How this calculator works
Point buy treats the six ability scores as a shopping list. Each score starts at 8 and costs nothing. Raising a score by one costs one point up to 13, then the last two steps cost two points each, so 14 costs seven and 15 costs nine. The total for all six scores is compared with the budget, which is 27 in the standard fifth edition variant. The modifier is the usual ability modifier: subtract 10 from the score, divide by two and round down, so 10 and 11 give +0, 12 and 13 give +1, and 8 and 9 give -1.
Formula
cost of a score: 8 = 0, 9 = 1, 10 = 2, 11 = 3, 12 = 4, 13 = 5, 14 = 7, 15 = 9. points used = sum of the six costs. points left = budget - points used. modifier = floor((score - 10) / 2).
Worked example
The standard array 15, 14, 13, 12, 10 and 8 costs 9 + 7 + 5 + 4 + 2 + 0 = 27 points, exactly the standard budget. The modifiers are +2, +2, +1, +1, +0 and -1. Putting 15 in three scores and 8 in the other three also costs 27, but leaves three dump stats; putting 13 in all six costs 30, which is three points over the standard budget.
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Frequently asked questions
Can I lower a score below 8?
Not in the standard point buy variant. Scores are allowed from 8 to 15 before racial or background bonuses. A table that allows lower scores is using a house rule, and this calculator deliberately follows the published range.
Do racial bonuses count against the budget?
No. Point buy sets the scores before racial, background and feat bonuses. A 15 bought with points can become a 17 after a +2 bonus, which is legal. This page shows only the pre-bonus cost.
Why is 14 so much more expensive than 13?
The cost curve is deliberately convex so that a very high score costs more of the budget. Climbing from 13 to 15 costs four points for two points of ability, while 8 to 10 costs two points for the same two points of ability. That makes a balanced spread cheaper than a peak.
Is 27 the only point budget?
It is the standard in the fifth edition Player's Handbook. Some tables use a higher budget for heroic campaigns, and organised play sometimes uses a fixed array instead. The budget field is editable so you can check a house rule, but the score costs stay the same.