Fibonacci Calculator
Explore the famous Fibonacci sequence where each number is the sum of the two preceding ones. Calculate the nth Fibonacci number, generate sequences, or check if a number belongs to the Fibonacci series. The sequence appears throughout nature, art, and mathematics.
Generate Fibonacci Sequence
Quick Reference
F1
0
F2
1
F3
1
F4
2
F5
3
F6
5
F7
8
F8
13
F9
21
F10
34
F11
55
F12
89
F13
144
F14
233
F15
377
F16
610
F17
987
F18
1597
F19
2584
F20
4181
About Fibonacci Sequence
The Fibonacci sequence is a series where each number is the sum of the two preceding ones.
F(n) = F(n-1) + F(n-2), where F(1) = 0 and F(2) = 1
The sequence starts: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
The ratio between consecutive Fibonacci numbers approaches the Golden Ratio (approximately 1.618).
FAQ
What is the Fibonacci sequence?
The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on.
What is the golden ratio connection?
The ratio of consecutive Fibonacci numbers approaches the golden ratio (approximately 1.618034) as the numbers get larger. This mathematical constant appears extensively in nature and art.
Where does Fibonacci appear in nature?
Fibonacci numbers appear in flower petals, seed arrangements in sunflowers, pine cone spirals, nautilus shells, and branching patterns in trees. It is one of nature's most common patterns.