Fibonacci Number Calculator

About this calculator

The Fibonacci sequence — 0, 1, 1, 2, 3, 5, 8, 13, 21, and onward, where each term is the sum of the two before it (F_n = F_n−1 + F_n−2) — was introduced to Europe by Leonardo of Pisa, known as Fibonacci, in his 1202 book Liber Abaci, though the pattern had already been described earlier in Indian mathematics. As the sequence grows, the ratio between consecutive terms converges toward the golden ratio, φ ≈ 1.618, which is why Fibonacci numbers turn up in discussions of the golden ratio's appearance in art, architecture, and nature.

The sequence is a staple of computer science education as a classic example for teaching recursion and dynamic programming, and it shows up in biology in phyllotaxis — the spiral arrangement of leaves, seeds, and pinecone scales often follows consecutive Fibonacci numbers because that spacing pattern packs growth most efficiently.

This calculator takes a position n and returns the corresponding term of the Fibonacci sequence.