Fibonacci Calculator

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Standard is the most common definition. Alternative uses 1-indexing. Custom lets you explore any Fibonacci-like sequence.
Enter a position from -100 to 1000. Negative positions extend the sequence backward.
Show terms from -n to n rather than 0 to n.
F(n)
55

The Fibonacci number at position n.

Digits in F(n)2
Sum of listed terms143
F(n) / F(n-1)1.61764706
Binet formula approximation55 (via Binet)
Sequence preview0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

The Fibonacci number at position 10 is 55.

  • F(10) = 55. Each term is the sum of the two before it, so the sequence grows exponentially, roughly multiplying by 1.618 each step.
  • The sum of all terms from F(0) to F(10) equals 143, which is always exactly F(12) minus 1, a handy shortcut.
  • The ratio F(10) / F(9) = 1.617647, converging on the golden ratio phi = 1.618034. The higher n goes, the tighter the match.
  • F(10) has 2 digits. Fibonacci numbers grow roughly 0.209 digits per step (log10 of phi), so expect about 209 digits by F(1000).

Next stepTry the sequence table below to watch the golden ratio emerge term by term.

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