Calculate any Fibonacci number instantly. Get the nth term, full sequence, golden ratio approximation, and sequence sum. Supports large numbers with BigInt. Free 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 to 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 to 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 to 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.