Frequently Asked Questions
What is the Fibonacci sequence?
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... where each term is the sum of the previous two.
Why is the golden ratio related?
Because F sub n divided by F sub n minus 1 converges to phi as n grows. The closed-form Binet formula expresses F sub n exactly in terms of phi.
How big can n be?
This calculator handles n up to 200, returning the exact value via BigInt. For larger n, matrix exponentiation or modular arithmetic is recommended.
What is the 100th Fibonacci number?
It is 354224848179261915075. Because Fibonacci numbers grow exponentially, this tool computes them with exact big-integer arithmetic rather than floating point, so large terms stay precise.
What are Lucas numbers?
Lucas numbers use the same add-the-previous-two rule as Fibonacci but start from 2 and 1 instead of 0 and 1, giving 2, 1, 3, 4, 7, 11, 18, and so on. They are closely tied to Fibonacci numbers and to the golden ratio.
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Estimates for informational purposes only.
Important Disclaimer: Estimates for informational purposes only.
This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.