Fibonacci Number Calculator
F(n) = F(n−1) + F(n−2). 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
Result
F(20)
6,765
Φⁿ/√5 ≈ 6,765.
- n20
- F(n)6,765
- F(n−1)4,181
- F(n)/F(n−1)1.61803396
- Golden ratio Φ1.61803399
- First 10 Fibonacci0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Step-by-step
- Iteratively compute F(0)=0, F(1)=1, then F(k) = F(k−1) + F(k−2) for k=2..20.
- F(20) = 6,765.
- Ratio F(n)/F(n−1) → Φ ≈ 1.618.
How to use this calculator
- Enter n.
- Read F(n) + ratio + golden-ratio comparison.
About this calculator
Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... Each term = sum of previous two. Defined by F(0)=0, F(1)=1, F(n)=F(n−1)+F(n−2). Ratio F(n)/F(n−1) → golden ratio Φ = (1+√5)/2 ≈ 1.618 as n → ∞. Closed form (Binet): F(n) = (Φⁿ − (−1/Φ)ⁿ) / √5. Appears in nature: pinecones, sunflowers, nautilus shells, branching patterns, art (Parthenon proportions).
Frequently asked
Sunflower seed spirals (34/55 commonly), pinecone scales, nautilus shell proportions, tree branching, leaf phyllotaxis.
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