40K Damage Calculator
Estimate expected hits, wounds, failed saves, and total damage for a Warhammer 40,000 attack sequence. This calculator follows the standard 10th edition rules flow.
Enter weapon and target stats
Set attacks, hit roll, Strength, Toughness, AP, save, damage, and any special rules.
Expected hits = attacks × hit chance + Sustained adjustments.
Expected wounds = (normal hits × wound chance) + auto-wounds from Lethal Hits.
Failed saves = wounds × fail-save chance (better of armour vs invuln).
Damage = failed saves × damage, reduced by Feel No Pain.
Warhammer 40K Damage Calculator: The Complete Guide to Expected Hits, Wounds, Saves & Damage Output
Every die rolled across a Warhammer 40,000 battlefield obeys the same underlying mathematics, and the commanders who understand those numbers have a tangible edge over those who do not. Whether you are evaluating a weapon loadout for a new army list, trying to work out whether your Lascannons can reliably crack a Monolith, or settling a table-side argument about which unit will kill more Marines in a single round of shooting — the answer lies in a clean, sequential probability calculation that our 40K Damage Calculator performs instantly. At WalDev, we build tools for gamers who want to play smarter.
This guide is the most thorough explanation of 40K damage mathematics available outside of a university statistics classroom. We cover the complete attack sequence step by step, the probability tables behind every hit and wound roll, the mechanics of Armour Penetration, invulnerable saves, Feel No Pain, and every major weapon special ability introduced in 10th edition — Sustained Hits, Lethal Hits, Devastating Wounds, Twin-Linked, Blast, Hazardous, and more. We then translate all of that theory into practical army-building application so that the numbers you calculate actually improve the decisions you make before a single model hits the table. You will also find links to our complete gaming calculators suite covering everything from Pokémon damage to Classic WoW talent builds.
One important note before we begin: this guide is deliberately written from a player’s perspective. The rules mechanics described reflect Warhammer 40,000 10th Edition as the current standard, but the mathematical principles apply equally to earlier editions — the hit probability tables, wound tables, and sequential probability logic are edition-agnostic. Where specific 10th Edition abilities are discussed, that is noted explicitly.
Why Math Hammer Matters: The Case for Calculating Before You Roll
The term “math hammer” has been part of the Warhammer 40K community’s vocabulary for decades — longer, arguably, than the word “meta.” It refers to the practice of calculating the statistically expected outcome of dice rolls rather than intuiting, guessing, or simply hoping the dice will fall your way. Players who use math hammer consistently make better decisions at the list-building stage, at the deployment stage, and at the moment of picking targets during a game. Players who rely on feel and instinct alone often discover, after a frustrating number of games, that their “reliable” unit is not actually reliable — that the expected number of kills per activation is lower than they assumed, or that a particular weapon loadout underperforms its point cost against the targets they regularly face.
None of this means Warhammer is purely a math exercise. The fog of war, positioning, mission objectives, threat management, and psychological pressure on an opponent are all dimensions the numbers do not capture. A unit that the math says should kill 2.3 Space Marines per activation is not going to kill exactly 2.3 Space Marines every time — it might kill zero, it might kill six. But across a game, across a tournament, across many games with many decisions, the player who understands expected values is playing with information the other player is not using. That is a real competitive advantage, and it is also just more intellectually satisfying to know why your army is configured the way it is rather than following a list you found online without understanding the reasoning.
The 40K Damage Calculator makes math hammer accessible to every player regardless of mathematical background. You enter a weapon profile and a target’s stats, and the calculator returns expected hits, expected wounds, expected failed saves, and expected final damage. The mechanics behind that output are what this guide explains — so that when the result surprises you, you understand why, and when you want to test a variant profile, you understand what you are changing.
Math hammer calculates expected values — the average result over infinitely many rolls. In any individual game, results will deviate from these averages due to random variance. Understanding both the expected value AND the variance is what separates genuinely advanced 40K analysis from basic math hammer. We cover variance in depth in the Variance vs Expected Value section of this guide.
The Full 40K Attack Sequence: Every Step From Roll to Damage
The Warhammer 40K combat resolution system is a beautifully consistent mechanism — the same five-step sequence governs every attack in the game from a basic Guardsman’s lasgun to a Titan’s plasma annihilator. Every step applies a probability filter that reduces the original pool of attacks, with the final product being a number of damage points applied to the target. Understanding each step individually — what it represents, what dice it involves, and what modifies it — is the prerequisite for understanding everything that comes after.
The attacking player rolls a number of dice equal to the weapon’s Attacks (A) characteristic. Each die must equal or exceed the attacker’s Ballistic Skill (ranged) or Weapon Skill (melee) value to score a hit. A result of 1 always fails regardless of modifiers; a result of 6 always succeeds (with some exceptions). This step can be affected by to-hit modifiers (applying +1 or -1 to the roll), re-roll abilities, and weapon special rules like Torrent (which auto-hits without requiring a roll) or Indirect Fire (which imposes -1 to hit against non-visible targets).
For each hit scored, the attacking player rolls a die and compares the weapon’s Strength (S) against the target unit’s Toughness (T). The Strength-versus-Toughness table determines the minimum roll needed to wound: S≥2×T wounds on 2+; S>T wounds on 3+; S=T wounds on 4+; S<T wounds on 5+; S≤T/2 wounds on 6+. A 1 always fails; a 6 always wounds (at the base level, before Lethal Hits or other abilities). Re-roll abilities such as Twin-Linked apply at this step.
The defending player assigns each wound to a model in the target unit. Generally they may assign wounds to any model within range and visibility of the attacker, but they cannot assign a second wound to a model that still has remaining wounds until every other model in the unit has been wounded. This step has no dice roll but creates important tactical decisions — particularly about whether to absorb wounds onto nearly-dead models or protect key model types within a unit.
The defending player rolls a die for each wound allocated. They roll against their model’s Save characteristic, modified by the weapon’s Armour Penetration (AP) value. AP -1 means add 1 to the save number needed (e.g., 3+ becomes 4+); AP -2 makes it 5+; AP -3 makes it 6+; AP -4 or worse means the armor save cannot be used. If the model has an invulnerable save, it can use the better of its invulnerable save and its modified armor save. A save of 1 always fails; a roll that meets or exceeds the required value saves the wound.
Each unsaved wound inflicts damage equal to the weapon’s Damage (D) characteristic. If the weapon has variable damage (e.g., D3 or D6), a die is rolled for each unsaved wound separately. If the target model has a Feel No Pain ability, the controlling player rolls a die for each individual point of damage — saving individual damage points on the appropriate roll. Excess damage beyond a model’s remaining wounds is lost (does not carry over to the next model in the unit in standard rules, though some abilities modify this). Once all damage has been applied, models with zero or fewer wounds remaining are removed as casualties.
Full Damage Formula:
Expected Damage = A × Hit% × Wound% × (1 − Save%) × (1 − FNP%) × D(avg)
Where: A = Attacks | Hit% = probability per BS/WS | Wound% = per S vs T table
Save% = probability of defender saving (accounting for AP and invuln saves)
FNP% = Feel No Pain pass probability | D(avg) = average Damage value
Hit Rolls: BS, WS, and the Probability Tables Every Player Should Know Cold
The hit roll is the first filter in the attack sequence and the one that benefits most directly from the simple insight that a six-sided die gives you a probability in neat sixths. Every improvement by one step on the BS or WS characteristic is an increase of one-sixth (16.7%) in the raw number of hits generated per attack. This linear relationship makes hit roll improvement extremely valuable, which is why re-roll abilities that apply at the hit step have an outsized effect on total damage output — they effectively close the gap between your actual BS value and a hypothetically higher one.
| BS / WS Value | Hits On | Hit Probability | Expected Hits (per 6 attacks) | Re-roll 1s adds | Re-roll all fails adds |
|---|---|---|---|---|---|
| 2+ | 2, 3, 4, 5, 6 | 83.3% | 5.00 | +2.8% (≈ 0.17 hits) | +13.9% (≈ 0.83 hits) |
| 3+ | 3, 4, 5, 6 | 66.7% | 4.00 | +11.1% (≈ 0.67 hits) | +22.2% (≈ 1.33 hits) |
| 4+ | 4, 5, 6 | 50.0% | 3.00 | +8.3% (≈ 0.50 hits) | +25.0% (≈ 1.50 hits) |
| 5+ | 5, 6 | 33.3% | 2.00 | +5.6% (≈ 0.33 hits) | +22.2% (≈ 1.33 hits) |
| 6+ | 6 only | 16.7% | 1.00 | +2.8% (≈ 0.17 hits) | +13.9% (≈ 0.83 hits) |
| Torrent | Auto | 100% | 6.00 | N/A | N/A |
A few important nuances apply at the hit roll step. First, a natural roll of 1 always fails regardless of bonuses — if a model has +1 to hit from an ability, this makes a 2+ hit roll effectively have a 5/6 hit rate rather than 6/6, not 6/6 with the bonus allowing a 1 to hit. Second, conversely, a natural roll of 6 always hits, meaning -1 to-hit modifiers cannot reduce a unit’s hit rate below 1/6. Third, hit roll modifiers cannot be modified beyond -1 or +1 in 10th Edition — excess modifiers are ignored. This cap matters significantly for the most heavily modified situations.
The Sustained Hits ability, introduced as a core mechanic in 10th Edition, generates additional hits on a natural 6 and interacts with this step in an important way for math hammer. With Sustained Hits 1, every natural 6 produces one extra hit — meaning 1/6 of attacks generate 2 hits instead of 1. This adds a fractional hit bonus equal to 1/6 × the Sustained Hits value to the base hit rate. For a BS 3+ weapon with Sustained Hits 1: base expected hits per attack = 4/6 = 0.667, plus Sustained Hits bonus = 1/6 × 1 = 0.167. Total expected hits per attack = 0.833. This is equivalent to a pure hit rate of 5/6 — effectively bumping the weapon to BS 2+ hit rate even though its printed BS is still 3+.
If you enjoy probability-based game tools, explore our gaming calculators — including the Pokémon Damage Calculator and Pokémon Type Calculator for similarly structured probability and effectiveness analysis across another beloved gaming system.
Wound Rolls: The Strength vs Toughness Table and What It Really Means
The wound roll is where the attacker’s weapon punches against the defender’s body — and the Strength-versus-Toughness table is one of the most elegantly designed probability systems in tabletop wargaming. It creates a smooth continuum between weapons that always wound reliably and weapons that struggle against hard targets, without requiring look-up tables for every possible pairing. Once you know the five bands of the S-vs-T relationship, you can calculate wound probability for any matchup instantly.
| Condition | Wound Roll | Probability | Example (S vs T) |
|---|---|---|---|
| Strength ≥ double Toughness | 2+ | 83.3% | S8 vs T4, S12 vs T6, S6 vs T3 |
| Strength > Toughness | 3+ | 66.7% | S5 vs T4, S9 vs T7, S4 vs T3 |
| Strength = Toughness | 4+ | 50.0% | S4 vs T4, S6 vs T6, S12 vs T12 |
| Strength < Toughness | 5+ | 33.3% | S3 vs T4, S7 vs T9, S4 vs T5 |
| Strength ≤ half Toughness | 6+ | 16.7% | S3 vs T7, S4 vs T9, S2 vs T5 |
The practical implications of this table are far-reaching for army building and target selection. The single biggest efficiency step in weapon design is whether a weapon sits above or below the doubling threshold against common targets. S8 against T4 (Space Marines without a transport) wounds on 2+, making it one of the most efficient ways to land wounds on the game’s most common infantry profile. Drop to S6 and you are wounding standard Marines on 3+ — still strong. Drop to S4 and you are at 4+, equivalent to a 50/50 flip, which is where most basic infantry weapons land against most infantry targets.
Against vehicles, T9 and above creates a very different landscape. At T10 (common for tanks), S5 is in the 6+ bracket — meaning basic infantry weapons need a natural 6 to wound, and almost all of them will fail to contribute meaningfully. S10 reaches the doubling threshold against T10, wounding on 2+, which is why dedicated anti-tank weapons in the S10-S14 range exist for exactly this matchup. Understanding where your weapons sit on the wound table against your expected targets is one of the most important pre-game calculations you can make.
Lethal Hits bypasses this step entirely for natural 6s on the hit roll — those hits auto-wound regardless of the S vs T result. This is especially valuable against very high-Toughness targets where the wound roll would normally require a 6+ anyway, effectively turning what would be a 1/6 wound chance for natural 6 hits into a 1/6 auto-wound chance — same rate, but it cannot be affected by wound roll modifiers. Against T5 (5+ wound threshold), Lethal Hits means that 1 in 6 hits auto-wounds while the other 5 in 6 still go through the normal wound roll, effectively improving wound output by the gap between the existing wound rate and the rate at which natural 6 hits would have failed their wound rolls.
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Goonhammer is the leading community resource for 40K competitive analysis, tactics articles, and tournament coverage — an invaluable companion to math hammer calculations with the meta context that numbers alone do not provide.
Saves, AP Values, and Invulnerable Saves: The Defender’s Last Line
The saving throw is where the defender gets to fight back against probability, and Armour Penetration is the mechanism by which the attacker degrades that defense. Understanding how AP interacts with save values — and when invulnerable saves become relevant — is essential for calculating the true throughput of any weapon profile because the difference in effective output between a weapon with AP -1 and AP -3 can be dramatic depending on the target’s save value.
The standard save modifier is additive on the required roll number. A Space Marine has a 3+ armor save. A weapon with AP -1 forces that Marine to roll a 4+ to save. AP -2 forces a 5+. AP -3 forces a 6+. AP -4 means the armor save cannot be used at all — only invulnerable saves apply. This is why Terminators with 2+ armor saves effectively take no penalty from AP -1 (forced to 3+, which is still better than most units’ base save), modest penalty from AP -2 (forced to 4+), and severe penalty from AP -3 (forced to 5+ or relying on their 5+ invulnerable). The mathematics of saves create natural “tiers” of AP relevance for each save value.
| Base Save | No AP | AP -1 | AP -2 | AP -3 | AP -4+ | Save Probability (No AP) |
|---|---|---|---|---|---|---|
| 2+ | 2+ | 3+ | 4+ | 5+ | No save (or invuln) | 83.3% |
| 3+ | 3+ | 4+ | 5+ | 6+ | No save (or invuln) | 66.7% |
| 4+ | 4+ | 5+ | 6+ | No save (or invuln) | No save (or invuln) | 50.0% |
| 5+ | 5+ | 6+ | No save (or invuln) | No save (or invuln) | No save (or invuln) | 33.3% |
| 6+ | 6+ | No save (or invuln) | No save (or invuln) | No save (or invuln) | No save (or invuln) | 16.7% |
Invulnerable saves change this picture entirely for the units that have them. A model with a 4+ invulnerable save is unaffected by any amount of AP — it will always save on a 4+ regardless of whether the weapon has AP 0 or AP -6. Against AP -3 or worse, a 4+ invulnerable save is better than the standard 6+ armor save that AP -3 forces, so the invulnerable save is used. Against AP -1 forcing a 4+, both saves are equal, so either can be rolled. Against AP 0 forcing a 3+, the armor save is better and is used instead of the invulnerable.
The practical implication for math hammer: when calculating expected saves against a model with both an armor save and an invulnerable save, always determine which save applies for the specific AP value being used, and use that probability. Never add the two saves together — they are not cumulative. The defender always uses whichever produces the better (lower number required) result.
Cover in 10th Edition
Cover improves a unit’s armor save by 1 against ranged attacks, provided the weapon’s AP has not already reduced the save below the printed value. This means cover only helps if the weapon’s AP value has not already exceeded the unit’s armor save degradation budget. A 3+ save unit in cover against AP -1 goes from a forced 4+ back to a 3+. The same unit against AP -3 (forced to 6+) gets no benefit from cover — the AP alone has already pushed the save past where cover’s +1 would matter. Cover never helps against melee attacks or mortal wounds.
The Armour of Contempt rule
Some Space Marine units have the Armour of Contempt ability, which allows them to re-roll armor save results of 1. This is not an invulnerable save but it does meaningfully improve save consistency for high-save units. In math hammer terms, re-rolling 1s on a 2+ save changes the save rate from 83.3% to 97.2%. On a 3+ save it improves from 66.7% to 77.8%. The practical effect is most pronounced on units whose base save is high — units already saving on 5+ gain minimal benefit from re-rolling 1s at that value.
Feel No Pain, Mortal Wounds, and the Final Layer of Damage Mitigation
Feel No Pain (FNP) is the last line of defense in the damage sequence — a final chance to shrug off individual damage points that have already passed through the hit roll, wound roll, and saving throw. It is typically expressed as a value like “5+” or “4+” which represents the minimum die roll needed to negate each individual point of damage. Unlike a saving throw, which applies once per wound regardless of the Damage characteristic, Feel No Pain is applied per damage point — meaning it is particularly valuable against high-Damage weapons.
Consider two scenarios: a weapon with Damage 1 versus a weapon with Damage 5, both producing one unsaved wound against a model with FNP 5+. Against the Damage 1 weapon, the FNP player rolls once — a 5 or 6 saves the entire wound, giving a 33% chance of negating the damage. Against the Damage 5 weapon, the FNP player rolls five separate dice. On average, 33% of those five points (1.67 damage points) will be negated, but the model is unlikely to escape all five. The expected damage from the Damage 5 weapon after FNP is 5 × 0.667 = 3.33, while the Damage 1 weapon after FNP delivers 1 × 0.667 = 0.667. The percentage reduction is identical, but the absolute effect scales differently — making FNP effectively “better” against many small Damage attacks than against a few high-Damage ones.
| FNP Value | Pass Probability | Damage Negated (per damage point) | Effective Damage Multiplier |
|---|---|---|---|
| 4+ | 50.0% | 50% of damage points negated | ×0.50 (halves incoming damage) |
| 5+ | 33.3% | 33% of damage points negated | ×0.667 |
| 6+ | 16.7% | 17% of damage points negated | ×0.833 |
Mortal Wounds and the FNP Exception
Mortal wounds are the bane of high-save models precisely because they completely bypass the hit roll, wound roll, and saving throw steps. They are generated by psychic powers, certain weapon abilities (most notably Devastating Wounds on a 6+ wound roll), special rules, and ability interactions. Each mortal wound deals one damage point directly to the target, skipping directly to the “inflict damage” phase. The only defense against mortal wounds is Feel No Pain — even invulnerable saves do not protect against standard mortal wounds.
This makes FNP abilities extraordinarily valuable in the current 10th Edition environment, where Devastating Wounds has been distributed to many weapons as a standard ability. A unit with FNP 4+ (50% negation rate) sitting behind a 3++ invulnerable save is genuinely difficult to kill efficiently because it defends against both regular wounds (with saves) and mortal wounds (with FNP). The combined effective damage reduction of a 3++ save plus 4+ FNP on an unsaved wound: each wound has a 33% chance of failing the invuln save, and each damage point from those wounds has a 50% chance of being negated by FNP. Net effective survival rate per wound rolled: 0.667 (save) + 0.333 × 0.5 (fail save but save FNP) = 0.667 + 0.167 = 0.833. Only 16.7% of wounds rolled actually translate to final damage. That is an extraordinary durability profile.
10th Edition Weapon Abilities: Sustained Hits, Lethal Hits, Devastating Wounds, and More
Warhammer 40K 10th Edition restructured weapon special rules into a standardized keyword ability system, making it much easier to understand what each weapon does while also making math hammer calculations more systematic. Each keyword applies at a specific step in the attack sequence and has a clear, calculable probability effect. Understanding each ability individually — and how they compound with each other and with re-roll abilities — is essential for getting accurate damage calculator outputs.
Sustained Hits X
Triggers on an unmodified hit roll of 6. Each natural 6 generates X additional hits beyond the initial hit. The calculator adds (1/6 × X) to the base hit probability per attack. With Sustained Hits 2, a natural 6 produces 3 hits total (the initial hit plus 2 extras). This ability stacks powerfully with re-roll abilities — re-rolling misses generates more dice that can roll natural 6s, compounding the output. Two separate weapons with Sustained Hits 1 on a single model effectively have a 22.2% trigger rate across their combined attacks, not 16.7%.
Lethal Hits
Triggers on an unmodified hit roll of 6. Each natural 6 auto-wounds the target without a wound roll. The wound roll probability for these hits is treated as 100% (bypassing S vs T). In practice, add (1/6) to the expected wound generation beyond what the normal wound roll would produce for the natural 6 hits. Against targets where S vs T already wounds on 2+, Lethal Hits adds very little (already 83% wound rate for those hits). Against targets requiring 6+, Lethal Hits is dramatically more impactful since it converts a 16.7% wound chance on those hits to 100%.
Devastating Wounds
Triggers on an unmodified wound roll of 6. Each natural 6 wound roll becomes a mortal wound equal to the weapon’s Damage characteristic, bypassing armor saves and invulnerable saves (only FNP applies). In math hammer, the natural 6 wound roll outputs are treated separately: they skip the save step and deal damage directly. Against a unit with a strong invulnerable save (e.g., 3++), the proportion of hits that trigger Devastating Wounds becomes significantly more valuable because those wounds bypass the invuln entirely.
Twin-Linked
Allows re-rolls of all wound rolls made with the weapon. This is a powerful ability that specifically targets the wound step bottleneck. For a weapon wounding on 5+ (33.3% base), Twin-Linked raises effective wound rate to: 1 − (2/3)² = 1 − 0.444 = 55.6%. For wounding on 4+ (50%), it raises to: 1 − (1/2)² = 75%. For wounding on 6+ (16.7%), it raises to: 1 − (5/6)² = 30.6%. Twin-Linked is most efficient where the base wound rate is lowest — anti-tank weapons benefit more from it against superheavy targets than anti-infantry weapons against basic troops.
Blast
Sets a minimum Attacks value when targeting units of 5+ models (minimum of the lowest dice result) and a higher minimum when targeting units of 11+ models (typically minimum of the full dice value). For a D6 Attacks Blast weapon, standard expected attacks = 3.5. Against a unit of 5+ models, minimum 3 attacks, average becomes (3+4+5+6)/4 × (4/6) + 3 × (2/6) ≈ 4.5. Against 11+ models, minimum 6 — every roll is at least 6, making expected attacks exactly 6. Always enter the adjusted expected attacks value for Blast weapons when using the calculator against horde targets.
Torrent
Auto-hits — no hit roll required. All attacks automatically hit, treating the hit probability as 100% regardless of BS or to-hit modifiers. Torrent weapons completely bypass the hit roll step, which means to-hit penalties (like Indirect Fire or shrouding) have no effect on them, and Overwatch (shooting at -1 to hit in the opponent’s turn) is irrelevant. Torrent is extremely efficient for clearing light infantry where volume of hits matters more than individual weapon quality, but the auto-hit advantage is negated if the weapon has low Strength or damage output.
Sustained Hits and Lethal Hits both trigger on natural 6 hit rolls. A weapon with both abilities generates both an extra hit AND an auto-wound from a single natural 6. These abilities are not mutually exclusive — the natural 6 produces the extra hit (which still requires a wound roll) and also generates an automatic wound as a separate output. Both are applied when calculating total expected wounds from a weapon with both keywords.
Our Classic WoW Talent Calculator applies the same philosophy — optimizing ability combinations for maximum output — to Blizzard’s legendary MMORPG. And our FFXI Skillchain Calculator helps Final Fantasy XI players chain weaponskills for optimal damage sequencing, a system with structural similarities to the 40K attack sequence.
Re-rolls, Modifiers, and Understanding How They Stack Through the Attack Sequence
Modifiers and re-roll abilities are the force multipliers of the 40K damage system — they do not change the fundamental structure of the attack sequence, but they push probabilities up or down at specific steps in ways that compound significantly through the full sequence. Getting re-roll interactions right in your math hammer is the difference between an accurate expected damage number and one that is subtly off in ways that accumulate to meaningful errors in list-building decisions.
Re-roll categories and their effects
There are several distinct categories of re-roll ability in 40K that each have different mathematical effects. Re-rolling 1s is the most common and least impactful — it adds a small fixed percentage to the probability at that step equal to the original failure rate divided by 6. Re-rolling all failed rolls is the most powerful — it applies the base success probability as a second-chance modifier to all failures. Re-rolling a specific result (e.g., Lethal Hits re-rolling 6s to get more natural 6s — a rare edge case) creates unusual interactions that require case-by-case analysis.
Re-roll 1s at hit step (BS 3+):
Base hit rate = 4/6 = 0.667 | 1s to re-roll = 1/6 = 0.167
Re-rolled 1s that now hit = 0.167 × 0.667 = 0.111 | New total hit rate = 0.667 + 0.111 = 0.778 (≈ 7/9)
Re-roll all failed hits (BS 3+):
Failures = 2/6 = 0.333 | Re-rolled failures that now hit = 0.333 × 0.667 = 0.222
New total hit rate = 0.667 + 0.222 = 0.889 (≈ 8/9)
An important rule in 10th Edition is that to-hit and to-wound modifiers cap at -1 or +1 — a unit cannot be at -2 or worse to hit regardless of how many penalty sources stack. This significantly changes the math for certain defensive abilities that apply to-hit penalties, as the second and third stacking penalties do nothing. When calculating expected hits against a unit with a to-hit penalty, apply -1 to the BS value (e.g., 3+ becomes 4+) and stop — do not apply further penalties even if multiple sources exist.
Modifiers to wound rolls work identically — the to-wound modifier cap also applies, capping at +1 or -1. A weapon with a built-in -1 to-wound and a character ability adding another -1 to-wound against a specific target type would only apply -1 total in 10th Edition. For older edition veterans transitioning to 10th: this is a significant rules change from previous editions where modifier stacking had a more liberal cap.
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Worked Examples: Full Damage Calculations for Real Units and Weapons
Nothing makes the attack sequence click like watching it applied to real numbers from actual unit datasheets. The following worked examples cover common matchups that come up regularly in games and list-building discussions, walking through every step of the calculation so you can follow the arithmetic and apply the same process to any other combination you need to evaluate. All profiles reflect 10th Edition standard values.
Example 1: Intercessors shooting at Chaos Space Marines
Weapon: Auto Bolt Rifle — A2, BS 3+, S4, AP -1, D1
Target: Chaos Space Marine — T4, Sv 3+
Calculation per model (2 attacks):
Attacks = 2 | Hit% (BS 3+) = 0.667 | Wound% (S4 vs T4 = 4+) = 0.500
Save% (3+ save with AP-1 = 4+ save) = 0.500 | Damage = 1
Expected Damage = 2 × 0.667 × 0.500 × (1 − 0.500) × 1 = 2 × 0.667 × 0.500 × 0.500 = 0.333
One Intercessor deals 0.333 expected damage per activation. A squad of 5 deals 1.67 expected damage.
Expected kills against CSM (2W each): 1.67 ÷ 2 = 0.83 kills per squad activation.
Example 2: Lascannon against a Predator tank
Weapon: Lascannon — A1, BS 3+, S12, AP -3, D D6+1 (avg 4.5)
Target: Predator Destructor — T9, Sv 3+ (no invuln)
Attacks = 1 | Hit% = 0.667 | Wound% (S12 vs T9: S > T but not double, so 3+) = 0.667
Save% (3+ save with AP-3 = 6+ save) = 0.167 | Damage (avg) = 4.5
Expected Damage = 1 × 0.667 × 0.667 × (1 − 0.167) × 4.5 = 0.667 × 0.667 × 0.833 × 4.5 = 1.668
One Lascannon shot deals ~1.67 expected damage per activation against a Predator.
Example 3: Terminator squad with Assault Cannons vs. Intercessors
Weapon: Assault Cannon — A6, BS 2+, S6, AP -1, D1, Sustained Hits 1
Target: Space Marine Intercessors — T4, Sv 3+, W2
Base Hit% (BS 2+) = 0.833 | Sustained Hits 1 adds: 0.167 × 1 = 0.167 extra hits per attack
Effective Hit% per attack = 0.833 + 0.167 = 1.000 expected hits per attack (average, not capped)
6 Attacks × 1.000 expected hits = 6.00 expected hits
Wound% (S6 vs T4: S > T, 3+) = 0.667 | Save% (3+ with AP-1 = 4+) = 0.500
Expected unsaved wounds = 6.00 × 0.667 × (1 − 0.500) = 6.00 × 0.667 × 0.500 = 2.00
Expected Damage = 2.00 × 1 = 2.00 damage | Against 2W Intercessors: 1 kill per activation
Example 4: Plague Marines with Devastating Wounds vs a character with 4++ invuln
Weapon: Plague Knife — A2, WS 3+, S4, AP 0, D1, Devastating Wounds
Target: Character — T4, Sv 3+, Invuln 4++, W4
Attacks = 2 | Hit% (WS 3+) = 0.667 | Expected Hits = 2 × 0.667 = 1.333
Of those hits: Wound rolls at S4 vs T4 (4+) = 0.500 probability per hit
— Of wound rolls: 5/6 are normal wounds (not natural 6) | 1/6 are Devastating Wounds (natural 6)
Normal wounds: 1.333 × 0.500 × (5/6) = 0.556 | After 4++ invuln save (50% blocked): 0.278 unsaved
Devastating wounds: 1.333 × 0.500 × (1/6) = 0.111 | Bypass invuln, straight to damage = 0.111
Total expected damage = (0.278 + 0.111) × 1 = 0.389 expected damage per activation
The Devastating Wounds component (0.111) represents 28.5% of total output despite being 1/6 of wounds.
Against targets without invuln, Devastating Wounds contributes proportionally less since saves are worse.
Using the 40K Damage Calculator for Army List Building and Meta Analysis
The damage calculator earns its keep most dramatically not in individual game moments but during the weeks you spend staring at Battlescribe, army builder apps, and spreadsheets trying to decide whether your list has the right mix of tools for the meta you expect to face. This is where math hammer transitions from academic exercise to practical competitive advantage — and where the discipline of calculating before you buy, build, and paint pays dividends in both performance and satisfaction.
The core army-building question that the damage calculator answers is efficiency: how much expected damage does each unit produce against a standard target profile, divided by its point cost? This “damage per point” metric is the fundamental tool for comparing options at the same role. A unit that produces 4.2 expected damage against T4 3+ saves per activation for 90 points is more efficient than a unit producing 3.8 expected damage for 95 points, and significantly more efficient than one producing 3.2 expected damage for 85 points even though the absolute price is lower. Without the calculator, these comparisons are based on feel and reputation rather than numbers.
Identify your target categories. Most metas require efficient tools against at least three distinct target types: light infantry (T3-4, poor saves), armored infantry (T4-5, 3+ or 2+ saves), and vehicles/monsters (T9-12, varied saves). Build the calculator profile for each of these “standard targets” and run every major weapon in your consideration set against them. The relative rankings of weapons against each target type reveal what roles your list is covering well and where it has gaps.
Compare damage per point, not raw output. A Hellblaster squad at 105 points producing 5.6 expected damage against Marines per activation is worse value than an equivalent option producing 4.8 expected damage for 75 points. Always divide expected damage output by the unit’s point cost for the meaningful comparison metric. Sort your options by this ratio and your list optimization choices become much clearer.
Model for your local meta, not the theoretical average. If your local scene runs heavy on Necron vehicles and Custodes infantry, the damage profiles you optimize for should reflect those specific targets — not an abstract average. Use the calculator to model expected output specifically against the units you face most often and weight your list choices accordingly. This is how competitive players tailor their builds to specific tournament environments.
Account for volume versus spike damage. Two units with the same expected damage can have radically different variance profiles. A unit making 20 Damage 1 attacks has much lower variance than a unit making 3 Damage D6+2 attacks. Against targets with exactly 3 wounds remaining on a key piece, high-variance Damage D6 weapons are actually better than their average output suggests — the spike potential creates kill shots that low-variance weapons cannot guarantee. Use the calculator for averages but think about variance separately when target priority matters.
Test your army’s output across multiple activations. A unit producing 1.5 expected kills per activation sounds strong, but if it costs 200 points and can only fire for 3 turns before being killed, its total game output is roughly 4.5 kills — for 200 points. Compare this to a 100-point unit producing 0.8 kills per activation but surviving 5 turns for 4.0 total kills. Survivability multiplies output over the length of the game, making durability calculations (the mirror image of damage calculations) equally important for list efficiency.
For breeding and inheritance optimization in other games, try the Palworld Breeding Calculator and the Uma Musume Inheritance Calculator. For Diamond Dynasty MLB The Show XP tracking, use our Diamond Dynasty PXP Calculator. All free at WalDev Gaming Calculators.
Variance vs Expected Value: What the Numbers Don’t Tell You
Expected value is the backbone of math hammer. But variance — the statistical measure of how widely outcomes spread around that average — is the factor that experienced players understand implicitly and beginners consistently overlook. Two weapon profiles with identical expected damage can play completely differently in practice because of their variance, and this difference matters enormously in specific game situations.
Low-variance weapons — those with flat Damage values, many small attacks, and high base accuracy — produce consistent, predictable output. They reliably deliver close to their expected value in most activations. High-variance weapons — those with variable Damage (D3, D6, D6+2), few attacks, or unusual trigger-dependent abilities — can dramatically over- or under-perform their expected value in any individual activation. The expected values are identical in isolation, but they behave differently in practice.
When high variance is actually good
High-variance weapons are preferable in situations where you need to guarantee a kill against a specific high-value target in a single activation. If an enemy warlord has 5 wounds remaining and you need to remove them this turn to complete an objective, a high-damage weapon with a spike potential of 8+ damage per successful hit is more likely to achieve the kill in a single activation than a flat-damage weapon that averages exactly 5 damage per activation — the flat weapon needs to hit its average exactly, while the high-variance weapon can spike over the threshold. This is the probabilistic argument for why D6 Damage weapons remain useful despite their inconsistency.
When low variance is mandatory
Tournament play over multiple games strongly rewards low-variance builds. A build that consistently produces 80% of its theoretical maximum damage output every game outperforms a build that produces 130% in some games and 50% in others over a 5-game tournament, even if the expected value is identical. Variance means some games will feel impossibly unlucky — and in a 5-round tournament, that “unlucky” game is statistically likely to occur. Flat damage, high attack volume, and consistent hit/wound probabilities reduce the risk of a blowout loss due to dice variance rather than play quality.
The community-created Stat Check resource provides advanced statistical analysis of 40K army and mission data, including distribution modeling that goes beyond expected value to show the full probability curve of outcomes — exactly the kind of variance analysis that complements standard math hammer.
AnyDice is a powerful online dice probability calculator that allows players to model custom dice expressions — useful for visualizing the full distribution of variable-damage weapon outputs (D3, D6, D6+1) to understand both expected values and variance in full detail.
Meta Efficiency, Point Costs, and the Real-World Context of Damage Calculations
All of the mathematics discussed in this guide feeds into the most practical question in competitive 40K: given a fixed point budget, what combination of units and weapons produces the best outcome against the armies I expect to face? This question is what separates list theory from list reality, and it requires combining math hammer outputs with meta knowledge in a way that the calculator assists but cannot replace.
Points costs in 40K are Games Workshop’s attempt to balance expected damage output, durability, mobility, and utility into a single price. They are imperfect and famously fluid — each points update adjusts prices up and down based on competitive performance data, attempting to keep the game balanced across the diversity of factions and build styles. A unit that appears efficient on paper may be overcosted for its actual competitive output, or it may be undercosted (a “broken” unit in meta parlance) and worth taking even in suboptimal configurations because the raw math makes it perform above its price point.
The way to use math hammer in this context is not to simply pick the unit with the highest damage-per-point calculation in isolation, but to build a list where the damage profile of the whole army addresses the entire target landscape efficiently. Pure anti-tank builds underperform when the opponent brings hordes. Pure anti-infantry builds cannot crack vehicles. The art of competitive list-building is assembling a set of damage profiles that collectively cover all target categories at reasonable efficiency while also satisfying the survivability, mobility, and objective-play requirements of the missions being played.
Following live meta data is essential context that math hammer alone cannot provide. Top-performing army lists at major tournaments reflect the combined wisdom of thousands of player-hours of testing across the specific target matchups and mission profiles of the current competitive season. Using our 40K Damage Calculator to understand why those top lists are structured the way they are — which weapons they are optimized around, which targets they prioritize, how their damage profiles complement each other — is how you move from following a copied list to building and adapting one with genuine understanding. For more gaming tools across different systems, our complete gaming calculators suite covers everything from Blox Fruits progression to Black Ops 6 puzzle solving.
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25-Question 40K Damage Calculator Master FAQ
How does the Warhammer 40K attack sequence work?
The attack sequence has five steps: (1) Hit Roll — roll dice equal to your Attacks characteristic, succeeding on your BS or WS value; (2) Wound Roll — roll for each hit using the Strength vs. Toughness table; (3) Allocate Attack — defender assigns each wound to a model; (4) Saving Throw — defender rolls their Save characteristic, modified by the weapon’s AP; (5) Inflict Damage — each unsaved wound deals damage equal to the weapon’s Damage characteristic. FNP applies after step 5 if the model has it. The full expected damage formula is: Attacks × Hit% × Wound% × (1 − Save%) × (1 − FNP%) × Damage.
What is the wound roll table in 40K?
The wound table compares attacker’s Strength (S) to defender’s Toughness (T): S ≥ 2×T = wound on 2+; S > T = wound on 3+; S = T = wound on 4+; S < T = wound on 5+; S ≤ T/2 = wound on 6+. A natural 1 always fails; a natural 6 always wounds at the base level before other modifiers. This table applies to both shooting and melee attacks identically.
What does AP mean in Warhammer 40K?
AP (Armour Penetration) is subtracted from the defender’s Save characteristic roll. AP -1 forces a 3+ save to 4+; AP -2 to 5+; AP -3 to 6+; AP -4 or worse means the armor save cannot be used and only invulnerable saves apply. Higher AP values make armor saves harder to pass, increasing damage throughput against well-armored targets. AP never affects invulnerable saves.
What is Feel No Pain (FNP) in 40K?
Feel No Pain gives a final chance to negate each individual damage point after a failed save. When a model with FNP 5+ suffers damage, roll one die per damage point — on a 5 or 6, that specific damage point is negated. FNP also applies to mortal wounds and to damage from all sources. It is the only defense against mortal wounds since saves do not apply to them.
How do you calculate expected hits in 40K?
Expected hits = Number of Attacks × Hit Probability. BS/WS 2+ = 83.3%, BS/WS 3+ = 66.7%, BS/WS 4+ = 50%, BS/WS 5+ = 33.3%, BS/WS 6+ = 16.7%. For Sustained Hits X weapons, add (1/6 × X) to the hit probability per attack. For Torrent weapons, hit probability is 100%. Enter these values into the 40K Damage Calculator to automate the full sequence.
What is ‘math hammer’ in Warhammer 40K?
Math hammer is the practice of calculating statistically expected dice outcomes in 40K to determine average hits, wounds, and damage output. It is used for list-building, weapon comparison, target efficiency analysis, and tactical planning. It calculates the average over infinite repetitions — real games will vary around this average, but players who understand expected values make better decisions over time. The 40K Damage Calculator automates math hammer for any weapon and target combination.
What are Sustained Hits in 10th edition?
Sustained Hits X triggers on an unmodified hit roll of 6, generating X additional hits beyond the initial hit. With Sustained Hits 1, a natural 6 produces 2 hits total. In math hammer, Sustained Hits adds (1/6 × X) to the expected hits per attack. A BS 3+ weapon with Sustained Hits 1 has an effective expected hit rate of 0.667 + 0.167 = 0.833 per attack — equivalent to a BS 2+ rate.
What are Lethal Hits in 10th edition?
Lethal Hits triggers on an unmodified hit roll of 6, causing that hit to automatically wound without a wound roll — bypassing the Strength vs. Toughness table entirely. This is most valuable against high-Toughness targets where the wound roll is the primary bottleneck (5+ or 6+ wounds), and least impactful against easy targets where you already wound on 2+ or 3+.
What are Devastating Wounds in 10th edition?
Devastating Wounds triggers on an unmodified wound roll of 6, converting that wound into a mortal wound equal to the weapon’s Damage value. This mortal wound bypasses armor saves and invulnerable saves — only Feel No Pain applies. Devastating Wounds is most valuable against targets with strong invulnerable saves (3++ or 4++), where it converts a fraction of wound output into save-bypassing damage.
How does an invulnerable save differ from an armor save?
Armor saves are worsened by AP — AP -1 forces a 3+ save to 4+. Invulnerable saves are completely unaffected by AP — a 4++ invulnerable save is always rolled on 4+ regardless of AP value. When a model has both, they use whichever gives the better (lower number) result for any specific weapon’s AP. Invulnerable saves are typically found on elite infantry, daemons, and characters.
How do mortal wounds work in 40K?
Mortal wounds bypass the entire attack sequence — hit rolls, wound rolls, and saving throws do not apply. Each mortal wound deals one damage point directly to the target (or the weapon’s Damage characteristic if from Devastating Wounds). Feel No Pain can still negate individual mortal wound damage points. This makes mortal wounds particularly dangerous against high-save targets like Terminators with 2+ armor and 5+ invulnerable saves.
What is the difference between BS and WS?
BS (Ballistic Skill) is the hit probability for ranged attacks. WS (Weapon Skill) is the hit probability for melee attacks. Both work identically in the dice mechanics — the minimum required roll to score a hit. The distinction exists purely to separate ranged and melee combat contexts, as some abilities specifically affect BS attacks or WS attacks and not both.
How do re-rolls affect expected damage output?
Re-rolling 1s on a 3+ hit adds approximately 11% more hits (1/6 of 2/3 failures). Re-rolling all failed hits on 3+ adds approximately 22% more hits. Re-rolls compound through the sequence — more hits produce more wound rolls, more failed saves, and more damage. At each subsequent step, the extra hits from re-rolls generate further amplification, making hit re-rolls particularly powerful as they affect the earliest and therefore most consequential step.
Does cover affect damage calculations in 40K 10th Edition?
Cover improves a unit’s armor save by 1 against ranged attacks, but only if the AP value has not already reduced the save below the printed armor value. A 3+ save model in cover against AP -1 goes back to a 3+. Against AP -3 (save at 6+), cover does not help — the AP has already pushed the save past the threshold where a +1 improvement matters. Cover never applies to melee attacks or mortal wounds.
What is the most efficient way to kill Space Marines in 40K?
Standard Space Marines (T4, Sv 3+, 2W) are most efficiently killed with weapons offering Strength 4-5 (wounding on 3+), AP -1 or -2 (forcing 4+ or 5+ saves), and Damage 2 (killing in one unsaved wound). Weapons with Sustained Hits or Lethal Hits further improve efficiency. Massed Damage 1 shooting at AP 0 underperforms because the 3+ save blocks two-thirds of wounds, while AP -2 Damage 2 weapons bypass saves more often and kill in one hit when they get through.
How does Damage 2 vs Damage 1 affect kills against multi-wound models?
Against 2-wound models, Damage 2 weapons kill in one unsaved wound while Damage 1 requires two — making Damage 2 twice as efficient per unsaved wound at removing 2W models. This efficiency multiplies against higher-wound targets. Damage D3 and D6 create variable kill rates that may or may not reach the damage threshold in a single unsaved wound, adding variance to the calculation that flat Damage values avoid.
How do blast weapons work in damage calculations?
Blast weapons set a minimum attack count when targeting units of 5 or more models. A D6 Blast weapon against a unit of 5-10 models has a minimum of 3 attacks; against 11+ models it becomes a minimum of 6 attacks. When using the calculator against horde targets, use the adjusted minimum-attack value for the target unit size rather than the raw average of the variable dice roll to get the correct expected output.
What is the Twin-Linked ability and how does it affect wound calculations?
Twin-Linked allows re-rolling all wound rolls. Against a target requiring a 5+ wound roll (33.3% base), Twin-Linked raises effective wound rate to 55.6% — a 1.69× multiplier. Against a 6+ wound roll (16.7% base), it raises to 30.6% — a 1.83× multiplier. Twin-Linked is most efficient where the base wound roll is hardest, making it particularly valuable for anti-tank weapons used against very high-Toughness targets.
How should I use a damage calculator when building an army list?
Calculate expected damage-per-point for your key weapons against three standard target archetypes: light infantry (T3-4, 5+/6+ save), armored infantry (T4-5, 3+/2+ save), and vehicles (T9-12, 3+ save). Compare units by this efficiency metric rather than raw output. A well-rounded list needs coverage across all three categories or concentrated excellence in one category with enough points to deal with the others through volume or objective play.
What is the difference between expected value and variance in 40K dice rolls?
Expected value is the mathematical average over many repetitions — what math hammer calculates. Variance describes how widely results spread around that average in individual rolls. High-variance weapons (variable Damage D6, few attacks) can dramatically spike over or under their expected output in any single game. Low-variance weapons (flat Damage, many attacks) produce consistent results close to expected value. Both metrics matter: expected value for list efficiency, variance for reliability in competitive play.
How does the Hazardous ability affect a unit’s expected net output?
Hazardous requires rolling one die per model that fired the weapon after use — on an unmodified 1, that model suffers 3 mortal wounds. Each Hazardous model suffers an average of 0.5 mortal wounds per use (1/6 probability × 3 damage). For net efficiency, subtract 0.5 from the effective output per Hazardous model per activation to account for self-inflicted damage — particularly important for expensive character models or elite infantry where 3 mortal wounds represents a significant fraction of total wounds.
How does Indirect Fire affect hit rolls?
Indirect Fire allows targeting units not visible to the firer but imposes -1 to hit against non-visible targets, and the target gains Benefit of Cover regardless of terrain. For math hammer, apply -1 to the BS value for non-visible shots (e.g., BS 3+ becomes effectively 4+ for those shots, dropping from 66.7% to 50% hit rate) and apply cover’s +1 armor save improvement to the target’s save calculation.
Can you use the 40K damage calculator for melee weapons?
Yes — melee weapons use the identical calculation process. Substitute WS in place of BS for the hit roll step and the rest of the sequence is unchanged. All weapon special abilities (AP, Damage, Lethal Hits, Devastating Wounds, Sustained Hits, re-rolls) apply equally to melee profiles. The 40K Damage Calculator handles both ranged and melee profiles using the same input format.
What is the most common mistake beginners make in 40K probability math?
The most common mistake is treating the steps additively rather than multiplicatively. Each step multiplies by the previous result — you cannot add hit probability plus wound probability. The correct formula is: Expected Damage = Attacks × Hit% × Wound% × (1 − Save%) × (1 − FNP%) × Damage. Other common errors include forgetting to apply FNP separately per damage point on multi-damage weapons, and misapplying saves below the 2+ floor (a modified save cannot go below 2+ in practice for models that still have access to an armor save).
Where can I find more gaming calculators for other tabletop and video games?
WalDev offers a full suite of free gaming calculators including the Pokémon Damage Calculator, Pokémon Type Calculator, Classic WoW Talent Calculator, Palworld Breeding Calculator, Blox Fruits Calculator, Blooket Calculator, FFXI Skillchain Calculator, Uma Musume Inheritance Calculator, Uma Musume Race Calculator, Diamond Dynasty PXP Calculator, and the Terminus BO6 Zombies Calculator.
Final Thoughts: Roll More Dice, but Know What They Mean
Warhammer 40K is a game of thousands of dice rolls played out across hundreds of activations over the course of a game — and behind every one of those rolls is a probability that can be calculated, compared, and used to make better decisions. Math hammer will never guarantee a win. The dice will always have their say, and the fog of tactical decision-making will always matter more in the moment than any pre-game calculation. But the player who understands what their dice are supposed to do, who chose their army list with clarity about what each unit is optimized against, and who knows during the game whether their results are running hot or cold relative to expectation — that player has a real edge over one who is guessing.
Use the 40K Damage Calculator before you play, not instead of playing. Use it to answer the questions that come up in list-building — “is this weapon worth it against my meta?”, “which loadout kills Marines more efficiently?”, “why am I not dealing as much damage as I think I should be?” — and then take that knowledge to the table. The numbers are there to make you a better player. The dice are there to keep it interesting. Both are indispensable. For more tools to sharpen your game across the full breadth of tabletop and video gaming, explore the complete WalDev Gaming Calculator Suite.
