Fibonacci n-ésimo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Fibonacci nth term calculator computes the nth element in the Fibonacci sequence. The sequence starts with 0 and 1, and each subsequent term is the sum of the two preceding ones. This calculation uses an iterative method instead of recursion for efficiency, especially with large n values.
For small n, computation is fast. However, for very large n, processing time increases linearly with n, which remains more efficient than recursive methods. The formula used is F(n) = F(n-1) + F(n-2), implemented with a loop that accumulates values up to the desired n.
Use this calculator for mathematical problems, algorithm testing, or numerical series analysis. It's commonly applied in programming exercises, pattern analysis in nature, and finance. Ensure your input n is a non-negative integer to get valid results.
Cautions: For extremely large n (e.g., above 10^6), processing may take several seconds. Invalid inputs (non-integers or negatives) return errors. The sequence starts with F(0) = 0, F(1) = 1, so confirm your problem's indexing before using the tool.
Frequently asked questions
How does the calculator compute Fibonacci terms?
It uses an iterative loop starting with F(0)=0 and F(1)=1, summing previous terms until reaching the desired position n.
What happens if I enter a negative number?
The calculator returns an error since Fibonacci sequence starts with n ≥ 0.
Why use iteration instead of recursion?
Iteration avoids recursive call overhead, making it more efficient for large n.
Can I compute terms larger than 100,000?
Yes, but processing time increases with the size of n.