Fibonacci Sequence Generator
Generate the Fibonacci sequence up to N terms or up to a maximum value.
Terms
20
Largest value
4,181
Golden ratio
≈ 1.618034
| n | F(n) | F(n)/F(n−1) |
|---|---|---|
| 0 | 0 | — |
| 1 | 1 | 1.000000 |
| 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 |
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How it works
Enter the number of terms you want, or a maximum value to stop at. The tool generates the Fibonacci sequence starting from 0 and 1, where each subsequent number is the sum of the two before it. It displays the full sequence in a table with term index, value, and ratio to the previous term (which converges toward the golden ratio φ ≈ 1.618). All calculation runs locally in your browser.
F(n) = F(n−1) + F(n−2), F(0)=0, F(1)=1
Common use cases
- Looking up a specific Fibonacci number for a math problem or puzzle.
- Demonstrating the golden ratio convergence in a Fibonacci sequence.
- Generating Fibonacci numbers for use in algorithm design or data structure sizing.
Frequently asked questions
What is the golden ratio?
The ratio of consecutive Fibonacci numbers converges to φ ≈ 1.6180339887, the golden ratio. This appears throughout nature, art, and architecture.
How many terms can I generate?
JavaScript numbers stay precise up to about F(78). Beyond that, numbers exceed integer precision. The tool handles up to 80 terms accurately.