Critical Hit Damage Calculator
Critical hits are a core mechanic in tabletop and video game combat systems. This calculator finds the average (expected) damage per attack when a character has a chance to deal amplified critical hit damage. Enter your base damage, critical hit chance, and critical hit multiplier. The formula weights normal hits and critical hits by their respective probabilities to give the true average, which is essential for comparing builds, balancing encounters, and optimizing character stats.
Critical hit damage formula
Avg damage = (1 - c) * d + c * m * d
= d * (1 + c * (m - 1))
where c = crit chance, d = base damage, m = crit multiplier
The first term is the normal-hit contribution and the second is the critical-hit contribution. Both are weighted by their probability, then summed for the overall average.
Critical hits in game balance
- At 20% crit chance with 2x multiplier, average damage increases by 20% over base, making crit and flat damage bonuses equal in this example.
- High crit chance with low multiplier (e.g. 50% at 1.5x) produces the same average as lower crit chance with higher multiplier (25% at 2x), both giving 25% over base.
- Game designers often cap crit chance below 100% to preserve the randomness that keeps combat exciting.
- Variance from crits can be smoothed by adding diminishing returns on crit chance at high values.
Critical hit damage: frequently asked questions
What is the average damage formula with critical hits?
Average damage per hit = (1 - c) * d + c * m * d, where c is the critical hit chance (as a decimal), d is base damage, and m is the critical hit multiplier. This simplifies to d * (1 + c * (m - 1)).
How does critical hit chance affect DPS?
Higher crit chance linearly increases average damage. Going from 10% to 20% crit chance at 2x multiplier adds 10% more average damage, the same as increasing base damage by 10%. The multiplier scales the benefit of crit chance.
What is a typical critical hit multiplier in RPGs?
Many RPGs use 2x as the default critical hit multiplier. Some systems use 1.5x for low-impact crits or 3x and higher for powerful builds. The calculator accepts any multiplier.
How do I use this for DPS calculations?
First find your average damage per hit using this calculator, then multiply by attacks per second or divide attack time into one second. The DPS calculator also handles this directly.
Does this account for armor or damage reduction?
No. This calculator computes raw average damage before any mitigation. Apply armor reduction separately after finding average damage, or use the Armor Damage Mitigation Calculator.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: itl.nist.gov/div898/handbook/.
- National Council of Teachers of Mathematics: nctm.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.