Does this start at 0 or 1?
F₀ = 0 and F₁ = 1.
Fibonacci Calculator
Find F_n for n = 0…90 and optionally display the sequence up to n.
Enter n
Choose n (0–90) and whether to list terms.
About this calculator
How to use Fibonacci Calculator, plus the formulas and logic behind the results.
Tool description
The Fibonacci sequence is F₀=0, F₁=1, F_n = F_{n−1}+F_{n−2}. This tool uses 64-bit integers up to n = 90.
How to use
- Enter an integer n from 0 to 90.
- Choose whether to list the sequence.
- Select Calculate.
- Read F_n and the optional list.
Formulas & reference
F₀ = 0, F₁ = 1F_n = F_{n−1} + F_{n−2} for n ≥ 2
Sample values
- F₁₀ = 55
- F₀ = 0, F₁ = 1, F₂ = 1
- Ratio F_n/F_{n−1} → φ ≈ 1.618
- n capped at 90 for safe integers
Calculation logic
Iteratively adds terms up to n using integers, avoiding floating-point drift.
Indexing uses F₀ = 0. Some texts start with F₁ = 1, F₂ = 1.
Fibonacci Calculator FAQ
Common questions about this calculator and how to use the results.
Why limit n to 90?
Keeps results within reliable integer range for this PHP implementation.
What is F₂?
1 (same as F₁).
Can I get only one term?
Yes—set show sequence to No.
Are negative indices supported?
Not in this tool.
Is the golden ratio shown?
Optional ratio F_n/F_{n−1} is shown when n ≥ 2.