resources

• Warhammer 40k Army Builder – Construct your roster using updated point values.
• Dice Probability Guide – A deep dive into D6 statistics and bell curves.
• Unit Statistics Comparison – Compare two units side-by-side to see who wins in a duel.
• Points Value Calculator – Determine the point efficiency of your damage output.
• Stratagem Efficiency Tool – Calculate if a 2CP stratagem is worth the damage boost.
• Victory Point Tracker – Keep track of your primary and secondary objectives during play.