Fibonacci Calculator
Calculate values related to the Fibonacci sequence using Binet's formula approximation.
Fib N
55
Golden Ratio1.61803399
Fib N Minus 134
Ratio1.61764706
Fibonacci Sequence
Definition
F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2)
Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Binet's Formula
F(n) = (phi^n - psi^n) / sqrt(5)
where phi = (1 + sqrt(5))/2 (golden ratio) and psi = (1 - sqrt(5))/2.
For large n, psi^n approaches 0, so F(n) ≈ phi^n / sqrt(5).
Golden Ratio
As n grows, F(n)/F(n-1) approaches the golden ratio phi ≈ 1.6180339887.
Example Calculation
Find the 10th Fibonacci number.
- 01F(10) = phi^10 / √5
- 02= 1.61803^10 / 2.23607
- 03≈ 122.992 / 2.236
- 04≈ 55
- 05Sequence up to F(10): 0,1,1,2,3,5,8,13,21,34,55
Frequently Asked Questions
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