View source for Math Forumlas for D&D

<big>A compilation of important formulas derived from d20 System sources.</big>

Most of these are well known, but posted here as a reference.


=== Ability Modifiers ===

<code>modifier = ability / 2 – 5</code> or <code>modifier = (ability – 10) / 2 , round down.</code>
* Division is rounded down. 
* Ability should be 0 or greater.

=== Bonus Spells ===

<code>bonus = (ability – (spellLevel + 1) * 2) / 8</code>

* Division is rounded down, to 0 minimum. 
* 0-level spells receive no bonuses.
* If the ability is less than 10+spellLevel, no spells of that level can be cast.
* Ability should be 0 or greater.
* SpellLevel should be between 1 and 9.

=== Base Attack Bonus ===

* <code>goodAttacks = classLevel * 1</code>
* <code>normAttacks = classLevel * 3 / 4</code>
* <code>poorAttacks = classLevel * 1 / 2</code>

* Division is rounded down.
* ClassLevel should be greater than 0.

=== Saving Throws ===

* <code>goodSave = classLevel / 2 + 2</code>
* <code>poorSave = classLevel / 3</code>

* Division is rounded down. 
* ClassLevel should be greater than 0.

=== Skill Max Ranks ===

* <code>inClassMax = characterLevel + 3</code>
* <code>crossClassMax = (characterLevel + 3) / 2</code>

* Division is not rounded. 
* CharacterLevel should be greater than 0.

=== Spell Cost ===

<code>cost = spellLevel * casterLevel * 10</code>

* 0-level spells count as ½ spell level.
* SpellLevel should be between 1 and 9. 
* CasterLevel should be greater than 0.

=== Treasure and Character Wealth ===

Neither the treasure tables, nor NPC or PC wealth tables, appear to follow a regular formula.

=== Speed ===

<code>encumberedSpeed = baseSpeed * 0.7</code>

* Rounding is done to the nearest multiple of 5.
* BaseSpeed should be greater than 0.
* (Note: The FAQ expands movement table in way that breaks any formula.)

=== Encumbrance ===

* <code>if strength  10, then: maxLoad = strength * 10</code>
* <code>if strength > 10, then: maxLoad = 1.1487 ^ (strength - 10) * 100</code>

* Rounding is done to the nearest multiple of 5, 10, 20, or 40 (in steps of 5 strength).
* Other modifiers may be made per the d20 System for character size, number of legs, etc.
* Light load is 1/3 the max load; medium load is 2/3 the max load (round down).
* (Note: 1.1487 approximates 104)
* Strength should be greater than 0.

=== Movement ===

* <code>movePerHour = speed / 10</code>
* <code>movePerDay = speed / 10 * 8</code>

* Terrain modifiers may apply to these figures.
* Speed should be greater than 0.

=== Experience Points ===

<code>requiredXP = level * (level – 1) * 500</code>

* (Note each level requires an added level * 1000 XP to advance through it.)
* Level should be greater than 0.

=== Challenge Ratings ===

* <code>Fractional CR	1/2   1/3   1/4   1/6   1/8   1/10</code>
* <code>Integral CR		 -1     -2     -3     -4    -5      -6</code>

* For the following formulas, fractional CRs may be converted to negative integers as above.
* ChallengeRating should be a fraction as above.

=== Encounter Levels ===

<code>EL = challengeRating + 2 * ln(number) / ln(2)</code>

* (Note that ln(number) / ln(2) = log2 (number).)
* ChallengeRating should be an integer.
* Number should be greater than 0.

=== Experience Awards ===

* <code>CD = challengeRating – partyLevel
* <code>if CD is even, then: award = partyLevel * 2 ^ (CD / 2) * 300</code>
* <code>if CD is odd and CD < 0, then: award = partyLevel * 2 ^ ((CD+1) / 2) * 200</code>
* <code>if CD is odd and CD > 0, then: award = partyLevel * 2 ^ ((CD-1) / 2) * 450</code>

* No award is given if |CD| > 7.
* PartyLevels of 1 or 2 are treated as 3, except when the CR is 1 or 2.
* (Note that the first “CD is even” case can be used as an approximation for all cases.)
* (The second case is basically x2/3 the first.)
* (The last case is basically x3/2 the first.)
* ChallengeRating should be an integer. 
* PartyLevel should be greater than 0.

[[Category:Info]]