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The Experience Formula based on the Level is as follows:

$\frac{50}{3} \left( x^{3} - 6x^{2} + 17x - 12 \right)$

where $x$ is the Level.

To find out how much experience you need to advance to the next level, simply subtract the amount of experience of the next level from the current amount of experience that your character has. You can also find a premade experience table here.
Another way to find out how much experience you need to advance to the next level, is the following formula (credit to Aopa Gody):
$A\left(x\right)$ is the amount of experience needed to level from level x-1 to level x.
$A\left(2\right) = A\left(3\right) = 100$
$A\left(x\right) = 2A\left(x-1\right)-A\left(x-2\right)+100$

If you want to know how many of the same creatures you need to kill in order to advance to the next level, you need to find out the amount of experience needed for the next level as explained before, and divide that by the total experience points that the creature gives you.

## Mathematics behind the formula

The experience needed to advance from level $x-1$ to level $x$ is
$50\left(x^{2} - 5x + 8\right)$
From this we can calculate the experience required to advance from level $1$ to level $x$ by the summation
$\sum_{n=2}^{x}\left(50\left(n^{2} - 5n + 8\right)\right) =$
$= 50\sum_{n=2}^{x}\left(n^{2}\right) - 250\sum_{n=2}^{x}\left(n\right) + 400\sum_{n=2}^{x}\left(1\right)$

By substituting the modified Gauss equations
$\sum_{n=2}^{x}\left(n\right) = \frac{n\left(n+1\right)}{2} - 1$
and
$\sum_{n=2}^{x}\left(n^2\right) = \frac{n\left(n+1\right)\left(2n+1\right)}{6} - 1$
We get
$50\left(\frac{x\left(x+1\right)\left(2x+1\right)}{6} - 1\right) - 250\left(\frac{x\left(x+1\right)}{2} - 1\right) + 400\left(x-1\right) =$
$= 50\left(\frac{2x^{3} + 3x^{2} + x}{6} - 1\right) - 250\left(\frac{x^{2} + x}{2} - 1\right) + 400x - 400 =$
$= \frac{100x^{3} + 150x^{2} + 50x}{6} - 50 - \frac{250x^{2} + 250x}{2} + 250 + 400x - 400 =$
$= \frac{50}{3}x^{3} + 25x^{2} + \frac{25}{3}x - 50 - 125x^{2} - 125x + 250 + 400x - 400 =$
$= \frac{50}{3}x^{3} - 100x^{2} + \frac{850}{3}x - 200 =$
$= \frac{50}{3}\left(x^{3} - 6x^{2} + 17x - 12\right)$

Or simply: $\frac{50 lvl^{3} - 150 lvl^{2} + 400 lvl}{3}$
For example, level 15:
$\frac{50 \cdot \left(15 - 1\right)^{3} - 150 \cdot \left(15 - 1\right)^{2} + 400 \cdot \left(15 - 1\right)}{3} = 37,800$

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