Damage Reduction Stacking Calculator

How this is calculated

REDUCTIONS MULTIPLY, THEY DO NOT ADD, and that is the whole brick. Each source removes a share of what is LEFT after the previous ones, not a share of the original. So 30% and 20% leaves 0.7 x 0.8 = 0.56 of the damage getting through, which is 44% reduction rather than 50%. Add three or four sources and the gap between the real figure and the sum grows quickly. THE MATHS IS ONE LINE: multiply what gets THROUGH each source and subtract from one. Reduction = 1 − (1−a)(1−b)(1−c)(1−d). Working in what gets through rather than what is stopped is the trick that makes it obvious, and it is worth doing in your head that way. WHY THIS MATTERS MORE AS YOU STACK: each further source is worth less in percentage POINTS than the one before, because it only acts on the shrinking remainder. A 10% source added to nothing gives 10 points. The same 10% source added on top of 52% gives under 5. That is not diminishing returns in the usual sense - see below - but it is why the naive sum drifts further from reality with every source you add. ⚠️ AND YET EACH SOURCE IS WORTH THE SAME IN SURVIVABILITY. This is the part that trips people up in the opposite direction. A 10% reduction always multiplies your effective health by 1 ÷ 0.9, about 1.11, no matter how much reduction you already have. So it looks weaker in percentage points and is exactly as valuable in hits survived. Judge reduction by effective health, not by the points on the tooltip - the Effective Health Calculator on this site takes the combined figure from here and does that half. ⚠️ NOT EVERY GAME STACKS MULTIPLICATIVELY. Most do, and multiplicative is the safe default assumption, but some add sources within a category before applying them, some apply a hard cap, and some treat armour and resistance on entirely different curves. Your game's own documentation or community testing is the authority. This tool assumes clean multiplicative stacking and says so rather than pretending to know your title. ENTER ZERO FOR SOURCES YOU DO NOT HAVE. A zero source multiplies by one and changes nothing, so unused fields are harmless. A SOURCE AT 100% ENDS THE CALCULATION - nothing gets through and further sources are irrelevant. That is arithmetically correct and almost always means you have entered something wrong, since few games permit total immunity from a stackable source.

Common questions

Why don't reductions just add up?

Because each source acts on what is LEFT after the ones before it, not on the original damage. A 30% reduction lets 70% through; a 20% reduction then takes a fifth of that 70%, not a fifth of the original. So you are left with 0.7 x 0.8 = 0.56 getting through, which is 44% reduction rather than the 50% adding them would suggest. The easy way to do it in your head is to work in what gets THROUGH rather than what is stopped - multiply those together and subtract from one at the end.

So is stacking reduction a waste of time?

No, and this is where people over-correct. Each further source does add fewer percentage POINTS than the last, because it only acts on the shrinking remainder - but it multiplies your effective health by exactly the same amount regardless. A 10% source always makes you take 90% of the damage you otherwise would, which is 1 divided by 0.9, about 11% more effective health, whether you had no reduction or 52% already. It looks weaker on the tooltip and is worth precisely as much in hits survived. Judge it by effective health, never by the points.

How is this different from an effective health calculator?

They chain rather than compete. This one turns several reduction sources into one honest figure; an effective health calculator turns one reduction figure into hits survived and how far your health bar really goes. So the output here is the input there - work out your combined reduction with this, then take that number to the Effective Health Calculator on this site. Splitting them keeps each tool doing one job properly, and it is why this one deliberately does not report effective health itself.

Does every game stack this way?

Most do, and multiplicative is the safe default assumption, but not all. Some games add sources within a category before applying the category as a whole, some apply a hard cap on total reduction, and some put armour and elemental resistance on entirely different curves that do not interact the way you would expect. Your game's own documentation or careful community testing is the authority. This tool assumes clean multiplicative stacking and states that plainly rather than pretending to know your title's rules.

What if I only have two sources?

Leave the others at zero. A zero source multiplies by one and changes nothing at all, so unused fields are completely harmless and you do not need to work around them. That is also worth knowing when you are evaluating an item that grants a reduction you already have from elsewhere: entering it as a separate source shows you exactly what the second copy is worth, which is usually a good deal less than the first and is the honest way to compare it against an item offering something else entirely.

Why does 100% in one source break everything?

Because nothing gets through, so every other source has nothing left to act on and the combined figure is 100% regardless of what else you enter. That is arithmetically correct rather than a bug, and it is almost always a sign that something has been entered wrong - very few games permit total immunity from a stackable percentage source, and the ones that do usually make it a brief effect rather than a stat. If you genuinely have a 100% source active, nothing else about your defences matters while it lasts.

Should I stack reduction or health?

They multiply together too, which means the answer is usually whichever you have less of. Effective health is your health multiplied by 1 divided by the share getting through, so doubling your health and halving the damage you take are worth exactly the same. In practice that makes the cheaper option the better one at any given moment, and it is why builds that stack only one of the two tend to lose to builds that keep both moving. Working out your combined reduction is the first step in making that comparison honestly.

Take it further with AI

Copy this into ChatGPT or Claude with your own numbers filled in. It hands over the figures this calculator worked out, so the answer is built on real arithmetic instead of a guess.

I used the Damage Reduction Stacking Calculator at https://www.bfcbrilliance.com/tools/damage-reduction-stacking-calculator.

What I entered:
- Reduction source 1 (%): ___
- Reduction source 2 (%): ___
- Reduction source 3 (%): ___
- Reduction source 4 (%): ___
- A further source you are considering (%): ___

What it calculated:
- Your real combined reduction: ___
- What adding them up would say: ___
- How far the naive sum overstates it: ___
- Share of damage that still gets through: ___
- Points the further source would add: ___

Use those figures as given — they are already worked out, so please don't recalculate or estimate your own. Help me turn them into a plan: what to buy or do, in what order, roughly what it should cost, and the mistakes people most often make with this job.

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