Warhammer 40K Mathhammer Calculator
Calculate average wounds dealt in Warhammer 40,000 by modelling hit rolls, wound rolls, and armour save failures.
Results
What is it?
Mathhammer is the community term for statistically analysing Warhammer 40K combat outcomes. Each attack goes through three sequential dice rolls: to-hit (vs BS/WS), to-wound (comparing Strength vs Toughness), and then the target's armour/invulnerable save. The average wounds formula chains these probabilities: Attacks x P(hit) x P(wound) x P(fail save).
How to use
Enter the number of attacks, BS/WS (e.g. 3 for 3+), attacking Strength, target Toughness, target Armour Save, and Invulnerable Save (0 if none). The calculator shows hit probability, wound probability, and expected average wounds dealt.
Example scenario
5 attacks, BS3+, S4 vs T4 (50% wound), Sv4+ with no invuln: P(hit) = 67%, P(wound) = 50%, P(fail save) = 50%. Average wounds = 5 x 0.67 x 0.5 x 0.5 = 0.83 wounds. A squad of 10 models with same profile would average 1.67 wounds.
Pro tip
Re-rolls dramatically increase output ? re-rolling 1s to hit adds approximately 1/6 of your base hit chance. AP (Armour Penetration) worsens the opponent's save: AP-1 against Sv3+ makes them save on 4+. Use this calculator to compare unit options: does a higher-strength weapon outperform more attacks at lower strength against T5 targets? Always run both scenarios.