Ability modifiers sit at the center of D&D 5th Edition math, quietly shaping every attack roll, save, check, and AC value. This D&D modifier chart reference explains how each score maps to a modifier, how to use modifiers in calculations, and why they matter for both players and DMs. Below you will find a canonical-style chart, step-by-step examples, common applications, and practical notes that remain useful across editions and campaigns.
Ability Score to Modifier Chart
The core table maps an ability score range to a fixed modifier value. Use the row that contains your score to find the correct modifier.
| Score Range | Modifier |
|---|---|
| 1 | −5 |
| 2–3 | −4 |
| 4–5 | −3 |
| 6–7 | −2 |
| 8–9 | −1 |
| 10–11 | 0 |
| 12–13 | +1 |
| 14–15 | +2 |
| 16–17 | +3 |
| 18–19 | +4 |
| 20–21 | +5 |
| 22–23 | +6 |
| 24–25 | +7 |
| 26–27 | +8 |
| 28–29 | +9 |
| 30 | +10 |
Modifier Formula
The quick formula floor((score - 10) / 2) produces the same values for every integer score. For example, a score of 16 gives floor((16 - 10) / 2) = floor(3) = +3, matching the chart.
How Ability Modifiers Are Used
Modifiers adjust the result of a d20 roll or a dN die roll so that higher ability scores consistently improve outcomes. They are added to rolls, to DCs, and to combat metrics. Understanding how and where they apply is more important than memorizing individual numbers.
Common Use Cases
- Attack rolls: modifier added to a d20 to determine if a hit occurs.
- Damage rolls: modifier added to weapon or spell damage on a hit.
- Saving throws: modifier added to a d20 when a creature resists an effect.
- Ability checks: modifier added to a d20 when attempting an action with an ability.
- AC and some defenses: some class features, spells, or items use modifiers in their AC calculation.
- Skill bonuses: skills directly tied to an ability add that ability’s modifier.
Step-by-Step Calculation Examples
Worked examples show how modifiers appear at different ability scores, with typical results for attacks, saves, and checks.
| Ability Score | Modifier | Example Attack Roll (d20 + modifier) | Example Save DC (DC 8 + modifier) | Example Skill Check (d20 + modifier) |
|---|---|---|---|---|
| 10 | 0 | 12–19 to hit (average) | DC 8 automatic success | Average chance at easy tasks |
| 14 | +2 | +2 to hit, improving hit probability by ~10% | DC 10 success on a 4+ | +2 to skill checks, e.g., Investigation |
| 18 | +4 | +4 to hit, significantly raising hit chance | DC 12 success on a 1+ | +4 to skill checks, e.g., Athletics |
Applying Modifiers in Play
When you calculate an effective result, always add the modifier to the d20 roll or to the base number, not both. For AC, use the formula relevant to the feature; many defenses or spells create a flat bonus rather than scaling it by additional modifiers beyond what’s stated. When a creature’s ability scores change—through level-up, magic items, or spells—update the associated modifiers immediately to keep math consistent.
Exceptional Scores and Extreme Modifiers
Official ability scores can range from 1 to 30 in most published rules, allowing modifiers from −5 to +10 in standard play and beyond in home games. Some effects, such as legendary actions or epic-tier play, may push scores higher, at which point the formula floor((score − 10) / 2) remains the consistent backbone. When interpreting unusual modifiers, note that not every system uses the same divisor or cap—always check the specific edition rules.
Tips for Players and DMs
- Carry a printable or bookmarked modifier chart for quick reference at the table.
- Recalculate modifiers whenever an ability score changes to avoid missed bonuses or penalties.
- Use modifiers to inform challenge design; DCs that assume a +2 or +3 modifier can be tuned for party power.
- Differentiate between ability modifiers and other flat bonuses to prevent stacking errors.
- Prep edge-case examples (score 1, score 30) so rulings stay consistent at extreme values.
Frequently Asked Questions
- Does a modifier change if my ability score changes? Yes, update the modifier immediately when an ability score increases or decreases.
- Are modifiers applied the same way to monsters? Yes, NPCs and monsters use the same modifier logic unless a stat block states otherwise.
- Do proficiency and expertise affect the modifier chart? No; proficiency applies to skills and some attacks separately, while modifiers adjust the base roll result.
- What about half- or fractional steps? Use the standard formula or table; do not invent intermediate values.
- Can a modifier be negative? Yes, low ability scores yield negative modifiers that impose penalties to rolls and DCs.