D&D Ability Modifier floor((score−10)/2)

Resolve signed floor-based D&D ability modifiers for actual bounded score ledger, including odd scores below ten; no edition-specific ability cap or total character proficiency inference.

Description

Dungeons & Dragons ability modifiers use downward rounding.

Dungeons & Dragons ability modifiers use downward rounding. Negative odd differences therefore round away from zero.^[1]

Enter a nonempty list of integer ability scores 1–1000. Return corresponding modifiers in input order.

When to use D&D Ability Modifier floor((score−10)/2)

Use D&D Ability Modifier floor((score−10)/2) when you need to evaluate the supplied records under the calculation and evidence rules below. No edition-specific score limit, proficiency or check outcome is supplied.

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.

How to use D&D Ability Modifier floor((score−10)/2) and understand its results

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
Enter abilityScores using the field table and calculation rules, then run the tool.
Read abilityModifiers. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
abilityScores	Ability scores	list of number	Required

Enter a nonempty list of integer ability scores 1–1000. Return corresponding modifiers in input order.

modifier=floor((ability−10)/2)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
abilityModifiers	Ability modifiers	list of number

json

{
  "input": {
    "abilityScores": [
      9,
      10,
      11,
      12,
      18
    ]
  },
  "output": {
    "abilityModifiers": [
      -1,
      0,
      0,
      1,
      4
    ]
  }
}

Limitations and assumptions

No edition-specific score limit, proficiency or check outcome is supplied.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 10,000 entries; string lists to 128 strings of at most 128 characters each. The rules above may impose smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use d20 Meet-or-Beat DC Probability: A d20 threshold check counts successful natural faces after a modifier. Advantage and disadvantage select a maximum or minimum of two independent rolls. For a complementary task, use Crit Chance Expected Damage Multiplier: A critical-hit model separates eligible base damage from an unaffected flat amount. The multiplier may be below one if supplied.

References

D&D Ability Modifier floor((score−10)/2) — tool.io

Similar or alternative tools

d20 Meet-or-Beat DC Probability
A d20 threshold check counts successful natural faces after a modifier. Advantage and disadvantage select a maximum or minimum of two independent rolls.
Crit Chance Expected Damage Multiplier
A critical-hit model separates eligible base damage from an unaffected flat amount. The multiplier may be below one if supplied.