Fibonacci Sequence Generator

Generate Fibonacci numbers and explore the golden ratio.

Term 20

4181

Standard Fibonacci sequence

Sum of all terms

10945

Ratio to previous term

1.6180340557

Golden ratio φ

1.6180339887

Difference from φ

0.000000066978

F(n) = F(n − 1) + F(n − 2)

The ratio between consecutive terms converges on the golden ratio, matching to eight decimal places by about the 20th term.
Terms are computed with BigInt, so the 500th term is exact rather than overflowing to infinity.

n	F(n)	Ratio to previous
1	0	—
2	1	—
3	1	1.00000000
4	2	2.00000000
5	3	1.50000000
6	5	1.66666667
7	8	1.60000000
8	13	1.62500000
9	21	1.61538462
10	34	1.61904762
11	55	1.61764706
12	89	1.61818182

What does Fibonacci Sequence Generator do?

Generate any number of terms in the Fibonacci sequence using exact BigInt arithmetic, look up the nth term directly, and see how the ratio between consecutive terms converges on the golden ratio.

How to Use Fibonacci Sequence Generator

1
Set how many termsOr ask for a specific nth term.
2
Adjust the start if you like0 and 1 by default; 2 and 1 gives Lucas numbers.
3
Read the sequenceWith ratios and running sums.

Key Features

Generate any number of terms, exactly, however large
Direct nth term lookup without listing everything before it
Ratio between consecutive terms, converging on 1.618…
Optional custom starting values, producing Lucas and other sequences
Running sum and the digit count of large terms
Copy or download the sequence

Frequently Asked Questions

What is the Fibonacci sequence?

Each term is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21. It appears in phyllotaxis, spiral shells and branching patterns, and underpins several algorithms.

How does it relate to the golden ratio?

The ratio of consecutive terms converges on φ ≈ 1.6180339887. By the 20th term it matches to eight decimal places. The ratio column shows the convergence directly.

Does the sequence start at 0 or 1?

Both conventions exist. Mathematicians usually start at 0 so that F(0) = 0, while some texts start at 1. This generator defaults to 0 and lets you change the starting values.

How large can the terms get?

Arbitrarily. Because BigInt arithmetic is used, the 1000th term is shown in full — all 209 digits — rather than overflowing to infinity as floating point would.

Runs in your browser

All arithmetic runs in your browser, using exact BigInt maths where whole numbers are involved so nothing is lost to floating-point rounding.

How the rest of the site handles data