Dungeons and Dragons Math


Most tabletop RPGs involve some amount of math, and Dungeons and Dragons is no exception. But don’t worry, there’s nothing here that you can’t handle. The most frequent math that you’ll need to do is quickly adding and subtracting modifiers to dice rolls and adding and subtracting hit points in combat. These numbers are generally no more than two digits, but if you’re not confident with your ability to do math quickly, there is no problem with using a calculator at the table.

Table of Contents

Modifiers, Bonuses, and Penalties

You will frequently add modifiers, bonuses, and/or penalties to rolls. These numbers are added to the total of the dice rolled. For example: you add your “attack bonus” to an “attack roll”, adding the bonus to the d20 roll for the attack. Similarly, you add a “damage bonus” to a “damage roll”, so a character attacking with a greatsword would roll 2d6 (the damage for a greatsword) and add their damage bonus to the total rolled.

A bonus is always positive, a penalty is always negative, and a modifier can be either.


“Stacking” is the concept of combining numerical values from different sources.

Stacking Modifiers

In 5th edition, all numerical modifiers stack. If you have two things which add +1 to your AC, they “stack” and you add both values.

Stacking Multipliers

Multipliers stack “additively”, which means that you add their effects rather than multiplying multiple times. For example: If you have two things which double a number, you instead triple the number. Each “double” adds the original value to the total one time, so doubling twice adds the original value to the total twice, resulting in three times the original value.

In some cases, multiple sources may tell you to “add double” some specific bonus. If two sources tell you to “add double” a number, you still only add double the number; these values don’t stack. For example: if two sources tell you to add double your proficiency bonus to a check, you still only add double your proficiency bonus to the check.

Stacking Effects

Beyond math, sometimes a creature is affected by two effects of the same name at the same time. In these cases, the effects don’t stack; you only get the effect once. For example, if a creature is affect by the Bless spell twice at the same time, they only gain the benefits of the spell once. However, if they have multiple effects with difference names but similar effects, those can still stack. For example: Mage Armor and Shield of Faith will both improve the target’s armor class.


When dividing numbers, always round down unless a piece of text specifically says otherwise. For example: Tieflings have resistance to fire, which means that any time they take fire damage they only take half as much damage as normal. If a tiefling takes 5 fire damage, they divide it in half and round down, resulting in the tiefling taking just 2 damage.

Average Dice Roll Values

While not strictly necessary, understanding the average result of rolling one or more dice can help you make decisions while playing. The average value of a single die isn’t hard, but finding the average for multiple dice can be more difficult. In those cases, I recommend using AnyDice.

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