Fibonacci Generator
Generate Fibonacci sequences, check if a number is Fibonacci, and see the golden ratio convergence.
Enter 1 to 1,000.
Golden Ratio (φ)
1.6180339887
F(n)/F(n−1) converges to
1.6180340557
20 terms
| n | F(n) | F(n)/F(n−1) |
|---|---|---|
| 0 | 0 | — |
| 1 | 1 | — |
| 2 | 1 | 1.0000000000 |
| 3 | 2 | 2.0000000000 |
| 4 | 3 | 1.5000000000 |
| 5 | 5 | 1.6666666667 |
| 6 | 8 | 1.6000000000 |
| 7 | 13 | 1.6250000000 |
| 8 | 21 | 1.6153846154 |
| 9 | 34 | 1.6190476190 |
| 10 | 55 | 1.6176470588 |
| 11 | 89 | 1.6181818182 |
| 12 | 144 | 1.6179775281 |
| 13 | 233 | 1.6180555556 |
| 14 | 377 | 1.6180257511 |
| 15 | 610 | 1.6180371353 |
| 16 | 987 | 1.6180327869 |
| 17 | 1597 | 1.6180344478 |
| 18 | 2584 | 1.6180338134 |
| 19 | 4181 | 1.6180340557 |
Formulae
F(0) = 0, F(1) = 1, F(n) = F(n−1) + F(n−2)
φ = (1 + √5) / 2 ≈ 1.618034
Fibonacci test: N is Fibonacci iff 5N² ± 4 is a perfect square
Binet's formula: F(n) = (φ^n − ψ^n) / √5, where ψ = 1 − φ
How to use
- 1
Choose a mode
Select Generate Sequence or Check Number.
- 2
Enter a value
For generation, enter how many terms. For checking, enter the number to test.
- 3
View results
The sequence is displayed in a table with index, value, and ratio columns.
Frequently asked questions
What is the Fibonacci sequence?
What is the golden ratio?
How do I check if a number is Fibonacci?
Is my data sent anywhere?
Generate the Fibonacci sequence up to the Nth term with BigInt support
for large values. Check whether any number belongs to the Fibonacci
sequence. See the golden ratio convergence as F(n+1)/F(n) approaches
phi. Supports custom starting values for generalized Fibonacci sequences.
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