Fibonacci Calculator

Find the nth Fibonacci number exactly (up to n = 5,000) and list the sequence, with the golden-ratio approximation.

Enter values

Result

F(20)

6765

Digits: 4
First terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181

Find the nth Fibonacci number exactly (up to n = 5,000) and list the sequence, with the golden-ratio approximation.

Also known as: fibonacci sequence, nth fibonacci number, fibonacci numbers, fib calculator.

Enter n (term number).
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F(0) = 0, F(1) = 1, F(n) = F(n−1) + F(n−2)

Using the values pre-filled in the calculator above:

the calculator returns:

F(20): 6765
Digits: 4
First terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181

The ratio of consecutive Fibonacci numbers F(n+1)/F(n) approaches the golden ratio φ ≈ 1.618 as n grows.