Math

Fibonacci Calculator

Get the nth Fibonacci number, browse the full sequence, and watch the ratio of consecutive terms converge to the golden ratio.

Position n (1 – 200)

F(n) — the n^th Fibonacci number

F(n−1)

Number of digits

F(n) is

F(n+1) & F(n+2)

Golden ratio (F(n)/F(n−1))

Sequence preview: -

Definition: F(0) = 0, F(1) = 1, and F(n) = F(n−1) + F(n−2) for n ≥ 2.
Binet's formula: F(n) = [φⁿ − (−φ)⁻ⁿ] / √5, where φ = 1.61803…

Uses arbitrary-precision arithmetic, so even F(200) — a 42-digit number — is shown exactly.

The ratio F(n)/F(n−1) approaches φ ≈ 1.6180339887 as n grows.

Fibonacci numbers appear in plant growth, stock retracement levels and algorithm design.

Scroll the first n terms to see how the sequence builds from 0 and 1.

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