Fibonacci Sequence Calculator
Enter a position in the sequence and this calculator finds that Fibonacci number, where each number is the sum of the two before it.
What This Calculator Does
The Fibonacci Sequence Calculator finds the value of any term in the Fibonacci sequence, one of the most famous number patterns in mathematics. It appears in nature, art, computer science, and finance-related modeling.
The Formula
The Fibonacci sequence starts with 0 and 1, and every following number is the sum of the two numbers before it: F(n) = F(n-1) + F(n-2), with F(0) = 0 and F(1) = 1. This produces the familiar sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.
The Golden Ratio Connection
As the position n grows larger, the ratio between consecutive Fibonacci numbers gets closer and closer to the golden ratio, approximately 1.618034. This calculator shows that ratio for the term you entered, along with the running sum of every term from F(0) up to F(n).
- F(0) = 0 and F(1) = 1 are the starting values of the sequence
- The sequence grows very quickly, so results are capped at a position where the values stay within safe numeric precision
- Provided for general educational and reference purposes