Dnd Combat Calculator – Cost Calculator | Online Quote & Profit Estimator

Authored & Reviewed by David Chen, CFA

A professional analysis of Dungeons & Dragons combat metrics, ensuring formulaic accuracy for tabletop game optimization.

Welcome to the definitive **D&D Combat Calculator**. This tool helps Dungeon Masters (DMs) and players estimate the average damage output of a creature or character per round, a crucial metric known as Damage Per Round (DPR). Optimize your builds and balance your encounters with precision.

D&D Combat Calculator

Attack Bonus (e.g., +5)

Target Armor Class (AC)

Damage Expression (e.g., 2d6+3)

Number of Attacks per Action

Critical Hit Damage Multiplier

Average Damage Per Round (DPR)

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Detailed Calculation Steps

D&D Combat Calculator Formula

The standard formula for Average Damage Per Round (DPR) is derived by combining the probability of hitting, the probability of scoring a critical hit, and the average damage of the attack.


                    R = Target AC - Attack Bonus

                    P_Hit = max(0.05, min(0.95, (21 - R) / 20))

                    P_Crit = 0.05 (Standard critical chance)

                    AvgDmg = Average Damage from Dice + Damage Modifier

                    

                    DPR = Attacks × [ (AvgDmg × (P_Hit - P_Crit)) + (AvgDmg × Crit Multiplier × P_Crit) ]

Formula Source: Roll20 D&D 5e Combat Rules Reference Source: D&D Beyond Basic Rules on Attack

Variables

Attack Bonus: The total modifier added to the d20 roll (e.g., Proficiency Bonus + Strength/Dexterity Modifier).
Target AC (Armor Class): The defensive stat the attacker must meet or exceed to hit.
Damage Expression: The dice and modifier that determine base damage (e.g., 2d6+4).
Number of Attacks per Action: The total number of attacks a character makes in a single combat round.
Critical Hit Damage Multiplier: How many times the damage dice are rolled on a critical hit (typically 2x in 5e).

Related Calculators

What is D&D Combat Calculator?

A D&D Combat Calculator is a specialized digital tool designed to help players and Dungeon Masters quantify a character’s offensive potential, usually expressed as Average Damage Per Round (DPR). This metric smooths out the randomness of dice rolls into a reliable average, making it invaluable for character optimization and encounter balancing.

For players, knowing their DPR allows them to compare different fighting styles, feat choices, and weapon options to find the most efficient build. For DMs, DPR is essential for designing challenging encounters. By comparing the party’s combined DPR to a monster’s Hit Points (HP), a DM can accurately estimate how many rounds a fight will last, preventing overly long or disappointingly short battles.

How to Calculate DPR (Example)

Determine the required roll (R): Subtract the Attack Bonus (+5) from the Target AC (15). $R = 15 – 5 = 10$.
Calculate Hit Probability ($P_{H}$): The attacker needs a 10 or higher. $(21 – 10) / 20 = 11 / 20 = 0.55$ (55%).
Determine Average Damage: For an attack of 1d8+3, the average roll on 1d8 is 4.5. Average Damage ($D_{A}$) is $4.5 + 3 = 7.5$.
Factor in Critical Hits: The non-crit hit chance is $0.55 – 0.05 = 0.5$. The Crit Chance ($P_{C}$) is 0.05. Crit Multiplier is 2.
Calculate Average Damage Per Attack (DPA): $DPA = (7.5 \times 0.5) + (7.5 \times 2 \times 0.05)$ $DPA = 3.75 + 0.75 = 4.5$.
Calculate Total DPR: Assuming 2 attacks per action: $DPR = 2 \times 4.5 = 9.0$.

Frequently Asked Questions (FAQ)

Why is DPR more useful than Max Damage?

DPR (Damage Per Round) provides a statistically reliable expectation of performance over time, minimizing the effect of luck from single, high-damage rolls. It’s the best metric for long-term character analysis and encounter design.

Does this calculator account for advantage/disadvantage?

This basic calculator assumes a straight roll. To account for Advantage, you can adjust the $P_{H}$ formula to $1 – (1 – P_{H})^2$. For Disadvantage, use $(P_{H})^2$. Use an external tool or manual calculation for this adjustment.

What if the damage is non-standard, like a condition or a saving throw?

DPR calculations typically focus on standard weapon/spell attacks. For damage tied to successful saving throws, you would calculate a Save Success Probability instead of a Hit Probability.

Is the Critical Hit Multiplier always 2?

In standard 5th Edition, a critical hit doubles the damage dice rolled and adds the normal damage modifiers once. However, some class features (like the Half-Orc’s Savage Attacks or Fighter’s Superior Critical) can increase the effective multiplier. The calculator allows you to adjust this factor.