Fibonacci Calculator
Compute the nth Fibonacci number and the golden-ratio link.
Fibonacci number F(20)
6,765
F(19)
4,181
Ratio to previous
1.61803396
Each term remembers two
Starting 1, 1, each Fibonacci number sums its two predecessors: 1, 1, 2, 3, 5, 8, 13… The sequence models branching growth — sunflower spirals, pinecone rows, and rabbit-population puzzles — anywhere the new generation adds to the old.
The golden limit
Consecutive ratios converge to the golden ratio φ = (1+√5)/2 ≈ 1.618 — by F(20)/F(19) the match is already eight digits deep. Binet's closed formula computes any term directly from powers of φ, no iteration required.
Frequently asked questions
- How does the Fibonacci Calculator work?
- Compute the nth Fibonacci number and the golden-ratio link.
- Is the Fibonacci Calculator free to use?
- Yes. The Fibonacci Calculator is completely free, runs entirely in your browser, and requires no account or sign-up. Your inputs never leave your device.
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