DPS calculator (damage per second)

What is a DPS calculator?

DPS stands for damage per second — the single number players use to compare weapons, builds, and skill rotations in role-playing games, shooters, MMOs, and roguelikes. A weapon that hits hard but swings slowly can easily lose to a weaker weapon that swings twice as often, and a big critical hit multiplier is worth very little if crits almost never happen. DPS folds all of those factors into one figure so the comparison becomes a single arithmetic question instead of a debate.

This calculator is deliberately game-agnostic. It contains no weapon tables, no class data, and no numbers from any particular title — you type in the stats your own game shows you, and it does the averaging. That means it works just as well for a spreadsheet build in an MMO, a modded sandbox, a tabletop damage estimate, or a game you are designing yourself.

How does the calculator work?

You supply up to five stats and it returns three results.

The inputs are:

• Average damage per hit — the damage a normal, non-critical hit deals. If your weapon rolls a damage range, use the midpoint.
• Attacks per second — how many times the weapon connects each second. If your game shows an attack interval instead (say, one swing every 0.8 seconds), take its reciprocal: $1 / 0.8 = 1.25$ attacks per second.
• Critical hit chance — the percentage of hits that crit. Defaults to 0%.
• Critical hit damage multiplier — how much damage a crit deals relative to a normal hit. A value of 2 means a crit hits for double. Defaults to 2.
• Accuracy (hit chance) — the percentage of attack attempts that actually land. Defaults to 100%, i.e. nothing ever misses.

The results are:

• Average damage per hit (with crits) — what a landed hit deals on average once crits are blended in.
• Effective damage per hit — the same figure after misses are accounted for. This is the damage you get per attack attempt, not per landing hit.
• DPS — the effective damage multiplied by your attack rate.

Everything the calculator produces is a long-run average. Any individual swing either crits or does not, hits or misses; the maths describes what happens over many attacks, which is exactly what matters when you are choosing between two weapons.

Formulas

Write $D$ for the base damage of a normal hit, $c$ for the critical hit chance in percent, $m$ for the critical damage multiplier, $a$ for the accuracy in percent, and $s$ for attacks per second.

A critical hit deals $m$ times normal damage, so it adds $(m - 1)$ extra hits’ worth of damage — but only on the $c/100$ fraction of hits that actually crit. Averaging that bonus over all hits gives:

$$D_{\text{hit}} = D \times \left(1 + \frac{c}{100} \times (m - 1)\right)$$

Misses deal nothing, so scaling by accuracy gives the damage per attack attempt:

$$D_{\text{eff}} = D_{\text{hit}} \times \frac{a}{100}$$

And multiplying by the attack rate turns damage-per-attack into damage-per-second:

$$\text{DPS} = D_{\text{eff}} \times s$$

Put together, the whole thing is one expression:

$$\text{DPS} = D \times \left(1 + \frac{c}{100} \times (m - 1)\right) \times \frac{a}{100} \times s$$

Note what the crit term does at its extremes. At $c = 0$ the bracket collapses to 1 and the multiplier is irrelevant — a huge crit multiplier on a weapon that never crits is worth exactly nothing. At $c = 100$ the bracket becomes $m$, because every hit is a crit.

Worked examples

Example 1 — a 25% crit chance at double damage

A weapon deals 100 damage per hit, swings 2 times per second, crits 25% of the time for 2× damage, and never misses (100% accuracy).

$$D_{\text{hit}} = 100 \times \left(1 + \frac{25}{100} \times (2 - 1)\right) = 100 \times 1.25 = 125$$ $$D_{\text{eff}} = 125 \times \frac{100}{100} = 125$$ $$\text{DPS} = 125 \times 2 = 250$$

So the crits are worth a flat 25% damage increase here, and the weapon lands 250 DPS.

Example 2 — the same weapon with no crits at all

Keep everything the same but drop the critical hit chance to 0%:

$$D_{\text{hit}} = 100 \times \left(1 + \frac{0}{100} \times (2 - 1)\right) = 100$$ $$\text{DPS} = 100 \times 2 = 200$$

The weapon now does 200 DPS. Comparing this with Example 1 is the cleanest way to price a crit stat: those 25 percentage points of crit chance were buying 50 DPS.

Example 3 — adding a 10% miss rate

Back to the 25% crit build, but now only 90% of attacks connect:

$$D_{\text{hit}} = 125$$ $$D_{\text{eff}} = 125 \times \frac{90}{100} = 112.5$$ $$\text{DPS} = 112.5 \times 2 = 225$$

Accuracy scales the whole thing linearly, so losing 10% of your attacks costs you exactly 10% of your DPS: 225 DPS instead of 250. Note that the average damage of a landed hit is unchanged at 125 — accuracy never changes how hard a hit lands, only how often one lands.

Example 4 — a slower, heavier weapon

A two-handed weapon deals 250 damage per hit but only attacks 1.5 times per second. It crits 40% of the time for 2.5× damage, and its accuracy is 95%.

$$D_{\text{hit}} = 250 \times \left(1 + \frac{40}{100} \times (2.5 - 1)\right) = 250 \times 1.6 = 400$$ $$D_{\text{eff}} = 400 \times \frac{95}{100} = 380$$ $$\text{DPS} = 380 \times 1.5 = 570$$

570 DPS — comfortably ahead of the fast weapon in Example 1, even though it swings less often, because its per-hit damage and crit stats are so much higher.

Practical notes

• Attack speed vs. attack interval. Games express this in both directions. If yours quotes seconds between attacks, invert it before typing it in — a 0.5-second interval is 2 attacks per second.
• Damage ranges. When a weapon rolls between a minimum and a maximum, feed in the average of the two. Over enough swings the midpoint is what you actually get.
• Crit chance and crit multiplier are not interchangeable. Their contribution is the product $\frac{c}{100} \times (m - 1)$, so whichever of the two is currently smaller usually gives more DPS per point invested. If your crit multiplier is 2 (a $m - 1$ of just 1), stacking more multiplier is often the better buy; if you almost never crit, chance is.
• What this calculator deliberately leaves out. Damage-over-time effects, armour and resistance reduction, buffs with limited uptime, cooldowns, reload and wind-up times, area damage hitting several targets, and skill rotations. Those are all game-specific, and each one would need rules this calculator does not assume. If your game has reloads or wind-up, one honest workaround is to divide your true attacks per second by the whole cycle time (including the downtime) rather than by the active window.
• Sustained vs. burst. Because DPS is an average, it describes sustained output. A burst weapon that front-loads damage may win a short fight it “should” lose on DPS.
• Percentages are percentages. Enter crit chance and accuracy as whole numbers out of 100 (25, not 0.25). If you need to convert between the two forms, the percentage calculator will do it.

FAQs

Why is a 0% crit chance still a valid input?

Because plenty of weapons and builds genuinely cannot crit, and DPS is perfectly well-defined for them — the crit term simply drops out and DPS becomes damage × accuracy × attack speed. A crit chance of 0 is a real answer, not a missing one, so the calculator computes with it rather than blanking the result.

What is the difference between “average damage per hit” and “effective damage per hit”?

The average damage per hit is what a hit deals when it lands, with crits already blended in. Effective damage per hit is what an attack attempt is worth on average, so it also carries the cost of your misses. When accuracy is 100% the two are identical; below that, the effective figure is smaller.

Does a bigger crit multiplier always mean more DPS?

Only if you actually crit. The crit contribution is the crit chance multiplied by $(m - 1)$, so a 3× multiplier on a build with 0% crit chance adds nothing whatsoever. Raising both stats together is what makes crit builds work.

Can I use this for a game I am designing?

Yes — that is a good use for it. Because it holds no game-specific data, it works as a balance sanity check: plug in the stats you are considering for two weapons and see whether their DPS figures land where you intended. Builders doing similar back-of-the-envelope planning for sandbox games may also find the Minecraft circle calculator useful.