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General Notes

At first level, your Hit Points are the maximum possible value of your Hit Die plus your Constitution Modifier. E.g. a fighter might have a hit die of 1d10, and a Constitution of 15 (+2) so their total health at level one is 12.

There are two ways to increment your maximum HP each level:

If your Constitution Modifier increases (i.e. you go from +2 to +3) then your benefit to HP is applied retroactively. See Elaboration.

Elaboration

Constitution Modifier Hit Point Increases

At level one, as a Cleric, my health is 8 + 2 (my Constitution Modifier).

At level two, I roll my Hit Die, and get a 6; my health is 8 + 6 + 4. Total 18.

At level three, I roll my Hit Die again, and get a 4, but I also increase my Constitution and end up with a modifier of +3. My health is 8 + 10 + 9. Total 27.