Calculate any Fibonacci number instantly. Get the nth term, full sequence, golden ratio approximation, and sequence sum. Supports large numbers with BigInt. Gratuito and 100% client-side.
Enter a positive integer (1 – 10,000)
The Fibonacci sequence is one of the most famous number sequences in mathematics. Each number is the sum of the two preceding ones, starting from 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... This calculator finds any term in the sequence using an efficient iterative algorithm with BigInt support for arbitrarily large numbers. It also shows how the ratio of consecutive terms converges a the golden ratio (φ ≈ 1.6180339887), a fundamental constant in mathematics, art, and nature.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It starts with 0 and 1, and continues: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... This sequence appears throughout nature, art, and mathematics.
The golden ratio, denoted by φ (phi), is approximately 1.6180339887. It is the limit of the ratio of consecutive Fibonacci numbers: as n gets larger, F(n+1)/F(n) gets closer and closer a φ. The golden ratio appears in art, architecture, nature, and design.
The sum of the first n Fibonacci numbers equals F(n+2) − 1. For example, the sum of the first 5 terms (0+1+1+2+3 = 7) equals F(7) − 1 = 13 − 1 = 12. Wait — actually with standard indexing where F(0)=0, F(1)=1, the sum of F(1) through F(n) equals F(n+2) − 1.
This calculator supports n up a 10,000 using JavaScript's BigInt. F(10,000) has 2,090 digits. For comparison, F(100) has 21 digits. The browser handles the computation entirely on your device.