# Experience

Experience, commonly abbreviated as EXP or XP, is a measure of progress in a certain skill. It is obtained by performing tasks related to that skill. Experience can also be gained through other means, such as quests, the book of knowledge from the Surprise Exam random event, a lamp from the genie random event, certain minigames, and lamps for completing parts of the Achievement Diary and Combat Achievements.

After gaining a certain amount of experience, players will advance to the next level in that skill, which can result in new abilities, and the chance to try more quests. The amount of experience needed for the next level is approximately 10% more than the last level. For example, 83 experience is required for advancement to level 2, while 91 experience is required for advancement to level 3. Reaching level 99 in a skill requires a total of 13,034,431 experience. By around level 30, the exponential factor predominates, so that the amount of experience required doubles for each 7th level. Accordingly, level 92 is nearly the exact halfway mark to level 99, requiring 6,517,253 experience, and level 85 requires very nearly one quarter of the experience needed for level 99.

Experience is stored as a 32-bit integer with one decimal point,[1] although the game does not display decimal values; for example, if a player receives two experience drops of 2.5, the first is shown as 2 and the second as 3 (or vice versa depending on their existing experience points). Experience values that would have multiple decimal points, such as through multiplication with experience-boosting sets, are rounded down to one decimal. The maximum experience that can be obtained in one skill is 200,000,000. The skill can still be trained afterwards, but no experience will be received.

## Experience table

### Levels 1-99

The experience difference between level ${\textstyle L-1}$ and level ${\textstyle L}$ is ${\textstyle {\frac {1}{4}}\left\lfloor L-1+300\cdot 2^{\frac {L-1}{7}}\right\rfloor }$. The tables below show this experience difference for each level and also the cumulative experience from level 1 to level ${\textstyle L}$.

Level Exp. Exp. Diff % to 99 Level Exp. Exp. Diff % to 99 Level Exp. Exp. Diff % to 99 Level Exp. Exp. Diff % to 99
1 0 N/A 0.00 26 8,740 898 0.07 51 111,945 10,612 0.86 76 1,336,443 126,022 10.25
2 83 83 0.00 27 9,730 990 0.07 52 123,660 11,715 0.95 77 1,475,581 139,138 11.32
3 174 91 0.00 28 10,824 1,094 0.08 53 136,594 12,934 1.05 78 1,629,200 153,619 12.50
4 276 102 0.00 29 12,031 1,207 0.09 54 150,872 14,278 1.16 79 1,798,808 169,608 13.80
5 388 112 0.00 30 13,363 1,332 0.10 55 166,636 15,764 1.28 80 1,986,068 187,260 15.24
6 512 124 0.00 31 14,833 1,470 0.11 56 184,040 17,404 1.41 81 2,192,818 206,750 16.82
7 650 138 0.00 32 16,456 1,623 0.13 57 203,254 19,214 1.56 82 2,421,087 228,269 18.57
8 801 151 0.01 33 18,247 1,791 0.14 58 224,466 21,212 1.72 83 2,673,114 252,027 20.51
9 969 168 0.01 34 20,224 1,977 0.16 59 247,886 23,420 1.90 84 2,951,373 278,259 22.64
10 1,154 185 0.01 35 22,406 2,182 0.17 60 273,742 25,856 2.10 85 3,258,594 307,221 25.00
11 1,358 204 0.01 36 24,815 2,409 0.19 61 302,288 28,546 2.32 86 3,597,792 339,198 27.60
12 1,584 226 0.01 37 27,473 2,658 0.21 62 333,804 31,516 2.56 87 3,972,294 374,502 30.48
13 1,833 249 0.01 38 30,408 2,935 0.23 63 368,599 34,795 2.83 88 4,385,776 413,482 33.65
14 2,107 274 0.02 39 33,648 3,240 0.26 64 407,015 38,416 3.12 89 4,842,295 456,519 37.15
15 2,411 304 0.02 40 37,224 3,576 0.29 65 449,428 42,413 3.45 90 5,346,332 504,037 41.02
16 2,746 335 0.02 41 41,171 3,947 0.32 66 496,254 46,826 3.81 91 5,902,831 556,499 45.29
17 3,115 369 0.02 42 45,529 4,358 0.35 67 547,953 51,699 4.20 92 6,517,253 614,422 50.00
18 3,523 408 0.03 43 50,339 4,810 0.39 68 605,032 57,079 4.64 93 7,195,629 678,376 55.20
19 3,973 450 0.03 44 55,649 5,310 0.43 69 668,051 63,019 5.13 94 7,944,614 748,985 60.95
20 4,470 497 0.03 45 61,512 5,863 0.47 70 737,627 69,576 5.66 95 8,771,558 826,944 67.30
21 5,018 548 0.04 46 67,983 6,471 0.52 71 814,445 76,818 6.25 96 9,684,577 913,019 74.30
22 5,624 606 0.04 47 75,127 7,144 0.58 72 899,257 84,812 6.90 97 10,692,629 1,008,052 82.03
23 6,291 667 0.05 48 83,014 7,887 0.64 73 992,895 93,638 7.62 98 11,805,606 1,112,977 90.57
24 7,028 737 0.05 49 91,721 8,707 0.70 74 1,096,278 103,383 8.41 99 13,034,431 1,228,825 100.00
25 7,842 814 0.06 50 101,333 9,612 0.78 75 1,210,421 114,143 9.29

### Virtual levels

Level Exp. Exp. Diff Level Exp. Exp. Diff Level Exp. Exp. Diff
100 14,391,160 1,356,729 109 35,085,654 3,307,711 118 85,539,082 8,064,254
101 15,889,109 1,497,949 110 38,737,661 3,652,007 119 94,442,737 8,903,655
102 17,542,976 1,653,867 111 42,769,801 4,032,140 120 104,273,167 9,830,430
103 19,368,992 1,826,016 112 47,221,641 4,451,840 121 115,126,838 10,853,671
104 21,385,073 2,016,081 113 52,136,869 4,915,228 122 127,110,260 11,983,422
105 23,611,006 2,225,933 114 57,563,718 5,426,849 123 140,341,028 13,230,768
106 26,068,632 2,457,626 115 63,555,443 5,991,725 124 154,948,977 14,607,949
107 28,782,069 2,713,437 116 70,170,840 6,615,397 125 171,077,457 16,128,480
108 31,777,943 2,995,874 117 77,474,828 7,303,988 126 188,884,740 17,807,283
Max 200,000,000 11,115,260

## Formula

The formula needed to calculate the amount of experience needed to reach level ${\textstyle L}$ is:

${\displaystyle {\text{Experience}}=\left\lfloor {{\frac {1}{4}}\sum _{\ell =1}^{L-1}}\left\lfloor {\ell +300\cdot 2^{\ell /7}}\right\rfloor \right\rfloor }$

If the floor functions are ignored, the resulting summation can be found in closed form to be:

${\displaystyle {\text{Experience}}\approx {\frac {1}{8}}\left({L}^{2}-L+600\,{\frac {{2}^{L/7}-2^{1/7}}{{2}^{1/7}-1}}\right)}$

The approximation is very accurate, always being within 14 experience of the true value.

One final approximation is

${\displaystyle {\text{Experience}}\approx {\frac {1}{8}}\left({L}^{2}-L+600\,{\frac {{2}^{L/7}-2^{1/7}}{{2}^{1/7}-1}}\right)-{\frac {L}{10}}-\gamma }$

where ${\textstyle \gamma }$ is the Euler–Mascheroni constant. This approximation always gives an answer within 1 experience of the true value.

## Graphs

The experience required for each level can be graphed. Graphing the experience required on a linear scale shows that the experience required is essentially exponential.

Graphing the same data on a logarithmic scale shows that the function starts being exponential around level 15.