Fibonacci Calculator
Fibonacci Calculator - Free online tool
Number of terms
max 78
F(12) — the 12th Fibonacci number
89
Golden ratio φ approximation
1.6181818182
φ = 1.6180339887…
First 12 terms
| n | F(n) | Ratio F(n)/F(n−1) |
|---|---|---|
| 1 | 0 | — |
| 2 | 1 | — |
| 3 | 1 | 1.00000000 |
| 4 | 2 | 2.00000000 |
| 5 | 3 | 1.50000000 |
| 6 | 5 | 1.66666667 |
| 7 | 8 | 1.60000000 |
| 8 | 13 | 1.62500000 |
| 9 | 21 | 1.61538462 |
| 10 | 34 | 1.61904762 |
| 11 | 55 | 1.61764706 |
| 12 | 89 | 1.61818182 |
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Reference
The Fibonacci sequence is defined by F(1)=1, F(2)=1 and F(n)=F(n−1)+F(n−2) for n>2 (convention with F(0)=0 is also common).
The ratio of consecutive terms converges to the golden ratio φ ≈ 1.6180339887…, linked to the golden proportion found in nature and art.
Membership test: a positive integer n is a Fibonacci number if and only if 5n²+4 or 5n²−4 is a perfect square.
Frequently asked questions
What does Fibonacci Calculator do?
Fibonacci Calculator - Free online tool
What should I check in the result?
Check units, rates, dates and assumptions. Compare a simple case by hand before using the result for a decision.