MATH · FIBONACCI
Fibonacci Calculator
Find the Nth Fibonacci number or list the first N terms of the Fibonacci sequence. Supports up to F(100) with exact integer precision.
F(10)
55
About This Calculator
Calculate any Fibonacci number up to F(100) or display the first N terms of the Fibonacci sequence. Results are computed with exact BigInt arithmetic so large values like F(100) = 354,224,848,179,261,915,075 are always correct.
How It Works
Starting with F(1) = 1 and F(2) = 1, each subsequent term is the sum of the two preceding terms: F(n) = F(n-1) + F(n-2). The calculator iterates this recurrence using BigInt arithmetic to avoid floating-point rounding for large values.
The Formula
F(n) = F(n-1) + F(n-2)
- F(n)
- the Nth Fibonacci number
- F(1) = F(2) = 1
- seed values
Frequently Asked Questions
- What are the first 10 Fibonacci numbers?
- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. Each number is the sum of the two numbers before it.
- Does this calculator start at F(0) or F(1)?
- This calculator uses the convention F(1) = 1 and F(2) = 1, which is the most common convention used in textbooks and homework problems.
- Why are large Fibonacci numbers exact?
- JavaScript's standard numbers lose precision for integers above 2^53 − 1. This calculator uses BigInt arithmetic internally so every result up to F(100) is an exact integer, with no rounding.
- What is the relationship between Fibonacci numbers and the golden ratio?
- The ratio of consecutive Fibonacci numbers F(n+1)/F(n) converges to φ ≈ 1.6180339887... (the golden ratio) as n increases. The exact formula is the Binet formula — but this calculator uses the iterative recurrence for exact integers.