Fibonacci Sequence Calculator
Find the nth Fibonacci number exactly (F(100) = 354,224,848,179,261,915,075).
Change the values and press Calculate to work out your own figures.
Enter n; F(0) = 0 and F(1) = 1.
Show the working
- F(0) = 0, F(1) = 1, F(n) = F(n − 1) + F(n − 2)
How to use it
Enter n; F(0) = 0 and F(1) = 1.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
F(n) = F(n − 1) + F(n − 2), F(0) = 0, F(1) = 1
The golden ratio
F(n) ÷ F(n − 1) approaches φ = 1.618…
Fibonacci numbers
| n | F(n) |
|---|---|
| 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 |
Questions
What is F(10)?
55.
Is F(0) 0 or 1?
0; F(1) = F(2) = 1.
Formulas
F(n) = F(n − 1) + F(n − 2), F(0) = 0, F(1) = 1
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).