Average Damage Calculator 5e

5e Average Damage (DPR) Calculator

Calculate your character's average Damage Per Round (DPR) to better understand your combat effectiveness in Dungeons & Dragons 5th Edition.

Attack Statistics

Attack Bonus

Target Armor Class (AC)

Damage Details

Number of Damage Dice

Type of Damage Die d4 d6 d8 d10 d12

Bonus Dice (e.g. Sneak Attack)

Type of Bonus Die d4 d6 d8 d10 d12

Flat Damage Modifier (e.g. Ability Mod)

Your results will be displayed here.

Calculation Results

'; outputHTML += 'Chance to Hit: ' + (chanceToHit * 100).toFixed(0) + '%'; outputHTML += 'Average Damage on a Hit: ' + avgNormalDamage.toFixed(2) + "; outputHTML += 'Average Damage on a Critical Hit: ' + avgCritDamage.toFixed(2) + "; outputHTML += '

'; outputHTML += 'Average Damage Per Round (DPR): ' + dpr.toFixed(2) + "; outputHTML += '

'; resultDiv.innerHTML = outputHTML; }

How to Calculate Average Damage Per Round (DPR) in 5e

Damage Per Round, or DPR, is a key metric used by D&D 5e players to estimate a character's average combat effectiveness over time. It's not just about how much damage you can do on a perfect hit, but about factoring in your chances to hit, miss, and land a critical hit. This gives a much more realistic picture of your damage output.

The core formula for DPR is:

DPR = (Average Normal Hit Damage × Chance of Normal Hit) + (Average Critical Hit Damage × Chance of Critical Hit)

Let's break down the components:

Chance to Hit: In 5e, you hit if your d20 roll + your attack bonus is greater than or equal to the target's Armor Class (AC). A roll of 1 always misses, and a 20 always hits. Your chance to hit is calculated based on the d20 roll you need.
Chance to Crit: A standard critical hit occurs on a d20 roll of 20, which is a 5% chance.
Average Damage: The average result of any die is (Number of Sides + 1) / 2. For example, a d8's average is (8+1)/2 = 4.5. Your total average damage on a hit is the sum of your average dice rolls plus any flat modifiers. On a critical hit, you roll all damage dice twice, then add the modifier.

Example Calculation

Let's take a Level 3 Rogue with a Dexterity of 16 (+3 modifier) and proficiency bonus of +2. They are using a shortsword against a goblin with an AC of 15.

Attack Bonus: +5 (+3 Dex, +2 Proficiency)
Target AC: 15
Damage: 1d6 (shortsword) + 3 (Dex mod)
Sneak Attack Damage: 2d6 (for a level 3 Rogue)

First, let's find the total damage on a normal hit. The Rogue uses one 1d6 and two 2d6 for a total of 3d6 + 3.

Average Dice Damage: The average of a d6 is 3.5. For 3d6, the average is 3 * 3.5 = 10.5.
Average Normal Hit Damage: 10.5 (dice) + 3 (modifier) = 13.5
Average Critical Hit Damage: On a crit, the dice are doubled to 6d6. The average is (6 * 3.5) + 3 = 21 + 3 = 24.
Chance to Hit: To hit AC 15 with a +5 bonus, the Rogue needs to roll a 10 or higher on the d20. This means 11 outcomes (10-20) hit. So, the chance to hit is 11/20 = 55%.
Chance Breakdown: The chance to crit is 5% (rolling a 20). The chance for a normal hit is 55% – 5% = 50%.
Final DPR: (13.5 × 0.50) + (24 × 0.05) = 6.75 + 1.2 = 7.95 DPR.

Why Does Average Damage Matter?

DPR is an invaluable tool for theorycrafting and character building. It helps you compare the effectiveness of different weapons, feats (like Great Weapon Master or Sharpshooter), and class features. While the dice can be swingy in any single round, DPR provides a solid mathematical foundation for understanding how a character is likely to perform over the course of an entire adventure. It helps Dungeon Masters balance encounters and allows players to make informed tactical decisions.