Fibonacci Calculator
Enter which term you want to find to see its value and the sequence leading up to it.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55
How the Fibonacci sequence works
The Fibonacci sequence starts with two 1s, and each following number is the sum of the two numbers before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. This calculator builds the sequence term by term up to your requested position.
This sequence appears throughout nature — in the spiral patterns of sunflower seeds, pinecones, and shells — and the ratio between consecutive Fibonacci numbers approaches the golden ratio (about 1.618) as the sequence grows.
Frequently asked questions
What is the Fibonacci sequence used for?
Beyond its mathematical interest, it appears in computer science (algorithm analysis, data structures), financial market analysis (Fibonacci retracement levels), art and design (compositions based on the golden ratio), and describing natural growth patterns.
What's the relationship between Fibonacci numbers and the golden ratio?
Dividing each Fibonacci number by the one before it produces a ratio that gets closer and closer to the golden ratio (φ ≈ 1.618034) as you go further into the sequence.
Why does this calculator have a maximum term limit?
Fibonacci numbers grow exponentially, and very large terms (beyond the 78th or so) exceed the range where standard floating-point numbers can represent integers exactly, which would make the displayed result inaccurate.