Fibonacci Number Calculator
Find Fibonacci number Fₙ for whole-number indices 0 through 50, with F₀=0 and F₁=1.
Formula
Fₙ=Fₙ₋₁+Fₙ₋₂; Binet: Fₙ=(φⁿ−ψⁿ)/√5, φ=(1+√5)/2, ψ=(1−√5)/2.
Fibonacci number Fₙ ≈ round((((1+sqrt(5))÷2)^(10)-((1-sqrt(5))÷2)^(10))÷sqrt(5))
How to use
- Enter a whole-number index n.
- Use 0 through 50.
- Read Fₙ under the F₀=0 convention.
Examples
- F₁₀=55; F₅₀=12,586,269,025.
Frequently asked questions
What are the first terms?
0, 1, 1, 2, 3, 5, 8, 13.
Why stop at 50?
The formula uses floating-point arithmetic; the finite range protects integer rounding accuracy.
Does the index start at one?
This tool uses F₀=0 and F₁=1.
Sources
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