Formula for calculating skill lvl from xp

Just out of curiosity I derived a formula for calculating the skill level from a known amount of experience points. The formula is

lvl = 99 + (log (xp/13M) / log 1.1041)

where xp is the known amount of experience points and 13M is the amount of experience points reguired for lvl 99, i.e. 13,034,431.

For example, let's say that I know that after a long mining project I will have 2,532,000 xp in mining. To calculate which mining lvl I will have after the project I can use the formula as follows

lvl = 99 + (log (2,532,000/13,034,431) / log 1.1041)
lvl = 99 + (log 0.1943 / log 1.1041)
lvl = 99 + (-0.7115 / 0.0430)
lvl = 99 + (-16.5465)
lvl = 82.4535

I will be on lvl 82 and about halfway to lvl 83.

Yes, I know it would be easier to just look it up in the table in rsbandb's skill guides, but just as a curiosity I thought I'd post it here. I use it myself in an Excel table that I use to keep track of what my skill lvls are going to be after I've finished mining about 32k coal and 8k mith that I need to smelt and smith in order to reach lvl 70 in smithing.

This formula is 0.4% accurate from lvl 50 and up (meaning the error is a maximum of 487 xp, which is not much at those amounts). It's pretty accurate even from lvl 30 and up. Below that the manual adjustments that Jagex has made to the xp reguirements have too big an impact and it throws the formula off. That's right, the xp reguirements do not grow at a steady rate, they have been adjusted somewhat, especially on the lower lvls, but at the higher lvls the growth rate is about 1.1041 times the xp reguirement of the previous lvl.

That's nice. I have no idea what else to say. o.0

Hehe, took me about 4 hours of calculating, testing and confirming. I had to look up the mathematical laws of exponential growth and natural logarithms from different sources on the web. Funny side note, after all that research online the ad banner on top of the forum page now reads:



Cookies are sometimes frighteningly efficient

wha...
wha...
wha...

wow

good maths work

wtf?

i didnt get 1 word of that.....u must be some supa smart ****

Hard to say what math lvl this is, I'm not from the States. I learned this at the age of 15 or 16. High school math in other words.

Anyhoo, it's not hard to use. Don't be scared by the "log". Even the simplest scientific calculator has a "log" button. There's one in the Windows calculator, too, if you switch it into scientific mode.

Here, try it: just start by dividing the known amount of xp with the xp reguired for lvl 99, e.g. 2,532,000/13,034,431=0.1943 (I'll use the same example as above). Then hit the "log" button and the readout should be -0.7115. I've rounded these, so they're off by a decimal or two. Hit the division button, enter 1.1041 and hit "log" again. The readout says 0.0430. Then hit enter and the calculator divides the two logarithms, giving -16.4565. This is the figure to add to 99 (or subtract from 99, however you want to see it): -16.4565 + 99 = 82.4535.

Note that when you don't round the figures during the calculations the formula gives a more accurate result.

But, like I said, it's not very useful for this kind of calculating, it's much more convenient to just check the skill table on rsbandb. I use this formula in my Excel table because the known xp keeps changing and this way I don't have to count it every single time. I just enter the amount of xp I have atm and what I expect to mine in the future and the formula instantly gives the mining skill lvl I will be on after that.

For gods sake. Turn off 3rd party cookies. BIG security hole there.