How does the Fibonacci sequence start?

This generator uses the common convention F(0) = 0 and F(1) = 1. Every subsequent term is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, and so on.

Why use BigInt instead of normal numbers?

Fibonacci numbers grow exponentially and quickly exceed the safe integer limit of JavaScript (about 9 quadrillion). BigInt stores them exactly, so even the 200th term is shown with full precision rather than rounded.

How many terms can I generate?

You can generate up to a few thousand terms. Very large counts produce extremely long numbers — the 1000th Fibonacci number alone has 209 digits — so the tool caps the count to keep the page responsive.

What is the golden ratio connection?

The ratio of consecutive Fibonacci numbers approaches the golden ratio (about 1.618) as the terms grow. This appears throughout mathematics, nature, and design, which is part of why the sequence is so famous.

Fibonacci Sequence Generator

The Fibonacci sequence is the classic series where each number is the sum of the two before it. This generator produces the first N terms exactly, using arbitrary-precision integers so even very large terms are correct to the last digit.

How it works

Starting from the two seed values 0 and 1, each new term adds the previous two:

F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2)

That gives 0, 1, 1, 2, 3, 5, 8, 13, 21, …. The tool iterates this rule with BigInt, which has no upper size limit, so terms far beyond the float64 safe range remain exact rather than rounding off.

Example and tips

Asking for 10 terms returns 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The ratio between consecutive terms steadily approaches the golden ratio φ ≈ 1.618 — by the 20th term it already matches to four decimal places. Because the numbers grow exponentially, generating thousands of terms yields some very long values, which is exactly why exact BigInt arithmetic matters here.