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I have a spreadsheet that tracks the XP for our group and I've gotten tired of manually looking up how much xp is needed for the next level.
I'd much prefer if there was a formula I could put on the spreadsheet that would calculate the level given the XP? (Without using a lookup table)
We'll start with this post:
"After 2nd level, the amount of experience you need to gain a level goes up by 250 points (i.e., you need +1,000 to reach level 2, +1,250 to reach level 3, etc.). After four levels of this, the 'additional' amount increases to 500. About the point you'd expect this to continue, it gets extremely erratic on levels 11 (+1,500) and 12 (+500), then reverts back to +1,000 at 13th and 14th. Levels 15-18 add +2,000 each, and 19-20 start at +4,000 -- this implies the amount added doubles every four levels.
Except that level 21 adds +8,000, and 22 adds +3,000. After that little bit of weirdness, it does +10,000 for four levels, and +25,000 for the last four."
Here's a rough chart of the results; the first column is from the RAW, the second removes the 'jagged' parts, and the third assumes a simple doubling every time. The numbers on the latter two look funny, but the progression itself is easier to predict.
RAW Smooth Doubler 1 0 0 0 2 1,000 1,000 1,000 3 2,250 2,250 2,250 4 3,750 3,750 3,750 5 5,500 5,500 5,500 6 7,500 7,500 7,500 7 10,000 10,000 10,000 8 13,000 13,000 13,000 9 16,500 16,500 16,500 10 20,500 20,500 20,500 11 26,000 25,500 25,500 <- 500 XP difference 12 32,000 31,500 31,500 13 39,000 38,500 38,500 14 47,000 46,500 46,500 15 57,000 56,500 56,500 16 69,000 68,500 68,500 17 83,000 82,500 82,500 18 99,000 98,500 98,500 19 119,000 118,500 118,500 20 143,000 142,500 142,500 21 175,000 170,500 170,500 <- 4,500 XP difference 22 210,000 202,500 202,500 <- 7,500 XP difference 23 255,000 244,500 242,500 <- 10,500/12,500 24 310,000 296,500 290,500 <- 13,500/19,500 25 375,000 358,500 346,500 <- 16,500/28,500 26 450,000 430,500 410,500 <- 19,500/39,500 27 550,000 527,500 490,500 <- 22,500/59,500 28 675,000 649,500 586,500 <- 25,500/88,500 29 825,000 796,500 698,500 <- 28,500/126,500 30 1,000,000 968,500 826,500 <- 31,500/176,500
There are no clean mathematical formulas to approximate this, according to the curve-fitting service ZunZun.com. While my prior equation did serve to ... output the rates of increase, a lookup table or your own XP chart should serve better.
Curiously, this does highlight some interesting questions about the relative time per level, suggesting that a custom XP chart may provide a more consistent levelling experience for your players.
Edit.
Here's a quick and dirty reverse lookup that worked in excel 2008.
=VLOOKUP(A1,{0,1;1000,2;2250,3;3750,4;5500,5;6500,6;10000,7;13000,8;16500,9;20500,10;26000,11;32000,12;39000,13;47000,14;57000,15;69000,16;83000,17;99000,18;119000,19;143000,20;175000,21;210000,22;225000,23;310000,24;375000,25;450000,26;550000,27;675000,28;825000,29;1000000,30},2)
While the progression isn't readily codified, here's the lookup formula (replace the reference to A1 with the cell with character level) so you don't have to look in the book:
=CHOOSE(MAX(MIN(31,A1),1),0, 1000, 2250, 3750, 5500, 7500, 10000, 13000, 16500, 20500, 26000, 32000, 39000, 47000, 57000, 69000, 83000, 99000, 119000, 143000, 175000, 210000, 255000, 310000, 375000, 450000, 550000, 675000, 825000, 1000000, "—")
Why the MAX() function? So that it doesn't choke on a blank field.
Why the MIN() function? The maximum entry from the table is level 29, so if the character
is 30 or above, it uses the 30th entry.
The choose function looks at the first entry for a numerical index value of 1-N, and the rest of the entry is a list N long of results.
I use a table and the VLOOKUP function in Excel for this kind of thing. You can input all the values for the levels in a table similar to what Brian has shown. Put this on another (or hidden) page and then use the lookup functions so the level is automatically updated when the value of the XP cell changes.
When using the VLOOKUP function, the first column needs to be the min XP required for that level, and the 2nd column is the level.
=VLOOKUP("cell address/name containing XP","address/name of table",2,TRUE) The '2' indicates that you will return the value from the 2nd column in the table. The 'TRUE' indicates that an exact match is not required on the XP value.
I'm sure there are better ways to do this... it works for me. AW9 being the XP cell.
=ifs(AW9>=355000,20,AW9>=305000,19,AW9>=265000,18,AW9>=225000,17,AW9>=195000,16,AW9>=165000,15,AW9>=140000,14,AW9>=120000,13,AW9>=100000,12,AW9>=85000,11,AW9>=64000,10,AW9>=48000,9,AW9>=34000,8,AW9>=23000,7,AW9>=14000,6,AW9>=6500,5,AW9>=2700,4,AW9>=900,3,AW9>=300,2,AW9<299,1)
EDIT Apparently they totally changed stuff for 4e, my answer is only for 3e.
This is a common misconception that there is no formula, in fact someone once told me there was a proof that there is no possible formula! But, in direct contradiction to that, I present to you the following formulas I just derived (you can check it easily in Excel):
If the level is n
XP to get to the next level: (n^2+n)*1/2*1000
XP to attain that level (as is how it is written in the DnD books): (n^2-n)*1/2*1000
