Damage reduction stacking calculator

What this calculator does

Three sources of 30 per cent damage reduction do not give 90 per cent. They give 65.7, because the second applies to what the first left behind and the third to what the second left. Reductions that stack multiplicatively can never reach 100 per cent, however many you collect.

There is a second and more useful consequence that almost nobody notices. In effective health terms, every additional source is worth exactly the same as the first. A 10 per cent reduction always multiplies your survivability by 1 ÷ 0.9, which is 11.1 per cent more, whether it is your only source or your tenth.

The formula

Formulatotal reduction = 1 − (1 − r₁)(1 − r₂)…(1 − rₙ), so each source applies to what is left rather than to the original damage

Each source leaves 1 − r of the damage behind, so several together leave the product of all those terms. Total reduction is 1 − (1 − r₁)(1 − r₂)…. Effective health is the reciprocal of what gets through, so multiplying the survival fraction by a constant multiplies effective health by the same constant every time. That is why the percentage looks like it is suffering diminishing returns while your actual survivability is not.

Term	Meaning
Multiplicative stacking	Each source applies to the damage remaining after the previous one. The usual design.
Additive stacking	Sources added together before being applied. Rarer, and it allows immunity.
Damage taken	The product of all the leftover fractions. The number that actually hits you.
Effective HP multiplier	One divided by damage taken. How much raw damage you can now absorb.

The inputs explained

Field	What to enter
Reductions, separated by commas	Your reduction sources as percentages, separated by commas. Order does not matter, because multiplication does not care.
One more source worth (%)	A further source you are considering, used to show what it would add.

When to use it

Checking whether another resistance is worth a slot

The effective HP figure is the one to compare, not the percentage. Adding 10 per cent always buys 11.1 per cent more survivability, so the question is only whether the slot could hold something better.

Spotting an additive system

If your game lets reductions reach exactly 100 per cent, or if two 50 per cent sources make you immune, it stacks additively and this calculator does not describe it. Multiplicative systems approach 100 without ever arriving.

Reading a tooltip honestly

A tooltip offering 20 per cent reduction is not offering 20 per cent of your current damage taken unless it is your only source. With 60 per cent already, it removes 20 per cent of the remaining 40, which is 8 points of total reduction and still 25 per cent more effective health.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

What do several 30 per cent reductions actually give?

Each row adds one more 30 per cent source.

Identical sources stacked one at a time

Sources	Total damage reduction	Effective HP multiplier	If the sources were simply added
none	0.000%	1.000×	0.000%
1 × 30%	30.0%	1.429×	30.0%
2 × 30%	51.0%	2.041×	60.0%
3 × 30%	65.7%	2.915×	90.0%
4 × 30%	76.0%	4.165×	120.0%
5 × 30%	83.2%	5.950×	150.0%

One source gives 30 per cent, two give 51, three give 65.7, four 76.0 and five 83.2. The naive sum reaches 150 per cent by the fifth, which would be nonsense. Look instead at the effective HP column: it goes 1.429, 2.041, 2.915, 4.165, 5.950, multiplying by the same 1.429 every single time. The percentage slows down and the survivability does not.

How close to immunity can you get?

Different mixes, from one large source to several.

Larger single sources and combinations

Sources	Total damage reduction	Damage you still take	Effective HP multiplier
50	50.0%	50.0%	2.000×
50, 50	75.0%	25.0%	4.000×
50, 50, 50	87.5%	12.5%	8.000×
80, 50	90.0%	10.00%	10.000×
90, 90	99.0%	1.000%	100.000×
99, 99	100.0%	0.010%	10,000.000×

Two 50 per cent sources give 75 per cent and four times the effective health, not immunity. Three give 87.5 and eight times. Two 90 per cent sources reach 99 per cent and a hundred times the effective health. Two 99 per cent sources leave just 0.01 per cent of the damage, which the reduction column rounds to 100 per cent while the effective health reports it honestly as ten thousand times. The total creeps towards 100 and never arrives, the effective health has no ceiling, and that is exactly why the second column is the one to read.

Questions

Why can multiplicative reduction never reach 100 per cent?

Because each term multiplies the survival fraction by something above zero, and a product of positive numbers is positive. Only a source of exactly 100 per cent can make it zero.

Does the order of my sources matter?

No. Multiplication is commutative, so any order gives the same answer. Games sometimes apply them in a fixed order for display purposes, but the result is identical.

Why does the effective HP gain never shrink?

Because effective health is the reciprocal of the damage you take, and each source multiplies that by a constant. Multiplying by 0.9 repeatedly always adds the same 11.1 per cent to survivability, however many times you have done it.

How is this different from an armour rating?

An armour rating has to be converted to a percentage first, usually through a curve like armour divided by armour plus a constant. The effective HP calculator does that conversion; this page takes percentages that are already worked out.

What about damage amplification?

Enter it as a negative is not supported here, but the principle reverses cleanly: amplifications multiply the damage taken rather than the fraction left, and they cancel reductions exactly when the multipliers are reciprocals.

For turning an armour rating into a reduction in the first place, see effective HP from armour, and the piece on diminishing returns explains why the tooltip and the survivability disagree. The attacking side is on the DPS calculator.