# DnD 5e - Math

Most 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 quickly is adding and subtracting hit points.

## Modifiers, Bonuses, and Penalties

You will frequently add mpdifiers, 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

"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.

## Rounding

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.