Fibonacci Sequence Calculator

Calculate the nth term in the Fibonacci sequence by entering the index n that you want to find.

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Fibonacci Number:

F_n =

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What is the Fibonacci Sequence?

The Fibonacci sequence is a series of numbers where each number is equal to the sum of the previous two numbers in the sequence. Each number in the sequence is denoted as F_n, where n is the index of the number in the sequence.

The Fibonacci sequence starts with F₀ and F₁ equalling 0 and 1, respectively.

The Fibonacci sequence is often represented as a spiral, which is formed when creating squares with the width of each number in the sequence.

Fibonacci spiral that is formed when forming squares with the widths of each term in the Fibonacci sequence

How to Calculate a Term in the Fibonacci Sequence

Because each term in the Fibonacci sequence is equal to the sum of the two previous terms, to solve for any term, it is required to know the two previous terms.

Formula to Solve the Nth Fibonacci Term

The equation to solve for any term in the sequence is:

F_n = F_n-1 + F_n-2

Thus, the Fibonacci term in the nth position is equal to the term in the nth minus 1 position plus the term in the nth minus 2 position.

Binet’s Formula

Named after French mathematician Jacques Philippe Marie Binet, Binet’s formula defines the equation to calculate the nth term in the Fibonacci sequence without using the recursive formula shown above.

Based on the golden ratio, Binet’s formula can be represented in the following form:

F_n = 1 / √5((1 + √5 / 2)ⁿ – (1 – √5 / 2)ⁿ)

Thus, Binet’s formula states that the nth term in the Fibonacci sequence is equal to 1 divided by the square root of 5, times 1 plus the square root of 5 divided by 2 to the nth power, minus 1 minus the square root of 5 divided by 2 to the nth power.

Binet’s formula above uses the golden ratio 1 + √5 / 2, which can also be represented as φ.

mathematical representation of Binet's formula, which is used to solve the nth term in the Fibonacci sequence

First 100 Numbers in the Fibonacci Sequence

The table below shows the first 100 numbers in the Fibonacci sequence.

First 100 numbers in the Fibonacci sequence.
n	Fibonacci Number
0	0
1	1
2	1
3	2
4	3
5	5
6	8
7	13
8	21
9	34
10	55
11	89
12	144
13	233
14	377
15	610
16	987
17	1,597
18	2,584
19	4,181
20	6,765
21	10,946
22	17,711
23	28,657
24	46,368
25	75,025
26	121,393
27	196,418
28	317,811
29	514,229
30	832,040
31	1,346,269
32	2,178,309
33	3,524,578
34	5,702,887
35	9,227,465
36	14,930,352
37	24,157,817
38	39,088,169
39	63,245,986
40	102,334,155
41	165,580,141
42	267,914,296
43	433,494,437
44	701,408,733
45	1,134,903,170
46	1,836,311,903
47	2,971,215,073
48	4,807,526,976
49	7,778,742,049
50	12,586,269,025
51	20,365,011,074
52	32,951,280,099
53	53,316,291,173
54	86,267,571,272
55	139,583,862,445
56	225,851,433,717
57	365,435,296,162
58	591,286,729,879
59	956,722,026,041
60	1,548,008,755,920
61	2,504,730,781,961
62	4,052,739,537,881
63	6,557,470,319,842
64	10,610,209,857,723
65	17,167,680,177,565
66	27,777,890,035,288
67	44,945,570,212,853
68	72,723,460,248,141
69	117,669,030,460,994
70	190,392,490,709,135
71	308,061,521,170,129
72	498,454,011,879,264
73	806,515,533,049,393
74	1,304,969,544,928,657
75	2,111,485,077,978,050
76	3,416,454,622,906,707
77	5,527,939,700,884,757
78	8,944,394,323,791,464
79	14,472,334,024,676,221
80	23,416,728,348,467,685
81	37,889,062,373,143,906
82	61,305,790,721,611,591
83	99,194,853,094,755,497
84	160,500,643,816,367,088
85	259,695,496,911,122,585
86	420,196,140,727,489,673
87	679,891,637,638,612,258
88	1,100,087,778,366,101,931
89	1,779,979,416,004,714,189
90	2,880,067,194,370,816,120
91	4,660,046,610,375,530,309
92	7,540,113,804,746,346,429
93	12,200,160,415,121,876,738
94	19,740,274,219,868,223,167
95	31,940,434,634,990,099,905
96	51,680,708,854,858,323,072
97	83,621,143,489,848,422,977
98	135,301,852,344,706,746,049
99	218,922,995,834,555,169,026
100	354,224,848,179,261,915,075