Fibonacci Generator
Generate Fibonacci, Lucas, Tribonacci and Pell sequences by term count or up to a maximum value, with custom starting values. See golden-ratio convergence and check whether any number is a Fibonacci number.
Input
Sequence
First term (default 0 for standard Fibonacci).
Second term (default 1 for standard Fibonacci).
Fibonacci checker
Optional — check whether a number belongs to the Fibonacci sequence.
Output
Statistics
| Metric | Value |
|---|---|
| No data yet | |
Golden ratio convergence
| n | Term | Term ÷ previous | Diff from φ |
|---|---|---|---|
| No data yet | |||
Checker result
Guides
The Fibonacci Generator builds Fibonacci-style number sequences instantly in your browser. Generate the classic Fibonacci sequence, or switch to Lucas, Tribonacci, or Pell numbers — by a fixed number of terms or up to a maximum value you choose. It also shows how consecutive terms converge on the golden ratio (φ ≈ 1.6180339887) and can check whether any number belongs to the Fibonacci sequence.
Every term is computed with arbitrary-precision integers, so results stay exact even at hundreds of digits — well past the point where ordinary floating-point math starts rounding.
How to use it
- Pick a sequence type: Fibonacci, Lucas, Tribonacci, or Pell.
- Choose whether to generate the first N terms (up to 1000) or every term up to a maximum value.
- For Fibonacci, optionally set custom starting values —
2, 1gives the Lucas-style run,3, 4starts anywhere you like. - Read the generated sequence, the statistics (term count, largest value, digit count), and the golden-ratio convergence table.
- To test a single number, type it into the Fibonacci checker — you'll see whether it's a Fibonacci number, its index, or the nearest Fibonacci numbers above and below.
Use the copy or download buttons to export the full sequence as a text file.
What is the Fibonacci sequence?
Each Fibonacci number is the sum of the two before it, starting from 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. The pattern appears throughout nature — in leaf arrangements, pinecones, sunflower seed spirals, and the branching of trees.
How do Lucas, Tribonacci, and Pell numbers differ?
Lucas numbers follow the same "sum of the previous two" rule but start with 2 and 1. Tribonacci numbers sum the previous three terms. Pell numbers use the rule Pₙ = 2·Pₙ₋₁ + Pₙ₋₂. Each is a well-known integer sequence with its own applications in mathematics and computer science.
What is the golden ratio connection?
Divide any Fibonacci (or Lucas) number by the one before it and the result homes in on the golden ratio, φ. The convergence table shows this ratio and its distance from φ shrinking row by row. Tribonacci and Pell numbers converge to different constants, so their "diff from φ" column stays large — a quick way to see that not every recurrence tends to φ.
How can I tell if a number is a Fibonacci number?
A positive integer n is a Fibonacci number if and only if 5n² + 4 or 5n² − 4 is a perfect square. The checker uses exactly this test, then reports the term's index — or, if it isn't Fibonacci, the closest Fibonacci numbers on either side.
Privacy
Everything runs entirely in your browser. Your inputs and the generated sequences are never uploaded, stored, or shared — the calculation happens locally on your device.