Fibonacci number calculator
Enter a position to get that term of the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8. The math uses exact whole numbers, so large results are never rounded.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter position n.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
F(0) = 0, F(1) = 1 and F(n) = F(n - 1) + F(n - 2) for n ≥ 2.
Example
Inputs: Position n = 10. Result: F(10): 55; Number of digits: 2.
Limits and caveats
- Accepts positions from 0 to 2000.
- The sequence starts at F(0) = 0 here; some books start at F(1) = 1.
Questions about this tool
What is the Fibonacci sequence?
A sequence that starts 0, 1 where every later term is the sum of the two before it.
How is it linked to the golden ratio?
The ratio of a term to the one before it approaches the golden ratio 1.6180339887 as n grows.
Why is the result shown as a long string?
Terms grow fast, F(100) has 21 digits, so the tool prints every digit instead of rounding to scientific notation.