Fibonacci Calculator
Explore the magic of the Fibonacci sequence. This tool calculates precise values for terms even deep into the sequence using BigInt support.
What is the Fibonacci sequence?
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
What is Binet's formula?
Binet's formula allows you to find the n-th Fibonacci number directly without calculating all previous terms: Fn = [Φⁿ - (1-Φ)ⁿ] / √5, where Φ (phi) is the golden ratio (~1.618).
How do Fibonacci numbers relate to the golden ratio?
As you go further in the sequence, the ratio of a Fibonacci number to the one before it (Fn / Fn-1) gets closer and closer to the golden ratio Φ (1.618033...).
What are Fibonacci numbers used for?
They appear frequently in nature (branching in trees, arrangement of leaves, fruit sprouts of a pineapple) and are used in computer science algorithms, stock market analysis, and architectural design.