Fibonacci Calculator

What this tool does

Calculate fibonacci instantly in your browser. Exact BigInt terms; consecutive ratios approach the golden ratio φ ≈ 1.6180339887 as n grows.

How to use the Fibonacci Calculator

1. Enter or select term index n (f₀ = 0, f₁ = 1).
2. Read the calculated result; change any measurement to compare alternatives.

Formula

Each Fibonacci number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, … computed iteratively with BigInt so large terms are exact.

x

Term index n (F₀ = 0, F₁ = 1)

Exact BigInt terms; consecutive ratios approach the golden ratio φ ≈ 1.6180339887 as n grows.

Worked example

For fibonacci calculator, the following measurements illustrate the exact method: Term index n (F₀ = 0, F₁ = 1): 20.

Results explained

F(20)

F(20) from the formula above. Exact BigInt terms; consecutive ratios approach the golden ratio φ ≈ 1.6180339887 as n grows.

F(21) (next term)

F(21) (next term) from the formula above. Exact BigInt terms; consecutive ratios approach the golden ratio φ ≈ 1.6180339887 as n grows.

Digits in F(n)

Digits in F(n) from the formula above. Exact BigInt terms; consecutive ratios approach the golden ratio φ ≈ 1.6180339887 as n grows.

Ratio F(n)/F(n−1) ≈ golden ratio

Ratio F(n)/F(n−1) ≈ golden ratio from the formula above. Exact BigInt terms; consecutive ratios approach the golden ratio φ ≈ 1.6180339887 as n grows.

Frequently asked questions