What is the Fibonacci sequence?

Each number is the sum of the two before it, starting 1, 1, 2, 3, 5, 8, 13… It appears throughout nature, art and computer science.

What is the golden ratio connection?

The ratio of consecutive Fibonacci numbers approaches the golden ratio φ = (1+√5)/2 ≈ 1.618 as n grows.

Fibonacci Calculator

Free Fibonacci calculator. Enter a position n to get the nth Fibonacci number (F₁ = F₂ = 1), the sum of the first n terms, and the ratio of consecutive terms that converges to the golden ratio φ ≈ 1.618.

Find the nth Fibonacci number, the sum of terms and the golden ratio.

F_{n} = F_{n - 1} + F_{n - 2}, F_{1} = F_{2} = 1

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