dnd-5e – How to Convert Monster CR into XP: Generalized Formulas

cr-calculationdnd-5eexperience-points

I am trying to make a spreadsheet to track encounters, and I was wondering if there is any generalised formula I can use to calculate the average XP for any given Challenge Rating, or is it like character advancement in that there's no consistent formula for such? An approximation is also acceptible.

Best Answer

As pointed out by @Thomas Markov, the Table is odd. I expect that some rounding occurred to get "nice-looking" numbers, plus 2 bumps (CR 17 and CR 20), and an acceleration of the growth rate post CR 20.

I expected a quadratic curve, so went looking for an arithmetic progression, and it turns out that the increase from CR N-1 to CR N is close to (N + N / 7) * 100, using integer division on N.

With an offset, we get the closed formula for CR N: 100 + \sum_{1}^{n} (i + i/7) * 100.

CR Actual XP Predicted XP Error
1 200 200 0
2 450 400 -50
3 700 700 0
4 1,100 1,100 0
5 1,800 1,600 -200
6 2,300 2,200 -100
7 2,900 3,000 +100
8 3,900 3,900 0
9 5,000 4,900 -100
10 5,900 6,000 +100
11 7,200 7,200 0
12 8,400 8,500 +100
13 10,000 9,900 -100
14 11,500 11,500 0
15 13,000 13,200 +200
16 15,000 15,000 0

From there on, however, the formula gets much more inaccurate:

  • There's a weird +1,000 bonus for CR 17.
  • There's another +1,000 bonus for CR 20.
  • The rate of growth increase from CR 21 onward.

I suppose further tweaks to the formula could fold in the bumps and increase in rate of growth, but at this point I expect it's just easier to use a look-up table.

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