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Is there a mathematical formula to determine how much XP is needed per level? In other words Is there a consistent formula for determining how much XP is needed to go up to any given level?

I originally thought it was the previous amount times 2, but that doesn't work for all levels.

I understand that there is a character advancement table, but I'm curious as to how they got those numbers and whether there is some mathematical formula to work it out.

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No, there is no simple formula for level-by-level XP requirements.

WOTC has stated that the advancement rate is not constant across all levels. Rather, according to Unearthed Arcana: Three-Pillar Experience (August 2017), the standard XP and leveling system presented in the PHB

has faster advancement in a few spots [than the variant rules proposed in the UA.]

Note that although the quote comes from a UA playtest article, the quote itself is not playtest material -- it's the designers' commentary comparing the playtest material to the standard PHB rules.

And indeed if you look at the XP values required to advance from level to level, you won't be able to work out a straightforward mathematical formula for them, such as simple linearity or even exponentiality.

And the reasoning behind that less-than-straightforward system is clear: the designers wanted to make it faster to reach certain levels. For example, per Mike Mearls, the designers found through research that campaigns tend to stall at level 10, so they shortened the advancement track from 10 to 11.

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After doing some interpolation I found that this equation was the best-fit (note \$x\$=level):

$$ \text{XP}=3.7825 x^4-134.59 x^3+2572.6 x^2-10699 x+10703 $$

Here is my data graph I hope it helps

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    \$\begingroup\$ Welcome to RPG.SE! Take the tour if you haven't already and see the help center or ask us here in the comments (use @ to ping someone) if you need more guidance. I made an edit to pretty up your equation, please double check I didn't bork anything up and ask if you have questions about the MathJax. Good Luck and Happy Gaming! \$\endgroup\$ – Someone_Evil Sep 2 '19 at 16:23
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If you are using an Excel spreadsheet, you could use:

=CEILING(3.7825*Level^4-134.59*Level^3+2572.6*Level^2-10699*Level+10703,10^(LEN(ROUND(3.7825*Level^4-134.59*Level^3+2572.6*Level^2-10699*Level+10703,0))-2))

Exchange "Level" for the cell containing the Level value, and you would get a nice rounded value.

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  • \$\begingroup\$ Hi Daniel, welcome to rpg.se! Take the tour and visit the help center or ask here in the comments (use @ to ping someone) for more information. This is a great first answer, you could improve it slightly by mentioning how you calculated this or how it works. But overall a great answer. Thanks for participating and happy gaming! \$\endgroup\$ – linksassin Apr 16 at 5:28

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