Fibonacci Sequence Table
A complete reference table for the Fibonacci sequence, showing each term, its value, and its ratio to the previous term. The sequence begins with 0 and 1, and each subsequent number is the sum of the two preceding ones — a pattern that appears throughout mathematics, nature, and art.
Fibonacci Calculator
Find the nth number in the Fibonacci sequence (F₀ = 0, F₁ = 1).
F(10)55
What is the Fibonacci Sequence?
The Fibonacci sequence is defined by the recurrence relation:
- F(0) = 0
- F(1) = 1
- F(n) = F(n−1) + F(n−2) for n ≥ 2
As the sequence progresses, the ratio between consecutive terms converges to the golden ratio φ ≈ 1.61803398875, one of the most remarkable constants in mathematics.
Fibonacci Sequence (F(0) to F(50))
The table below shows the term index n, the Fibonacci value F(n), and the ratio F(n)/F(n−1) converging toward the golden ratio φ.
| n | F(n) | F(n) / F(n−1) |
|---|---|---|
| 0 | 0 | — |
| 1 | 1 | — |
| 2 | 1 | 1.000000 |
| 3 | 2 | 2.000000 |
| 4 | 3 | 1.500000 |
| 5 | 5 | 1.666667 |
| 6 | 8 | 1.600000 |
| 7 | 13 | 1.625000 |
| 8 | 21 | 1.615385 |
| 9 | 34 | 1.619048 |
| 10 | 55 | 1.617647 |
| 11 | 89 | 1.618182 |
| 12 | 144 | 1.617978 |
| 13 | 233 | 1.618056 |
| 14 | 377 | 1.618026 |
| 15 | 610 | 1.618037 |
| 16 | 987 | 1.618033 |
| 17 | 1,597 | 1.618034 |
| 18 | 2,584 | 1.618034 |
| 19 | 4,181 | 1.618034 |
| 20 | 6,765 | 1.618034 |
| 21 | 10,946 | 1.618034 |
| 22 | 17,711 | 1.618034 |
| 23 | 28,657 | 1.618034 |
| 24 | 46,368 | 1.618034 |
| 25 | 75,025 | 1.618034 |
| 26 | 121,393 | 1.618034 |
| 27 | 196,418 | 1.618034 |
| 28 | 317,811 | 1.618034 |
| 29 | 514,229 | 1.618034 |
| 30 | 832,040 | 1.618034 |
| 31 | 1,346,269 | 1.618034 |
| 32 | 2,178,309 | 1.618034 |
| 33 | 3,524,578 | 1.618034 |
| 34 | 5,702,887 | 1.618034 |
| 35 | 9,227,465 | 1.618034 |
| 36 | 14,930,352 | 1.618034 |
| 37 | 24,157,817 | 1.618034 |
| 38 | 39,088,169 | 1.618034 |
| 39 | 63,245,986 | 1.618034 |
| 40 | 102,334,155 | 1.618034 |
| 41 | 165,580,141 | 1.618034 |
| 42 | 267,914,296 | 1.618034 |
| 43 | 433,494,437 | 1.618034 |
| 44 | 701,408,733 | 1.618034 |
| 45 | 1,134,903,170 | 1.618034 |
| 46 | 1,836,311,903 | 1.618034 |
| 47 | 2,971,215,073 | 1.618034 |
| 48 | 4,807,526,976 | 1.618034 |
| 49 | 7,778,742,049 | 1.618034 |
| 50 | 12,586,269,025 | 1.618034 |
Key Properties
- Golden ratio: lim F(n+1)/F(n) = φ = (1 + √5) / 2 ≈ 1.61803398875…
- Every 3rd term is divisible by 2, every 4th by 3, every 5th by 5 (Pisano periods).
- Sum of first n terms: F(1) + F(2) + … + F(n) = F(n+2) − 1.
- Binet's formula: F(n) = (φⁿ − ψⁿ) / √5, where ψ = (1 − √5) / 2.
- Perfect squares: F(1) = 1, F(2) = 1, F(12) = 144 are the only perfect square Fibonacci numbers.