Fibonacci Number Generator
Generate the Fibonacci sequence to any term count, or find the value at a single position.
Fibonacci Number Generator
First 10 terms
How many terms
The sequence starts 0, 1, 1, 2, 3, 5 and grows from there
Single term
Copy separatorHow to use the Fibonacci generator
- Set how many terms you want, starting from 0 and 1.
- Tick single term to read just the value at that position.
- Copy the sequence or download it as a CSV.
About Random Nr's Fibonacci Number Generator
The Fibonacci number generator builds the Fibonacci sequence to any term count you ask for, or returns the single value that sits at one position in the sequence. Set how many terms you want, or a single index, and Random Nr shows the running sequence where each number is the sum of the two before it, which is handy for maths lessons, coding practice and pattern work.
How Fibonacci numbers relate to the golden ratio
Divide any Fibonacci number by the one before it and the answer homes in on the golden ratio, 1.6180339887. The convergence is fast and you can verify every row with this generator.
| Ratio | Value |
|---|---|
| 5 / 3 | 1.667 |
| 8 / 5 | 1.600 |
| 13 / 8 | 1.625 |
| 21 / 13 | 1.615 |
| 55 / 34 | 1.6176 |
| 144 / 89 | 1.6180 |
By the twelfth term the ratio is already correct to four decimal places. The golden ratio is the limit, never quite reached but approached forever, and it is the reason Fibonacci numbers appear wherever growth compounds by proportion.
Where Fibonacci numbers appear in nature
Count the seed spirals in a sunflower head and you will usually find 21 one way and 34 the other, or 34 and 55 on a larger head, consecutive Fibonacci numbers. Pineapples typically carry 8 and 13 spiral rows, and pinecones 5 and 8. The pattern comes from the golden angle of about 137.5 degrees between successive seeds, the packing angle that the golden ratio produces, which lets each new seed take the least crowded position. Generate the first dozen terms above and the same numbers appear, 8 and 13, then 21 and 34, the very counts you would tally on a real sunflower or pinecone.
How fast do Fibonacci numbers grow
Fibonacci numbers grow geometrically, multiplying by roughly the golden ratio each step, which adds about one digit every five terms. The 100th term is 354,224,848,179,261,915,075, already 21 digits, and the 1000th term runs to 209 digits. This generator computes them with exact big integer arithmetic, so every digit is correct however deep you go. A useful pattern to check on the way: every third term is even, because odd plus odd makes even and the cycle then repeats.
More math and sequence generators
Frequently asked questions
What is the Fibonacci sequence
It is a sequence where each term is the sum of the two before it, starting 0, 1, 1, 2, 3, 5, 8 and so on.
Can I find one term by position
Yes. Tick the single term option and set the number of terms to the position you want, and the tool shows just that value.
Are large terms exact
Yes. The tool uses whole number big integer maths, so even far along the sequence the digits are exact rather than rounded.
How many terms can I generate
Up to 1000 terms, which reaches numbers hundreds of digits long.
Is it free
Yes, free and with no sign up. Everything runs in your browser and nothing you enter leaves your device.
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For other sequences try the number list generator, the square number list or the prime number list.