Experience Table

Note: Enabling "Virtual Levels" in the Settings will show the player if they would be on a level higher than 99, even though this gives no benefits. The experience difference between level [math]\displaystyle{ L-1 }[/math] and level [math]\displaystyle{ L }[/math] is [math]\displaystyle{ \left\lfloor \frac{1}{4} \left( L-1+300 \left\lfloor 2^{\frac{L-1}{7}} \right\rfloor \right) \right\rfloor }[/math]. The table below show this experience difference for each level and also the cumulative experience from level 1 to level [math]\displaystyle{ L }[/math].

Level	XP	Difference		Level	XP	Difference		Level	XP	Difference		Level	XP	Difference
1	0	0		26	8,740	898		51	111,945	10,612		76	1,336,443	126,022
2	83	83		27	9,730	990		52	123,660	11,715		77	1,475,581	139,138
3	174	91		28	10,824	1,094		53	136,594	12,934		78	1,629,200	153,619
4	276	102		29	12,031	1,207		54	150,872	14,278		79	1,798,808	169,608
5	388	112		30	13,363	1,332		55	166,636	15,764		80	1,986,068	187,260
6	512	124		31	14,833	1,470		56	184,040	17,404		81	2,192,818	206,750
7	650	138		32	16,456	1,623		57	203,254	19,214		82	2,421,087	228,269
8	801	151		33	18,247	1,791		58	224,466	21,212		83	2,673,114	252,027
9	969	168		34	20,224	1,977		59	247,886	23,420		84	2,951,373	278,259
10	1,154	185		35	22,406	2,182		60	273,742	25,856		85	3,258,594	307,221
11	1,358	204		36	24,815	2,409		61	302,288	28,546		86	3,597,792	339,198
12	1,584	226		37	27,473	2,658		62	333,804	31,516		87	3,972,294	374,502
13	1,833	249		38	30,408	2,935		63	368,599	34,795		88	4,385,776	413,482
14	2,107	274		39	33,648	3,240		64	407,015	38,416		89	4,842,295	456,519
15	2,411	304		40	37,224	3,576		65	449,428	42,413		90	5,346,332	504,037
16	2,746	335		41	41,171	3,947		66	496,254	46,826		91	5,902,831	556,499
17	3,115	369		42	45,529	4,358		67	547,953	51,699		92	6,517,253	614,422
18	3,523	408		43	50,339	4,810		68	605,032	57,079		93	7,195,629	678,376
19	3,973	450		44	55,649	5,310		69	668,051	63,019		94	7,944,614	748,985
20	4,470	497		45	61,512	5,863		70	737,627	69,576		95	8,771,558	826,944
21	5,018	548		46	67,983	6,471		71	814,445	76,818		96	9,684,577	913,019
22	5,624	606		47	75,127	7,144		72	899,257	84,812		97	10,692,629	1,008,052
23	6,291	667		48	83,014	7,887		73	992,895	93,638		98	11,805,606	1,112,977
24	7,028	737		49	91,721	8,707		74	1,096,278	103,383		99	13,034,431	1,228,825
25	7,842	814		50	101,333	9,612		75	1,210,421	114,143

The formula needed to calculate the amount of experience needed to reach level L is:

[math]\displaystyle{ \mathit{Experience} = \left \lfloor{\frac{1}{4}\sum_{\ell=1}^{L-1}}\left\lfloor{\ell + 300\cdot2^{\ell/7}}\right\rfloor\right\rfloor }[/math]

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

[math]\displaystyle{ \mathit{Experience} \approx \frac{1}{8} \left( {L}^{2} - L + 600 \, \frac{{2}^{L/7}-2^{1/7}} {{2}^{1/7}-1} \right) }[/math]

The approximation is very accurate, always within 100 experience but usually less than around 10 experience.

Melvor Idle version v1.2.2 (Released: 15th November 2023)
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