Gaming math lab · Combat · Original calculator
Critical hit expected damage calculator
On this page
Expected hit damage equals normal damage multiplied by one plus critical chance times the extra critical multiplier. Expected damage is an average, not a guaranteed hit.
Generic mathematical model, not a named game’s simulator. All starting values are invented examples. Supply verified values for your game and check the assumptions below.
Your scenario
Formula and units
Mean hit = D × [1 + p × (M − 1)]. Total mean = n × mean hit. Total standard deviation = D × (M − 1) × √[n × p × (1 − p)]. P(at least one critical) = 1 − (1 − p)^n.
Worked example
For 100 normal damage, 25% critical chance and a 2× total multiplier, the expected hit is 125 damage. Ten independent hits average 1,250 total damage across repeated sequences. They do not guarantee that exact outcome. At least one critical has probability 1 − 0.75^10, approximately 94.37%.
How to use this comparison
Use the full critical multiplier: a critical that deals twice normal damage is 2, not 1 or 200. Compare chance and multiplier changes separately. Keep normal damage fixed if you want to isolate the effect of a critical-stat change.
Read the result correctly
The standard deviation describes spread around the total mean under this model. It is not an interval that guarantees an outcome. If the target needs a precise burst threshold, expected damage alone is insufficient; the normal and all-critical bounds show how wide the possible range can be.
Model boundaries
Critical events are independent with a constant chance and a single multiplier. There is no pseudo-random distribution, critical cap, guaranteed critical after a streak, target resistance or different critical scaling for separate damage components.
Method: original arithmetic implementation and editorial examples reviewed October 16, 2026. Outputs follow the displayed formula and your inputs. We have not tested these mechanics inside a particular game.