40K Maths Lab

Attacks used

Within half range Stayed still Charged this turn

Models

Benefit of cover

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Wounds removed

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Models killed

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Chance to wipe the unit

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Share of the unit destroyed

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Damage per 100 points

Where the attacks go

Wounds removedExact, not simulated

Every weapon against this targetOne weapon at a time, all its models firing

Click any unit in the sidebar to open its card.

The wound roll has five stepsS ≥ 2×T → 2+ · S > T → 3+ · S = T → 4+ · S < T → 5+ · S ≤ ½T → 6+

Strength only matters when it crosses a step. The table below is the whole game: every Toughness in it, weighted by the share of points that has it, so you can see what one more point of Strength is actually worth.

Strength

Against Toughness

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Wound roll needed

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Chance to wound

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+1 Strength here

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+1 Strength across the game

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Best step, S3 to S14

What +1 Strength is worthAverage chance to wound across the game's Toughness, by points

Where that step comes from

Only the Toughness values that change are worth anything. Anti-X, Lance and Devastating Wounds are ways round a breakpoint; they aren't in this table.

The battlefield by Toughness

Attacker: extra damage

Target: harder to kill

Best buff for every unit in the game

Each buff applied to every unit. Damage buffs are scored against the game's real defences, defensive buffs against its real weapons.

Open this tab to run the numbers.

Toughness in the game

Share of points at each Toughness. Weighted by points, not by model count: vehicles and monsters carry more points than the infantry that outnumber them.

Saves and extra saves

Feel No Pain isn't shown: almost all of it comes from abilities and army rules, which this data doesn't include.

The defences every unit is scored against

The attacks every unit is scored against

Efficiency MatrixD100 × E100 · relative to the typical unit

Melee counts at a charge of

A unit's fight only happens if it gets into combat, so D100 counts melee weapons at the chance of rolling this charge on 2D6. 9" is the closest a unit arriving from reserves can be set up.

D100: the share of an enemy unit destroyed per 100 points in one activation (shooting, then fighting if the charge comes off), against the points-weighted mix of every unit's defence. E100: effective wounds per 100 points against the attack-weighted mix of every weapon, scaled to a Toughness 4 target so a unit's own Toughness counts. One gridline step is double or half. Pick a faction in the sidebar to highlight it.

Faction shapesPoints-weighted · click a row to highlight

Where the data comes from

Every unit comes from data/w40k-units.csv in the Statshammer GitHub repository, built from the BSData 11th edition catalogues. The lab reads that file and works out all the probabilities itself.

Data file on GitHub Edit the data file

Edit the data file on GitHub and the lab shows the change on its next load, with nothing to rebuild. ↻ Refresh reloads it straight away. If the file can't be reached (for example when this page is opened from your computer), the lab uses the copy built into the page.

Left out, or worth knowing about

Method and limits

Rules used (11th edition Core Rules, checked 15 Sep 2026):
- An unmodified 1 always fails and an unmodified 6 is a critical hit or wound. Hit and wound modifiers are capped at ±1.
- The save is the better of armour with the attack's AP and any invulnerable save; an unmodified 1 always fails.
- Damage goes to one model at a time and never carries over, so the last model wastes what it can't take. Feel No Pain is rolled for each lost wound.
- Lethal Hits auto-wound (and are not critical wounds), Sustained Hits add normal hits, Devastating Wounds end the sequence with mortal wounds. Benefit of cover worsens a shooting attack's Ballistic Skill by 1.
- Units with different models (a sergeant, a bodyguard, a character) use one wound pool, and CHARACTER models are allocated last.
D100 resolves shooting first, then the fight. The fight is counted at the chance of making the charge set above the matrix (default 9", 28% on 2D6); losses on the way in and fights where the unit is charged are not modelled. The Attack tab always counts the whole fight.
E100 is the expected number of the game's attacks needed to destroy the unit, times the damage each would do to a Toughness 4 model with no save. A unit's Toughness therefore counts: T7 against Strength 4 (wounded on 5+, not 4+) is worth half as much again as T4.
Each unit uses its default loadout at its base size. Detachment rules, army rules, stratagems, auras, leaders attached to units and re-rolls from abilities are not included: this is the datasheet on its own.
Weapons with several firing modes (marked ➤) are read on one profile. A variable ability such as Sustained Hits D3 is read at its average, and an ability that only works against some targets, such as Lethal Hits against non-vehicles, is left out. Both kinds are listed in the panel above.
Feel No Pain is only counted where a datasheet gives it without conditions, which is two units. Most Feel No Pain in the game comes from abilities and army rules.
Units over 1,000 points are left out so Apocalypse-scale models don't distort a matched-play reference.
Twin-linked, Anti-X, Blast, Torrent, Melta, Rapid Fire, Heavy and Lance follow the 10th edition wording; they have not yet been re-read in the 11th edition text.
Because of the missing army rules, factions that lean on them — T'au and the Knights especially — sit lower on the matrix than they play.