40 CARROTHow does 40K mathhammer work in 11th edition?
Four fractions multiplied together, then a second look at the spread the average hides. Every number on this page was computed by the engine behind the free 40 Carrot Damage Calculator, with the inputs shown so you can check it by hand.
TL;DR
Mathhammer multiplies four fractions: the chance to hit, the chance to wound from Strength against Toughness, the chance the save fails after AP, and the Damage per failed save. Ten BS 3+ shots at S4, AP-1, D1 into a T4 model with a 3+ save average 1.67 damage, about 0.6 of a two-wound model. The free Damage Calculator runs the same arithmetic and adds the spread.
What are the four rolls mathhammer multiplies?
The 11th edition attack sequence resolves each attack in four steps: a hit roll, a wound roll, a save roll, then damage. Each roll is one D6 that succeeds on a threshold, so each step is a fraction out of 6. A 3+ succeeds on 4 of the 6 faces, which is 0.667; a 4+ on 3 faces, 0.5; a 5+ on 2 faces, 0.333; a 6+ on 1 face, 0.167; a 2+ on 5 faces, 0.833.
Two edge cases sit outside the fractions. On the hit roll and the wound roll an unmodified 1 always fails and an unmodified 6 always succeeds, no matter what the modifiers add or subtract. On the save roll an unmodified 1 always lets the damage through. That is why a modifier never pushes a 2+ past 5 chances in 6, and why a 6 can still hit a target that would otherwise need a 7.
Paraphrased from the Warhammer 40,000 Core Rules, section 05 (Attack Sequence), pages 18 and 19 of the free PDF published on the Warhammer Community downloads page, read 13 October 2026. Check the PDF itself before an event; the rules are theirs, the paraphrase is ours.
How do you work out the wound roll from Strength and Toughness?
Compare the weapon's Strength with the target's Toughness. The required result steps through five bands: Strength at least twice the Toughness wounds on a 2+; Strength greater than Toughness on a 3+; equal on a 4+; less on a 5+; and Strength at half the Toughness or lower on a 6+. S4 into T4 is a 4+, S4 into T5 is a 5+, and S9 into T10 is a 5+ because 9 is less than 10 but more than half of it.
The save step has two routes and the defender takes the better one. AP worsens the ordinary save by its value, so a 3+ save against AP-1 needs a 4+ and a 2+ save against AP-3 needs a 5+. An invulnerable save ignores AP entirely and passes on its own unmodified number. A model with a 2+ save and a 4+ invulnerable save uses the 2+ against AP0 and the 4+ against AP-3.
| Strength against Toughness | Needs | Chance |
|---|---|---|
| Twice the Toughness or more | 2+ | 5 in 6 (0.833) |
| Greater than the Toughness | 3+ | 4 in 6 (0.667) |
| Equal to the Toughness | 4+ | 3 in 6 (0.5) |
| Less than the Toughness | 5+ | 2 in 6 (0.333) |
| Half the Toughness or less | 6+ | 1 in 6 (0.167) |
Thresholds paraphrased from Core Rules 05.02 (Wound Rolls) and 05.03 (Save Rolls), read 13 October 2026. The 40 Carrot Damage Calculator applies the same table and the same invulnerable-save choice.
What do five typical volleys come to, step by step?
Each row multiplies attacks by the four fractions. Volley A is the reference: 10 attacks at BS 3+ (0.667) with S4 into T4 (0.5), AP-1 against a 3+ save so the save needs a 4+ and fails half the time (0.5), and Damage 1. That is 10 × 0.667 × 0.5 × 0.5 × 1 = 1.67 expected damage. The engine's closed-form answer is 1.667, and a 50,000-game simulation lands on 1.67.
| Volley | Inputs | Fractions | Expected damage | Models removed |
|---|---|---|---|---|
| A | 10 attacks, BS 3+, S4, AP-1, D1 into T4, Sv 3+, W2, 10 models | 10 × 0.667 × 0.5 × 0.5 × 1 | 1.67 | 0.59 |
| B | Same 10 attacks into T5, Sv 3+, W3, 5 models | 10 × 0.667 × 0.333 × 0.5 × 1 | 1.11 | 0.09 |
| C | 2 attacks, BS 3+, S9, AP-3, D D6 into T10, Sv 2+, W12, 1 model | 2 × 0.667 × 0.333 × 0.667 × 3.5 | 1.04 | 0.00 |
| D | 20 attacks, BS 4+, S4, AP0, D1 into T4, Sv 3+, W2, 10 models | 20 × 0.5 × 0.5 × 0.333 × 1 | 1.67 | 0.59 |
| E | Volley A with the target in cover, so the hit roll needs a 4+ | 10 × 0.5 × 0.5 × 0.5 × 1 | 1.25 | 0.38 |
Expected damage is the engine's exact closed form; models removed is the mean of a 50,000-game simulation with sequential damage allocation, computed on 13 October 2026 by the same code that powers /damage-calc/. The profiles are illustrative numbers, not any unit's datasheet.
Three things fall out of the table. Volley D shows that 20 shots at BS 4+ with no AP equal 10 shots at BS 3+ with AP-1 into this target, so a bigger number of attacks is not a better volley by itself. Volley B shows one point of Toughness cutting the result by a third, from 1.67 to 1.11, and cutting models removed far harder because every model now needs three failed saves instead of two. Volley E shows cover, which in 11th edition worsens BS by 1 (Core Rules 13.08), taking a quarter off the volley.
Enter the attacks, skill, Strength, AP and Damage, then the target's Toughness, save, wounds and model count. No account needed.
Why is the average not the whole answer?
Volley A averages 1.67 damage, yet the result you see on the table is one of eleven whole numbers. Each of the 10 attacks inflicts a damage with probability 0.667 × 0.5 × 0.5 = 0.167, so the count of damage is binomial. The chance of no damage at all is 0.833 to the power 10, which is 16%. The chance of two or more, enough to remove one two-wound model, is 1 minus the chance of zero minus the chance of exactly one, which comes to 52%.
In cover (volley E) the per-attack chance drops to 0.125, and the chance of removing at least one model drops to 36%. Against the T5 target in volley B each model needs three failed saves, and the chance of removing even one of the five models is 9%. The average said B was two thirds of A; the kill chance says it is one sixth of A. Decide on the kill chance when a kill is what the play needs.
That is the number the calculator adds that the hand method does not: it simulates the whole volley, including which model the damage lands on, and reports models removed and the wipe chance beside the mean. The damage probability guide covers how to turn that spread into a decision.
How do you check the trade on a true-scale table?
A volley only happens if the weapon is in range of the target it was calculated against. The frame below keeps measurement and the damage odds on one 40 Carrot table at true scale, which is the step the arithmetic skips.
What this page does and does not cover
This page does
- ✓Paraphrase the 11th edition hit, wound, save and damage steps from the Core Rules read on 13 October 2026.
- ✓Show five volleys with every input and every fraction, computed by the shipping damage engine.
- ✓Give the kill chance beside the average, worked by hand so you can check it.
This page does not
- ✕Reproduce any datasheet, weapon profile or points value. The numbers here are illustrative.
- ✕Cover re-rolls, Lethal Hits, Devastating Wounds or Feel No Pain. The calculator supports the 11th edition modifiers it lists; the hand method here does not.
- ✕Replace the rulebook. Check the Core Rules PDF before an event.
The Virtual Tabletop, measuring, dice and army file import are free with an account. The Damage Calculator needs none.
Straight answers
Is an unmodified 6 always a hit in 40K?
Yes. In the 11th edition attack sequence an unmodified 6 on a hit roll is a critical hit and always hits, and an unmodified 1 always fails, whatever the modifiers say. The same pair applies to wound rolls. On a save, an unmodified 1 always lets the damage through.
Does AP reduce an invulnerable save?
No. AP modifies the ordinary save only. A model with an invulnerable save passes if the unmodified result equals or beats that characteristic, so against AP-3 a 2+ armour save becomes a 5+ while a 4+ invulnerable save stays a 4+. Use whichever of the two gives the better chance, which the 40 Carrot Damage Calculator does for you.
Is the 40 Carrot Damage Calculator free?
Yes. The Damage Calculator at /damage-calc/ needs no account and no payment. A free account adds the Virtual Tabletop, measuring, dice and army file import, so you can set the matchup you just calculated on a true-scale table. Snapshots, replay and cloud saves are part of Full Access.
Does the calculator ship official unit stats?
No. 40 Carrot ships unit names and base sizes only. The attacks, skill, Strength, AP, Damage, Toughness, save and wounds in every example on this page are illustrative numbers, and the ones you enter in the calculator come from your own books and profiles.