“Mathhammer” is the habit of working out the average result of an attack before you commit to it — how many wounds those ten Attacks will really put through, once hits, wounds and saves are accounted for. This calculator does it instantly for 10th and 11th edition, so you can compare weapons and targets without rolling a single dice.
Enter the attacker’s profile and the target’s defences; the average damage updates live.
How to read the result
The calculator walks the full 40K sequence: Attacks → hits → wounds → failed saves → damage. It picks the wound roll automatically from Strength versus Toughness, applies AP to the save, uses the invulnerable save when it’s better, and shows the average damage plus an approximate number of models slain. Toggle the re-roll options to see how a re-roll aura changes the odds.
Put the numbers to work
- Weighing a Combat Patrol’s key unit? Pair this with the Combat Patrol rules guide.
- Building a Space Marine list? Cross-check profiles in the 11th-edition Codex Space Marines guide.
- Not sure which army suits you yet? Try the army quiz first.
Frequently asked questions
What is mathhammer?
It’s using probability to find the average outcome of an attack, so you can make better target and list-building decisions instead of relying on gut feel.
How do you calculate average damage in 40K?
Multiply the number of attacks by the chance to hit, then by the chance to wound, then by the chance the save fails, then by the weapon’s damage. This tool does all four steps for you.
Does it handle re-rolls and invulnerable saves?
Yes — tick “re-roll 1s” to hit or wound, and enter an invulnerable save; the calculator always uses the better of armour or invuln.
How do you work out the wound roll in Warhammer 40k?
Compare the attack’s Strength with the target’s Toughness. If Strength is at least double the Toughness you wound on a 2+, if it’s higher you need a 3+, if they’re equal it’s a 4+, if it’s lower it’s a 5+, and if it’s half or less you need a 6+. The calculator does this for you automatically.
What are the odds of rolling a 3+ on a D6?
About 67%, or two in three. The other targets go like this: 2+ is about 83%, 4+ is 50%, 5+ is about 33% and 6+ is about 17%. Re-rolling 1s on a 3+ lifts your chance to about 78%. A full re-roll of failed 3+ rolls lifts it to about 89%.
How does AP change my saving throw?
AP makes the target’s armour save worse by that amount. For example, AP -2 turns a 3+ save into a 5+. AP has no effect on invulnerable saves, so a model with a 4+ invulnerable save still saves on a 4+ against high-AP weapons. The calculator always uses whichever save is better after AP is applied.