Generate the first N terms of the Fibonacci sequence with BigInt precision.
The Fibonacci sequence starts with F(0) = 0 and F(1) = 1, and every later term is the sum of the two before it: F(n) = F(n−1) + F(n−2). That simple rule produces 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … and, remarkably, the ratio of consecutive terms F(n)/F(n−1) converges to the golden ratio φ ≈ 1.6180339887. This generator builds the first N terms (up to 500) iteratively with BigInt, so every value is exact, no floating-point rounding, even though the 500th term, F(499), already has 104 digits. Alongside the table it reports the last term, its digit count, and the current golden-ratio approximation from the last two terms. It is handy for classwork, coding-interview practice, and exploring where Fibonacci shows up in nature and design.
Fibonacci is a sequence defined by a recurrence: with F(0) = 0 and F(1) = 1 fixed, each new term is the sum of the two before it. That is why the generator computes the values one by one, adding the most recent pair, an iterative method that is fast and exact with BigInt.
There is also a closed form, Binet's formula: F(n) = (φⁿ − ψⁿ) / √5, with φ = (1 + √5)/2 and ψ = (1 − √5)/2. It is elegant, but it uses floating point and loses precision for large n, which is why the tool prefers the iterative method.
Example 1, ten terms: starting at F(0), the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, reaching F(10) = 55. The ratio F(10)/F(9) = 55/34 ≈ 1.617647 is already very close to φ.
Example 2, convergence: further along, F(20) = 6765 and F(19) = 4181, so F(20)/F(19) = 6765/4181 ≈ 1.6180340, practically equal to the golden ratio, showing how quickly the ratio settles.
In nature, the number of spirals in sunflowers, pinecones, and pineapples is often a Fibonacci number, and leaf arrangement (phyllotaxis) follows the same pattern, a consequence of the golden ratio optimizing packing. Indexing may start at 0 (F(0) = 0) or, in older texts, at 1, 1, 2, 3…; both are valid.
In computing, Fibonacci appears in algorithm analysis (worst case of AVL trees), in Fibonacci heaps, in Zeckendorf's representation, and as the standard example of recursion and memoization.
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
<iframe
src="https://jkit.tools/embed/en-US/fibonacci-sequence-generator"
width="100%"
height="600"
style="border:0"
loading="lazy"
title="Fibonacci Sequence Generator"
></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
It is a sequence of integers where each term is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… It is defined by the recurrence F(n) = F(n−1) + F(n−2), with F(0) = 0 and F(1) = 1. It was popularized by Leonardo of Pisa ('Fibonacci') in the 13th century, in a problem about breeding rabbits.
First 10 Fibonacci terms
0112358132134All calculations stay in your browser. No data is sent to any server.