5ePointBuy

Ability score modifiers, 1 to 30

A score is a number on the sheet; a modifier is what the dice actually use. Every attack roll, saving throw, skill check and spell save DC in the game reads the modifier, and the score exists mainly to produce it.

Every score from 1 to 30

This is the whole range the rules define. Scores above 20 need a feature that raises the cap, such as an epic boon or an artefact, and the two columns to the right show how much of the range a first-level character will ever touch.

The complete defined range. The right-hand column marks the eight scores the 8–15 purchase table actually sells.
Score Modifier Buyable at level 1
1 -5
2 -4
3 -4
4 -3
5 -3
6 -2
7 -2
8 -1 Yes
9 -1 Yes
10 +0 Yes
11 +0 Yes
12 +1 Yes
13 +1 Yes
14 +2 Yes
15 +2 Yes
16 +3
17 +3
18 +4
19 +4
20 +5
21 +5
22 +6
23 +6
24 +7
25 +7
26 +8
27 +8
28 +9
29 +9
30 +10

The formula

Subtract 10 and halve the result, rounding down: floor((score - 10) / 2). Rounding down is what makes the table step rather than slope, and it is the reason two different scores so often produce the same modifier.

modifier = floor( ( score − 10 ) ÷ 2 )

Why odd scores are worth nothing on their own

Because the formula rounds down, an odd score shares its modifier with the even score below it. A 15 and a 14 are both +2, so the point that lifted 14 to 15 changes nothing until a second point arrives to make it 16.

Each odd score and the even score it shares a modifier with.
Even score Odd score Shared modifier
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

Modifier questions

How do you calculate an ability modifier in 5e?

Subtract 10 from the score and halve what is left, rounding down. A 16 gives +3, a 10 gives +0, and a 7 gives -2. The same formula applies to every ability and to every score from 1 to 30.

What is the modifier for a 20 ability score?

A 20 gives +5, which is the highest modifier a character reaches without a feature that lifts the usual cap of 20. Scores of 21 and above appear only through epic boons, artefacts, and a handful of monster stat blocks.

Why do odd ability scores not help?

Because the formula rounds down, an odd score always shares a modifier with the even number below it. A 13 and a 12 are both +1, so an odd score only becomes useful once another increase pushes it up to the next even number.

Does the modifier table change between 2014 and 2024?

No. The formula and the resulting table are identical in both rule sets. What changed in 2024 is where increases come from — the background rather than the species — not what a score converts into once you have it.

  • See what each score costs — The purchase table stops at 15, which is the only part of this range you can buy at first level.