Fibonacci Calculator
Calculate any term of the Fibonacci sequence, where each number is the sum of the two before it.
- Free to use
- Accurate results
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- Works on all devices
Enter a term number to calculate that term of the Fibonacci sequence, where each number is the sum of the two before it.
Which term of the sequence to find (1st term = 1, 2nd term = 1, 3rd term = 2, ...).
Your result
55
nth Fibonacci number
Sequence so far1, 1, 2, 3, 5, 8, 13, 21, 34, 55
AI explanation
Formula
F(n) = F(n−1) + F(n−2), with F(1) = 1 and F(2) = 1Worked example
10th Fibonacci number
| Field | Value |
|---|---|
| Term number (n) | 10 |
| nth Fibonacci number | 55 |
| Sequence so far | 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 |
Assumptions
- Uses the common 1-indexed convention where F(1) = 1 and F(2) = 1.
- The displayed sequence shows at most the first 25 terms, even when a larger term number is requested — the exact nth term is still computed correctly for any n up to 1000.
Frequently asked questions
What is the Fibonacci sequence?
It's a sequence where each number is the sum of the two numbers before it, starting from 1, 1: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
Where does the Fibonacci sequence show up in nature?
It's often cited in the arrangement of leaves, sunflower seed spirals, and pinecones, though the connection is sometimes exaggerated in popular science — the mathematical pattern itself is well established regardless.
How large can the numbers get?
Very large, very quickly — the 100th Fibonacci number already has 21 digits. This calculator computes exact values using arbitrary-precision arithmetic, not floating-point numbers, so there's no loss of precision even for large term numbers.