Fibonacci Calculator
Fibonacci calculator finds the arbitrary terms of the Fibonacci sequence.
F(14)377zero-indexed, so F(0) = 0
Sum of all terms986equals F(n+2) − 1
Ratio to the previous term1.618025751073approaches φ = 1.61803398875
Golden ratio φ1.61803398875
Binet check377the closed form for F(n)
Terms
| n | Term |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 1 |
| 3 | 2 |
| 4 | 3 |
| 5 | 5 |
| 6 | 8 |
| 7 | 13 |
| 8 | 21 |
| 9 | 34 |
| 10 | 55 |
| 11 | 89 |
| 12 | 144 |
| 13 | 233 |
| 14 | 377 |
The formula
F(n) = F(n−1) + F(n−2), starting 0, 1
The ratio converges on φ
Divide any Fibonacci number by the one before and the answer approaches the golden ratio (1 + √5)/2 ≈ 1.618034, alternating above and below it. Binet’s formula gives F(n) in closed form from φ alone — remarkable for a sequence defined purely by addition.