Is Con modifier × level added to HP every level-up?

Question

I am new to D&D and I'm starting with the 5th edition. I have a question about how many hit points I have for a level. I am confused about the con modifier per level and if it is added to first level.

Let's say my con modifier is +3 and I decide to take 6 instead of rolling the d10 (as a Ranger).

• Hit Points at 1st level: 10 + Constitution Modifier

• Hit Points at Higher Levels: 1d10 (or 6) + your Constitution Modifier per ranger level after 1st.

At first level, my HP is 13. OK. That I understand. At the 2nd level is it 6 + 3 (con. modifier) equal to 9, then added to my first level's HP, for a total of 22? Or is it 6 + 3 (con modifier for first level) + 3 (con modifier for second level) equal to 12? Then is this added to the HP from first level?

If you could give me an example of, say, the first 4 levels of a ranger using the numbers I gave you (6 instead of d10 and +3 as a con modifier), that might make it easier to explain.

Answer 1

Each level, you get Hit Die + Constitution modifier additional Maximum HP. You always take the maximum of the Hit Die at 1st level; afterward, you may roll the Hit Die or take its average rounded up.

Therefore, with a 1d10 Hit Die and +3 Constitution modifier, assuming you take 6 each time instead of rolling:

\begin{array}{rrcrcrcr} \text{1st level:} & 10 & + & 3 &&& = & 13 \\ \text{2nd level:} & 6 & + & 3 & + & 13 & = & 22 \\ \text{3rd level:} & 6 & + & 3 & + & 22 & = & 31 \\ \text{4th level:} & 6 & + & 3 & + & 31 & = & 40 \\ \end{array}

In short, you will add 9 HP for each level beyond 1st.

If your Constitution modifier later changes, it will apply the new bonus for every level you had so far. So if at level 4 your Constitution modifier is boosted to +4 instead of +3 (for a difference of 1), you will add 4 HP because you are level 4, which will make your HP 44 instead of 40. (It's basically as if your Constitution modifier were +4 all along.)

Answer 2

1st level: 10 + Con mod hit points = 13

2nd level: 6 + Con mod additional hit points for a total of 13 + 9 = 22 hit points

3rd level: 6 + Con mod additional hit points for a total of 22 + 9 = 31 hit points

4th level: 6 + Con mod additional hit points for a total of 31 + 9 = 40 hit points

Answer 3

To calculate hp using the default unrolled amount per level you need to know 3 variables: Hit Dice, Current Level, and Constitution Modifier.

Hit Dice(hd): The die size for the class you are playing.
1d6 - Sorceror, Wizard
1d8 - Bard, Cleric, Druid, Monk, Rogue, Warlock
1d10 - Fighter, Paladin, Ranger
1d12 - Barbarian

Current Level(lvl): The level you want to calculate hitpoints for.

Constitution Modifier(cm): Your bonus or penalty to constitution. If you have 14 con your bonus would be +2. For the sake of this calculation if you have the tough feat add an additional +2 to your con modifier. Because changes to constitution modifier are applied retroactively one formula can calculate your total hitpoints at any level or change in constitution modifier.

The calculation is: hd + (lvl - 1) x (hd/2 + 1) + cm x lvl

Example: A level 20 Barbarian, hit dice size 12, constitution modifier +6.

Total HP = 12 + (20 - 1) x (12/2 + 1) + 6x20
= 12 + 19x7 + 6x20
= 12 + 133 + 120
= 265

In excel you can use the following formula assuming A1 = hit dice, A2 = level, A3 = constitution modifier: =A1+(A2-1)*(A1/2+1)+A3*A2

tl;dr Short answer is the con mod is added each time you level, but should it change at any time your hitpoints gained previously need to be recalculated with the updated constitution modifier. More information about hitpoints as you level can be found on page 15 of the Players Handbook.