What is the Fibonacci sequence?

The Fibonacci sequence is a series starting with 0 and 1, where each subsequent number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

What is the maximum n this calculator supports?

This calculator supports n up to 1,000. Beyond that, numbers become extremely large (thousands of digits) and can slow the browser.

Does indexing start at 0 or 1?

You can choose either convention. In zero-based indexing F(0)=0, F(1)=1. In one-based indexing the 1st term is 0, the 2nd is 1, etc. Both conventions are common.

How accurate are very large Fibonacci numbers?

This tool uses JavaScript BigInt for exact integer arithmetic, so every digit is correct regardless of how large the number grows.

What is the connection to the golden ratio?

The ratio of consecutive Fibonacci numbers (F(n+1)/F(n)) converges to the golden ratio, approximately 1.6180339887, as n increases.

Fibonacci Calculator

Name: Fibonacci Calculator
Availability: InStock
Author: Nham Vu

Enter a term index (n) to compute the nth Fibonacci number and display the full sequence up to that term.

Sequence Settings

Term index (n)

1 to 1,000

Index convention

One-based (1st term = 0) Zero-based (F(0) = 0)

Result

—

Full Sequence

Enter n and click Calculate.

Summary

Enter a term index (n) to compute the nth Fibonacci number and display the full sequence up to that term.

How it works

Enter the term index n in the input field (1 = first term, which is 0).
Choose whether to start the sequence at index 0 or index 1.
Click "Calculate" or press Enter to generate the result.
The nth Fibonacci number is shown prominently at the top.
The full sequence up to term n is displayed below, scrollable for large values.
Use "Copy Sequence" to copy all terms as a comma-separated list.

Use cases

Verify homework or textbook Fibonacci problems quickly.
Generate a Fibonacci sequence for use in code or spreadsheets.
Explore how rapidly Fibonacci numbers grow with increasing n.
Find specific Fibonacci numbers for algorithm design or math research.
Teach or demonstrate the Fibonacci pattern to students.
Check Fibonacci ratios related to the golden ratio (phi).

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu