Combat Calculator 5e

Streamline your D&D 5e battles with real-time combat calculations.

5e Combat Calculator

Calculate attack rolls, damage, and critical hits for D&D 5e encounters. Enter your attack bonus, target’s Armor Class (AC), and damage dice to get instant results.

Attack Roll Probabilities

Roll (d20)	Hit Chance	Crit Chance	Damage Scenario
Calculate to see probabilities.

What is 5e Combat Calculation?

In the context of Dungeons & Dragons 5th Edition (5e), 5e Combat Calculation refers to the process of determining the success or failure of an attack, the amount of damage dealt, and other critical combat outcomes. It’s the engine that drives the action economy of the game, ensuring fairness and emergent tactical depth. Mastering these calculations is crucial for Dungeon Masters (DMs) and players alike to run smooth, engaging combat encounters. This involves understanding the interplay between attack bonuses, Armor Class (AC), dice rolls, damage dice, critical hits, and special abilities.

Essentially, 5e Combat Calculation translates player and monster actions into tangible results on the battlefield. It’s not just about rolling dice; it’s about understanding the probabilities and modifiers involved. Whether you’re a seasoned veteran aiming to optimize your character’s damage output or a new DM trying to keep track of monster stats and probabilities, a reliable combat calculator for 5e can significantly enhance your gameplay experience. It helps to demystify the math, allowing for quicker decision-making and more focus on the narrative and strategic elements of the game.

Who Should Use a 5e Combat Calculator?

• Dungeon Masters (DMs): To quickly assess monster attack effectiveness, calculate average damage per round for encounters, and understand enemy capabilities.
• Players: To optimize their character’s build, understand their average damage output with different weapons and abilities, and strategize their actions in combat.
• Game Designers: When creating new monsters, magic items, or subclasses, to balance their power levels and ensure they fit within the 5e ruleset.
• New Players: To learn the core mechanics of attack rolls and damage in D&D 5e in an accessible way.

Common Misconceptions about 5e Combat Calculation

• “It’s just about rolling high”: While high rolls are good, modifiers, critical hits, advantage/disadvantage, and specific abilities significantly influence outcomes. A low roll with strong modifiers can sometimes outperform a moderate roll with no modifiers.
• “Average damage is the only thing that matters”: Damage distribution is also important. A weapon that averages lower damage but has a wider range (e.g., 1d12) can sometimes be riskier but offer higher potential bursts than a weapon with a narrower range (e.g., 3d6) that averages higher.
• “Critical hits are rare and insignificant”: Critical hits (often on a natural 20) double the damage dice, which can drastically change the tide of battle. Understanding the probability and impact of critical hits is vital.
• “Advantage/Disadvantage simply adds/subtracts a flat bonus”: Advantage means rolling two d20s and taking the higher result, while disadvantage means rolling two and taking the lower. This is not equivalent to a +5 or -5 bonus. The probability shift is significant.

5e Combat Calculation Formula and Mathematical Explanation

The core of 5e Combat Calculation revolves around the d20 roll. Here’s a breakdown of the key formulas:

Attack Roll Calculation

The fundamental formula for an attack roll is:

Attack Roll = d20 + Attack Bonus

This roll is compared against the target’s Armor Class (AC). If the Attack Roll equals or exceeds the target’s AC, the attack hits.

Hit Chance Calculation

The base probability of hitting a target with AC ‘T’ and an Attack Bonus ‘A’ is calculated by determining the number of successful rolls on a d20.

The minimum roll needed to hit is Target AC - Attack Bonus. Let’s call this ‘R’.

The number of successful outcomes on a d20 is 21 - R (since a roll of R, R+1, …, 20 hits).

Base Hit Chance = (21 – R) / 20 * 100%

However, this is modified by advantage and disadvantage:

• Normal Roll: Uses the Base Hit Chance.
• Advantage: You roll two d20s and take the higher. The probability of *missing* is the probability of both rolls being less than R. P(miss with advantage) = [(R-1)/20] * [(R-1)/20]. Therefore, Hit Chance (Advantage) = 1 – [((R-1)/20)^2].
• Disadvantage: You roll two d20s and take the lower. The probability of *hitting* is the probability of both rolls being at least R. P(hit with disadvantage) = ( (21-R) / 20 ) * ( (21-R) / 20 ). Therefore, Hit Chance (Disadvantage) = [( (21-R) / 20 )^2].

Note: Rolls of 1 always miss, and rolls of 20 always hit (unless modified by specific abilities).

Critical Hit Calculation

A critical hit typically occurs on a natural d20 roll of 20. Some abilities (like the Champion fighter’s improved critical) extend this range (e.g., 19-20).

Let ‘C’ be the lowest natural roll required for a critical hit (default is 20).

Base Crit Chance = (21 – C) / 20 * 100%

This is also affected by advantage/disadvantage using the same logic as hit chance, but with ‘C’ as the threshold.

Damage Calculation

When an attack hits (or critically hits), damage is calculated.

Normal Hit Damage = Sum of Damage Dice + Attack Bonus (if applicable)

Example: 1d8 + 3 means roll one 8-sided die, and add 3 to the result.

Critical Hit Damage = (Sum of Damage Dice * 2) + Attack Bonus (if applicable)

Example: For 1d8 + 3, a critical hit deals (1d8 * 2) + 3. This means rolling the 1d8 *twice* and adding the bonus.

Average Damage Per Round (DPR)

This is a crucial metric for comparing different attacks or character builds.

Average DPR = (P(Hit) * Avg Normal Damage) + (P(Crit) * Avg Crit Damage)

Where P(Hit) is the probability of hitting and P(Crit) is the probability of a critical hit. Note that critical hits are a subset of hits, so the formula is more accurately:

Average DPR = (P(Miss) * 0) + (P(Normal Hit) * Avg Normal Damage) + (P(Crit Hit) * Avg Crit Damage)

Where P(Normal Hit) is the probability of hitting *without* it being a critical hit, and P(Crit Hit) is the probability of a critical hit occurring.

A simplified approach often used for general comparison is:

Average DPR (Simplified) = P(Hit) * Avg Normal Damage + P(Crit Hit) * Avg Normal Damage (This approximates the extra damage from crits).

The calculator uses a more precise method considering the distinct damage values.

Variables Table

Variable	Meaning	Unit	Typical Range
d20	A twenty-sided die roll	Integer	1-20
Attack Bonus (A)	Sum of proficiency bonus and relevant ability modifier	Integer	-5 to +15+
Target AC	Armor Class of the target	Integer	10 to 25+
R	Roll needed to hit (Target AC – Attack Bonus)	Integer	-10 to 25+
C	Natural roll needed for critical hit	Integer	15-20 (commonly 20)
Damage Dice	The dice rolled for damage (e.g., 1d8, 2d6)	Dice Notation	N/A
Flat Damage Bonus	Static bonus added to damage (e.g., from Strength modifier)	Integer	-5 to +10+
P(Hit)	Probability of hitting	Percentage (%)	0% to 100%
P(Crit)	Probability of a critical hit	Percentage (%)	0% to ~45% (with advantage and low AC)
Avg Normal Damage	Average damage dealt on a normal hit	Points	0+
Avg Crit Damage	Average damage dealt on a critical hit	Points	0+

Practical Examples (Real-World Use Cases)

Example 1: The Mighty Fighter vs. Goblin

Scenario: A Fighter with a +5 to hit and dealing 1d8+3 (longsword) attacks a Goblin with AC 15. The Fighter has no advantage or disadvantage.

Inputs:

• Attack Bonus: 5
• Target AC: 15
• Damage Dice: 1d8+3
• Advantage: Normal
• Critical Range: 20

Calculations:

• Roll needed to hit (R) = 15 (AC) – 5 (Bonus) = 10.
• Roll needed to crit (C) = 20.
• Hit Chance: Rolls 10-20 hit. That’s (21 – 10) = 11 outcomes. P(Hit) = 11/20 = 55%.
• Crit Chance: Roll 20 hits. That’s (21 – 20) = 2 outcomes (20 itself). P(Crit) = 1/20 = 5%.
• Normal Hit Damage: Avg of 1d8 is 4.5. So, 4.5 + 3 = 7.5 average damage.
• Crit Hit Damage: (Avg of 1d8 * 2) + 3 = (4.5 * 2) + 3 = 9 + 3 = 12 average damage.
• Overall Average Damage:
  P(Miss) = 1 – P(Hit) = 45%.
  P(Normal Hit) = P(Hit) – P(Crit) = 55% – 5% = 50%.
  P(Crit Hit) = 5%.
  Avg DPR = (0.50 * 7.5) + (0.05 * 12) = 3.75 + 0.6 = 4.35 average damage per attack.

Interpretation: The Fighter has a decent 55% chance to hit the Goblin. On average, each attack will deal about 4.35 damage. They’ll need multiple successful hits to defeat the Goblin (which typically has 7 HP).

Example 2: Rogue with Advantage vs. Bandit

Scenario: A Rogue with a +6 to hit and dealing 1d8+4 (rapier) attacks a Bandit with AC 14. The Rogue has advantage thanks to Sneak Attack conditions.

Inputs:

• Attack Bonus: 6
• Target AC: 14
• Damage Dice: 1d8+4
• Advantage: Advantage
• Critical Range: 20

Calculations:

• Roll needed to hit (R) = 14 (AC) – 6 (Bonus) = 8.
• Roll needed to crit (C) = 20.
• Hit Chance (Advantage): P(Hit) = 1 – [((8-1)/20)^2] = 1 – (7/20)^2 = 1 – (0.35)^2 = 1 – 0.1225 = 0.8775 or 87.75%.
• Crit Chance (Advantage): P(Crit) = 1 – [((20-1)/20)^2] = 1 – (19/20)^2 = 1 – (0.95)^2 = 1 – 0.9025 = 0.0975 or 9.75%.
• Normal Hit Damage: Avg of 1d8 is 4.5. So, 4.5 + 4 = 8.5 average damage.
• Crit Hit Damage: (Avg of 1d8 * 2) + 4 = (4.5 * 2) + 4 = 9 + 4 = 13 average damage.
• Overall Average Damage:
  P(Miss) = 1 – P(Hit) = 12.25%.
  P(Normal Hit) = P(Hit) – P(Crit) = 87.75% – 9.75% = 78%.
  P(Crit Hit) = 9.75%.
  Avg DPR = (0.78 * 8.5) + (0.0975 * 13) = 6.63 + 1.2675 = 7.8975, approximately 7.9 average damage per attack.

Interpretation: With advantage, the Rogue has a very high 87.75% chance to hit. Their average damage per attack is approximately 7.9. This highlights the significant benefit of advantage in combat, making the Rogue much more reliable.

How to Use This 5e Combat Calculator

Using the 5e Combat Calculator is straightforward and designed to provide instant insights into your D&D battles.

1. Input Your Character/Monster Stats:
   • Attack Bonus: Enter your character’s or monster’s total bonus to hit. This is typically your proficiency bonus plus your relevant ability modifier (e.g., Strength for melee, Dexterity for ranged/finesse).
   • Target’s AC: Input the Armor Class of the creature you are attacking.
   • Damage Dice: Enter the weapon or spell’s damage in the standard D&D format (e.g., 1d8, 2d6+3, 1d4+2).
   • Advantage: Select ‘Normal’ for a standard roll, ‘Advantage’ if you are rolling two d20s and taking the higher, or ‘Disadvantage’ if you are rolling two and taking the lower.
   • Critical Hit Range: By default, critical hits occur on a natural 20. If your character or a monster has an ability that allows critical hits on a lower roll (e.g., 19-20), adjust this setting accordingly.
2. Calculate: Click the “Calculate Combat” button. The calculator will process your inputs and display the results immediately.
3. Understand the Results:
   • Main Result (Average Damage Overall): This is the most important number, representing the average damage you can expect to deal per attack, considering hit and critical hit probabilities.
   • Hit Chance: The percentage likelihood that your attack will hit the target.
   • Crit Chance: The percentage likelihood that your attack will result in a critical hit.
   • Average Damage (Hit): The average damage dealt on a successful normal hit.
   • Average Damage (Crit): The average damage dealt on a critical hit.

   The calculator also provides a visual representation in the Damage Distribution Chart and a breakdown of probabilities in the Attack Roll Probabilities Table.

4. Make Decisions: Use the results to inform your tactical choices. Should you attack the heavily armored knight or the weaker mage? Which weapon offers better damage potential? Is it worth using a resource to gain advantage?
5. Copy Results: Use the “Copy Results” button to quickly paste key combat metrics into your notes or share them with your group.
6. Reset: The “Reset Defaults” button will restore the calculator to common starting values.

Key Factors That Affect 5e Combat Results

Several factors significantly influence the outcomes of combat calculations in D&D 5e. Understanding these helps in strategizing and optimizing performance:

1. Attack Bonus vs. Target AC: This is the most direct factor influencing hit chance. A higher attack bonus against a lower AC drastically increases the probability of hitting. Conversely, a low bonus against high AC makes landing hits difficult. The “sweet spot” for hitting often lies where your Attack Bonus equals or exceeds the target’s AC.
2. Advantage and Disadvantage: As demonstrated, rolling with advantage significantly boosts hit and crit chances, while disadvantage dramatically reduces them. This mechanic is core to balancing actions, spells, and environmental effects. Using abilities or spells that grant advantage is often a high-priority tactical choice.
3. Critical Hit Range: Extending the critical hit range (e.g., to 18-20) significantly increases burst damage potential. Characters built around critical hits, like the Champion Fighter, benefit immensely from this. It means more frequent application of doubled damage dice.
4. Damage Dice and Flat Bonuses: The type and number of damage dice, combined with flat bonuses (like from Strength or Dexterity modifiers, or magic weapon enchantments), determine the average damage output. Weapons with higher average dice rolls or multiple dice (like 2d6 vs. 1d12) have different risk/reward profiles. Flat bonuses become more impactful as the number of dice increases.
5. Critical Hit Damage Multiplier: The standard rule of doubling damage dice on a critical hit is a massive damage boost. This makes critical hits incredibly valuable, especially for attacks that already deal high damage. Understanding the difference between average normal damage and average critical damage highlights this disparity.
6. Number of Attacks: Many abilities and features allow characters to make multiple attacks per turn (e.g., Extra Attack). The Average Damage Per Round (DPR) calculation is vital here. A feature that grants an extra attack, even with a slightly lower bonus or damage die, can often increase overall DPR significantly by adding more chances to hit and critically hit.
7. Critical Hit Effects: Some damage types or spells have additional effects on critical hits beyond just doubled damage (e.g., a spell that imposes a condition might have a higher chance of success or a stronger effect on a crit). This adds another layer of complexity and reward to critical hits.
8. Damage Type Resistances/Vulnerabilities: While not directly calculated here, a creature’s resistances halve damage of a certain type, while vulnerabilities double it. This is a critical factor in choosing which attacks to use against specific enemies, often outweighing raw damage numbers.

Frequently Asked Questions (FAQ)

Q1: What is the difference between a normal hit and a critical hit in 5e?

A: A normal hit occurs when your attack roll meets or exceeds the target’s AC. A critical hit typically occurs when you roll a natural 20 on the d20. On a critical hit, you roll all the damage dice twice and then add any applicable bonuses.

Q2: Does advantage affect critical hit chance?

A: Yes, if you have advantage and roll two d20s, you take the higher roll. If that higher roll is a 20, it’s a critical hit. If the lower roll was a 20 and the higher was not, it’s still a normal hit. The calculator handles this probability.

Q3: How do I calculate my attack bonus?

A: Your attack bonus is usually your proficiency bonus plus your relevant ability modifier (Strength for most melee, Dexterity for ranged/finesse weapons, spellcasting ability modifier for spells). Magic items can also add to this bonus.

Q4: What does “average damage” really mean?

A: Average damage is the expected damage you’ll deal over many attacks. It accounts for the probability of hitting, missing, and scoring a critical hit, and the different damage amounts associated with each. It’s a useful metric for comparing weapons or abilities but doesn’t guarantee the exact damage on any single roll.

Q5: Can my attack bonus be higher than what’s shown in the calculator’s typical range?

A: Yes, with powerful magic items, specific class features (like the Barbarian’s Brutal Critical or the Paladin’s Improved Divine Smite), or certain spells, your attack bonus and critical hit range can be significantly modified. The calculator allows for a wide range of inputs.

Q6: What if my damage dice include a variable number of dice (e.g., a spell that deals 3d6 damage)?

A: For spell damage or abilities that vary the number of dice rolled, you’ll need to calculate the average damage for the maximum number of dice allowed. For example, if a spell can deal 3d6 to 5d6 damage, you’d typically calculate the average for 5d6 to understand its peak potential.

Q7: Does this calculator account for Sneak Attack or other special damage riders?

A: The “Damage Dice” input field is designed to include these. For example, if you have Sneak Attack dealing an additional 3d6 damage, you would enter 1d8+3d6+4 (for a rapier with +4 Dex). The calculator sums the average dice rolls and adds flat bonuses.

Q8: What happens if my roll needed to hit is 1 or less, or 21 or more?

A: A natural roll of 1 always misses, regardless of modifiers. A natural roll of 20 always hits, regardless of AC or modifiers (unless the target has a specific ability like the Shield spell, which negates the hit *after* the roll). If your calculated ‘R’ is 1 or less, you hit on a 1 (crit) or higher. If ‘R’ is 21 or more, you miss on a 20 (crit).